classicalstatsexamples.ipynb

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     "source": [
      "Classical Statistics in Python"
     ]
    },
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     "source": [
      "\n",
      "Daniela Huppenkothen and Fernando Perez\n",
      "\n",
      "This notebook is intended for the newcomer to scientific inference in the classical (frequentist) statistics framework. Below is a number of simple explanations (which by no means replace a good textbook; see literature suggestions at the end) interspersed with bits of (interactive) python code aimed at illustrating key concepts on the one hand, and allowing the user to become familiar with simple statistical computations in python. \n",
      "\n",
      "Some familiarity with python would be helpful for understanding the code below, but much of it, especially the interactive sections, can be understood without. Introductions into python on the internet abound, see the list of literature at the end for a few suggestions."
     ]
    },
    {
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     "source": [
      "## Preliminaries and Requirements\n",
      "\n",
      "Much of this ipython notebook is built on **numpy** and **scipy** functionality, crucial to modern statistical analysis. These must be installed. For the interactive elements to work, **ipython 2.0** or newer is required. \n",
      "Plotting requires **matplotlib**. On top of that, we have built some of the plots using the package **seaborn**. \n",
      "\n",
      "**[also requires special html package?]**\n",
      "\n",
      "Except for the additional plotting functionality (and prettiness!) provided by seaborn, we have attempted to keep dependencies low, and show that many statistical analyses require not much more than numpy and scipy. At the end of the notebook, we also provide a list of potentially useful, more advanced packages for statistical analyses."
     ]
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     "input": [
      "## Need to run this to render MathJAX\n",
      "#from IPython.external import mathjax; mathjax.install_mathjax()\n",
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import scipy.stats\n",
      "import scipy.optimize\n",
      "import seaborn as sns\n",
      "sns.set_style(\"whitegrid\")\n",
      "sns.set_style(\"ticks\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 149
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     "source": [
      "## Introduction\n",
      "A *statistic* is nothing else but a way to encode the information contained in a data set in such a way that it is useful to the question we want to answer. When we talk about *statistics*, what we really mean is that we wish to find a way to reduce our data (an image, a light curve, ...) to one (or more) numbers that summarise the information we are interested in. In turn, based on this encoded information, we can try to make a *decision* about the question at hand: this is the basis of scientific inference.\n",
      "\n",
      "In what follows below, we are mainly concerned with *classical statistics*, as opposed to another approach to scientific inference, called *Bayesian statistics*. The difference between the two lies mainly in the interpretation of what the word probability truly means. To a classical (also *frequentist*) statistician, probability describes the long-term frequency of an outcome given infinite trials. This definition is born out of early games of chance: if I toss a coin 100 times, I can count the number of favourable outcomes (say, heads) and define probability as the frequency of that outcome compared to all coin tosses: $$\\frac{\\mathrm{number of favourable outcomes}}{\\mathrm{total number of trials}}$$.\n",
      "\n",
      "In contrast, for a Bayesian statistician, probability encodes an uncertainty in measuring a quantity. In contrast to classical statistics, where, by definition, probability is only defined for random processes (such as coin tosses, games of cards etc.), this allows to assign probabilities to quantities that are not inherently random. This is an important distinction that accounts for much of the differences between the two approaches.\n",
      "\n",
      "Below we limit ourselves to classical statistics, but perhaps this tutorial could be extended in the future to include the alternative approaches as well.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Simple Representations of Data\n",
      "\n",
      "Any data set can be represented very simply with just a few numbers: mean, median, variance are among the most popular ones, but the \"best\" representation depends on the problem at hand. \n",
      "Most of those are really easy to do in python using numpy. In general, it will be preferable to use numpy implementations of many standard functions included in the library; they usually link to an underlying C-package, and will thus be much faster than any pure python implementation.\n",
      "\n",
      "The **mean** is the average of the sample: it is calculated by summing up all elements in the sample, and then dividing by the total number of elements. In contrast, the **median** encodes the value that cuts the sample in half: 50% of values fall below this number, the other 50% above it. In many cases the median may be preferable as a measure of average properties of a sample, because it is less sensitive to strong outliers.\n",
      "\n",
      "The code and the figure below illustrate this. The figure shows a two-dimensional distribution of two quantities (here $a$ and $b$, but they could be anything you measure!), with a single outlier (in black). We also show the mean and median of the sample. The slider bars allow you to change the number of samples and the value of the outlier (i.e. the distance from the sample). \n",
      "\n",
      "#### Exercise:\n",
      "- For a given sample size, how far away can you put the outlier such that the mean and median will still be comparable?\n",
      "- How many samples do you need to be insensitive to a single, very far outlier?\n"
     ]
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     "input": [
      "def outlier_test(samples,outlier):\n",
      "    xsamples = list(np.random.normal(10,10, size=samples))\n",
      "    ysamples = list(np.random.normal(10,10, size=samples))\n",
      "\n",
      "    s = samples\n",
      "    o = outlier\n",
      " \n",
      "    xsamples.append(o)\n",
      "    ysamples.append(o)\n",
      "    \n",
      "    #print(xsamples)\n",
      "\n",
      "    mn = np.mean(xsamples)\n",
      "    md = np.median(xsamples)\n",
      "    \n",
      "    \n",
      "    fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
      "    plt.subplots_adjust(top=0.9, bottom=0.1, left=0.06, right=0.97, wspace=0.12, hspace=0.1)\n",
      "\n",
      "    cmap = sns.cubehelix_palette(start=0, light=1, as_cmap=True)\n",
      "    \n",
      "    ax.hexbin(xsamples, ysamples, cmap=cmap, gridsize=50)\n",
      "    #ax.scatter(xsample_small, ysample_small, s=20)\n",
      "    ax.scatter(o,o, s=100, marker=\"h\", color=sns.cubehelix_palette()[5])\n",
      "    #ax.scatter(a_true, b_true, s=200)\n",
      "    ax.set_xlim(0, o+10)\n",
      "    ax.set_ylim(0, o+10)\n",
      "    ax.set_xlabel(\"a\", fontsize=30)\n",
      "    ax.set_ylabel(\"b\", fontsize=30)\n",
      "    #ax.legend([\"mean = \" + str(mn)])\n",
      "    ax.text(0.1*o, 0.9*o+10, \"mean = %.4f\"%mn, fontsize=20)\n",
      "    ax.text(0.1*o, 0.8*o+10, \"median = %.4f\"%md, fontsize=20)\n",
      " \n",
      "    return\n",
      "\n",
      "from IPython.html.widgets import interact\n",
      "interact(outlier_test, samples=(10, 10000, 10), outlier=(10, 1000, 10));"
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K7Ft4YowjY4ydYoz5wFDgrzHGS4BngWHpZsOAKenlZ4GhIYRGIYR8oAvw5u7u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\nSarF/we3kXiqnJBbswAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f35d650>"
       ]
      }
     ],
     "prompt_number": 150
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In contrast to the mean and the median, the **standard deviation** (and relatedly, the **variance**) do not measure the average properties of a sample, but rather the scatter around this average. \n",
      "Below is another figure of a sample drawn from a normal distribution; the lever allows you to change the standard deviation of the distribution that produced the sample. We also show variance and standard deviation of the sample.\n",
      "\n",
      "#### Exercise\n",
      "- Play with the lever. What do you observe? What happens to the distribution as you pull the lever left or right?\n",
      "- Observe how the variance and the standard deviation change as you pull the lever. Can you tell what the relationship is between standard deviation and variance?\n",
      "- Assume you have a fixed number of points in your sample. You want to estimate the mean of that sample. Is it better to have a small or large standard deviation? Why?\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def standarddeviation(std):\n",
      "    xsamples = list(np.random.normal(10,std, size=1000))\n",
      "    ysamples = list(np.random.normal(10,std, size=1000))\n",
      "    \n",
      "    vr = np.var(xsamples)\n",
      "    st = np.std(xsamples)\n",
      "\n",
      "    fig, ax = plt.subplots(1, 1, figsize=(6,6))\n",
      "    plt.subplots_adjust(top=0.9, bottom=0.1, left=0.06, right=0.97, wspace=0.12, hspace=0.1)\n",
      "\n",
      "    cmap = sns.cubehelix_palette(start=0, light=1, as_cmap=True)\n",
      "     \n",
      "    ax.hexbin(xsamples, ysamples, cmap=cmap, gridsize=50)\n",
      "    ax.set_xlim(-1000, 1000)\n",
      "    ax.set_ylim(-1000, 1000)\n",
      "    ax.set_xlabel(\"a\", fontsize=30)\n",
      "    ax.set_ylabel(\"b\", fontsize=30)\n",
      "    #ax.text(0.1*o, 0.9*o+10, \"standard deviation = %.4f\"%st, fontsize=20)\n",
      "    #ax.text(0.1*o, 0.8*o+10, \"variance = %.4f\"%vr, fontsize=20)\n",
      " \n",
      "    return\n",
      "\n",
      "from IPython.html.widgets import interact\n",
      "interact(standarddeviation, std=(10, 500, 10));    \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DValhVxdRYYjb3p6JlCLc3ojpwx3QNAqXV7DKeTB07PJCXNfHEC3Fwr52rCwf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\nPleukJ4UNAwt+z5EUeb9VErhDtLJSQB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e4cHi/XppvkOm78Te5KdcZ2rVUz5/T+2Zksqc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\nU1/svUEPu7GTsBv1R0NGe1uE01YbKdCKZSRtYuUlSanEOiEEdnM3Os8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EcYhsYieDOIDf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       "text": [
        "<matplotlib.figure.Figure at 0x10f4e7cd0>"
       ]
      }
     ],
     "prompt_number": 151
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Also popular are *quantiles*. To compute these, put all data points in order (from smallest to largest), and then find the point where you have summed up $q\\%$ of your total sample. For example, order your data points, then find that data point in your sample below which the number of data points corresponds to $25\\%$ of all data points you have collected. This data point is the $25\\%$ quantile. \n",
      "\n",
      "The code below draws 10000 numbers from a normal distribution, a Poisson distribution and a Chi-square distribution (see further below for details) with a mean of 2 and a standard deviation of 2, then computes the mean (blue vertical line), median (red vertical line), variance, standard deviation and quantiles (yellow: $25\\%$, purple: $50\\%$, red: $75\\%$) for that sample, then prints it to the screen below and plots all three distribution with their respective properties. Note that all three quantiles extend from the leftmost edge of each plot; but only for the yellow ($25\\%) is this visible!\n",
      "\n",
      "#### Exercise\n",
      "- Play with the number of samples (variable $s$). Given that you know the mean and standard deviation of the normal distribution on the left ($\\mu = 2$, $\\sigma = 2$), how many samples do you need to approximate the expected values? Does this number of samples change if you change the mean or standard deviation of the distribution?\n",
      "- Why is the mean the same as the median for some of the data sets below, but not others? Can you think of a reason why?\n",
      "- Compare the median to the quantiles. What do you observe? Does this observation surprise you?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## import quantiles from scipy\n",
      "from scipy.stats.mstats import mquantiles as quantiles\n",
      "## a popular choice are the 0.25, 0.5 and 0.75 quantiles\n",
      "\n",
      "## create s random normally distributed numbers with a mean of 2 and a standard deviation of 2\n",
      "s = 10000\n",
      "\n",
      "def statistics(chisquare_mean, poisson_mean):\n",
      "    samples = [np.random.normal(2,2, size=s), np.random.chisquare(chisquare_mean, size=s), np.random.poisson(poisson_mean, size=s)]\n",
      "    dists = [\"Normal\", \"Chi-square\", \"Poisson\"]\n",
      "    fig, ax_all = plt.subplots(1, 3, figsize=(16,6))\n",
      "\n",
      "    for i,(samp, dist) in enumerate(zip(samples, dists)):\n",
      "        mn = np.mean(samp)\n",
      "        md = np.median(samp)\n",
      "        vr = np.var(samp)\n",
      "        st = np.std(samp)\n",
      "        qn = quantiles(samp, [0.25, 0.5, 0.75])\n",
      "\n",
      "        if dist == \"Poisson\":\n",
      "            h1, b1, p1 = ax_all[i].hist(samp, bins=25, range=[0,25],color=\"black\", facecolor=\"white\", \n",
      "                                        histtype=\"step\", lw=1, zorder=1.)\n",
      "\n",
      "        else:\n",
      "            h1, b1, p1 = ax_all[i].hist(samp, bins=50, color=\"black\", facecolor=\"white\", \n",
      "                                        histtype=\"step\", lw=1, zorder=1.)\n",
      "\n",
      "        ax_all[i].vlines(mn, 0, np.max(h1), lw=3, color=sns.color_palette(\"Paired\")[1], label=\"mean\")\n",
      "        ax_all[i].vlines(md, 0, np.max(h1), lw=3, color=sns.color_palette(\"Paired\")[5], label=\"median\")\n",
      "        \n",
      "        #colours = sns.cubehelix_palette(len(qn), start=2.5, rot=.75)\n",
      "        for c,q in zip(sns.color_palette()[2:len(qn)+2],reversed(qn)):\n",
      "            b_ind = b1.searchsorted(q)\n",
      "            ax_all[i].fill_between(b1[:b_ind]+0.5*(b1[1]-b1[0]), 0, h1[:b_ind], color=c,\n",
      "                                 alpha=1.0, label=\"%i quantile\"%(q*100.))\n",
      "\n",
      "        ax_all[i].legend(loc=\"upper right\")\n",
      "        ax_all[i].set_ylim(0.0, None)\n",
      "        ## print results\n",
      "    print(\"The mean of the sample is: \" + str(mn))\n",
      "    print(\"The median of the sample is: \" + str(md))\n",
      "    print(\"The variance of the sample is: \" + str(vr))\n",
      "    print(\"The standard deviation of the sample is: \" + str(st))\n",
      "    print(\"The 25% quantile of the sample is: \" + str(qn[0]))\n",
      "    print(\"The 50% quantile of the sample is: \" + str(qn[1]))\n",
      "    print(\"The 75% quantile of the sample is: \" + str(qn[2]))\n",
      "    return\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 152
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(statistics, chisquare_mean=(1, 20), poisson_mean=(1, 20));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The mean of the sample is: 10.0535\n",
        "The median of the sample is: 10.0\n",
        "The variance of the sample is: 10.13263775\n",
        "The standard deviation of the sample is: 3.18318044572\n",
        "The 25% quantile of the sample is: 8.0\n",
        "The 50% quantile of the sample is: 10.0\n",
        "The 75% quantile of the sample is: 12.0\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eo+RVRqWjK7v7PwIkIl1Zr1PES5qamti1axfBrk52lT1IMOjeVP1oUzOJaMy1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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11029a5d0>"
       ]
      }
     ],
     "prompt_number": 153
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To summarise, below is, in a concise form, how to compute simple representations of a data set in python."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "## create s random normally distributed numbers with a mean of 2 and a standard deviation of 2\n",
      "s = 10000\n",
      "samples = np.random.normal(2,2, size=s)\n",
      "\n",
      "mn = np.mean(samples)\n",
      "md = np.median(samples)\n",
      "vr = np.var(samples)\n",
      "st = np.std(samples)\n",
      "qn = quantiles(samples, [0.25, 0.5, 0.75])\n",
      "\n",
      "print(\"The mean of the sample is: \" + str(mn))\n",
      "print(\"The median of the sample is: \" + str(md))\n",
      "print(\"The variance of the sample is: \" + str(vr))\n",
      "print(\"The standard deviation of the sample is: \" + str(st))\n",
      "print(\"The 25% quantile of the sample is: \" + str(qn[0]))\n",
      "print(\"The 50% quantile of the sample is: \" + str(qn[1]))\n",
      "print(\"The 75% quantile of the sample is: \" + str(qn[2]))\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The mean of the sample is: 1.97793262815\n",
        "The median of the sample is: 1.96617546827\n",
        "The variance of the sample is: 4.00591529855\n",
        "The standard deviation of the sample is: 2.00147827831\n",
        "The 25% quantile of the sample is: 0.655412448749\n",
        "The 50% quantile of the sample is: 1.96617546827\n",
        "The 75% quantile of the sample is: 3.3186827989\n"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Accuracy Versus Precision"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Measurements taken with any kind of scientific instrument are never perfect. Images observed from a telescope, for example, will be affected by seeing---random jitters in the atmosphere---, manmade light sources, the CCD of the camera recording the infalling light, and others. These effects will add an *uncertainty* in whatever quantity measured from the data set that was taken. In this context, we have to distinguish two types of uncertainty:\n",
      "\n",
      "On the one hand, your data may be affected by random fluctuations in the atmosphere, your apparatus, or some other source. This leads to a scatter around some mean value that we would have measured if these fluctuations didn't exist. This type of uncertainty is often referred to as **precision**: the larger the scatter introduced by the measurement process (although sometimes, these errors can be due to a physical process as well!), the harder it will be to measure the mean quantity, especially for low numbers of samples. Often, it is assumed that this type of uncertainty follows a normal distribution (which has nice properties that make the analysis easier), although this need not be true!\n",
      "\n",
      "The other type of uncertainty comes from a systematic offset in your measurement. Perhaps the calibration of the instrument is wrong, such that all the stars in your image are systematically brighter than you'd expect them to be based on previous measurements. The term **accuracy** describes how strong these systematic effects are in a data set: the larger the offset is between a measured quantity and its true value, the less accurate the measurement is. Characterising and correcting for the systematic effects in a data set is a very important step in data analysis, and should be taken very seriously; make sure your data set is as accurate as can be!\n",
      "\n",
      "The plot below demonstrates the principles of accuracy and precision defined above. Imagine you have two quantities, $a$ and $b$, whose true values are $a=1$ and $b=2$. We collect data with a given *accuracy* (which encodes your systematic bias, for example due to an incomplete model or an error in the instrument that measured the data) and *precision* (which encodes the random error on the data, perhaps due to measurement uncertainty or due to the source itself).\n",
      "\n",
      "The left panel shows a sample of measured data points with a specified accuracy and precision, scattered in parameter space together with the true value. On the right side, we show a histogram of quantity $a$ only, with the true value of $a$ as a black vertical line superimposed. The horizontal arrow to the left shows the distance between the sample mean and the true value of $a$, i.e. the accuracy. The horizontal arrow towards the right is a measure of precision. \n",
      "\n",
      "#### Exercise\n",
      "- Which quantity would you use to characterise the precision of your data set?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "from matplotlib.patches import FancyArrow\n",
      "\n",
      "## TODO: put in some labels and arrows for accuracy and precision\n",
      "## TODO: Add sliders\n",
      "def plot_ap(accuracy, precision):\n",
      "    \n",
      "    # Hardcoded values good for illustration\n",
      "    a_true = 1.0\n",
      "    b_true = 2.0\n",
      "    xlim = (-2, 4)\n",
      "    ylim = (-1, 5)\n",
      "    \n",
      "    # So users get an intuitive idea of '0==low', '1==high'\n",
      "    accuracy, precision = np.clip(1-np.array([accuracy, precision]), 0.001, 1)\n",
      "    \n",
      "    xsample = np.random.normal(a_true+2*accuracy, precision**2.0, size=10000)\n",
      "    xsample_small = xsample[:5000]\n",
      "    xmean = np.mean(xsample_small)\n",
      "    xstd = np.std(xsample_small)\n",
      "    \n",
      "    ysample = np.random.normal(b_true+2*accuracy, precision**2.0, size=10000)\n",
      "    ysample_small = ysample[:5000]\n",
      "    ymean = np.mean(ysample_small)\n",
      "\n",
      "    d = pd.DataFrame(zip(xsample_small, ysample_small), columns=[\"x\", \"y\"])\n",
      "    \n",
      "    fig, (ax, ax2) = plt.subplots(1, 2, figsize=(12,6))\n",
      "    plt.subplots_adjust(top=0.9, bottom=0.1, left=0.06, right=0.97, wspace=0.2, hspace=0.1)\n",
      "\n",
      "    cmap = sns.cubehelix_palette(start=0, light=1, as_cmap=True)\n",
      "    ax.hexbin(xsample_small,ysample_small, cmap=cmap, gridsize=50)\n",
      "    #ax.scatter(xsample_small, ysample_small, s=20)\n",
      "    ax.scatter(a_true, b_true, s=200, marker=\"h\", color=sns.cubehelix_palette()[5])\n",
      "    #ax.scatter(a_true, b_true, s=200)\n",
      "    ax.set_xlim(xlim)\n",
      "    ax.set_ylim(ylim)\n",
      "    ax.set_xlabel(\"a\", fontsize=30)\n",
      "    ax.set_ylabel(\"b\", fontsize=30)\n",
      "    \n",
      "    h1, b1, p1 = plt.hist(xsample, bins=100, histtype=\"stepfilled\", color=cmap.colors[150], alpha=1.0, normed=True)\n",
      "    hmax = np.max(h1)\n",
      "    plt.vlines(a_true, 0.0, np.max(h1), lw=6)\n",
      "    \n",
      "    ar1 = FancyArrow(xmean,hmax*0.1, a_true-xmean,0.0, length_includes_head=True,\n",
      "                    color='k', head_width=0.03*hmax, head_length=0.2, width=0.001, linewidth=3)\n",
      "    \n",
      "    ar2 = FancyArrow(xmean,hmax*0.5, xstd,0.0, length_includes_head=True,\n",
      "                    color='k', head_width=0.03*hmax, head_length=0.2, width=0.001, linewidth=3)\n",
      "\n",
      "\n",
      "    # Add the arrow to the axes.\n",
      "    ax2 = plt.gca()\n",
      "\n",
      "    ax2.add_artist(ar1)\n",
      "    ax2.add_artist(ar2)\n",
      "\n",
      "\n",
      "    ax2.set_xlim(xlim)\n",
      "    ax2.set_ylim([0.0, hmax*1.1])\n",
      "    ax2.set_xlabel(\"a\", fontsize=24)\n",
      "    ax2.set_ylabel(\"p(a)\", fontsize=24)\n",
      "    return\n",
      "\n",
      "#accuracy = 0.5\n",
      "#precision = 0.5\n",
      "#plot_ap(accuracy, precision)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 154
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(plot_ap, accuracy=(0, 1.0, 0.1), precision=(0, 1.0, 0.1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pk4h0cEg55zmbMs9QeYK7uoqYVdL8iFsPabSvYXmzH/cUjkTnGd3vdyii2cUX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\n+Nd/6if4WvsOFQWW65AU8Pj+PmkyfV2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o7SGVpsgz8mF3KrgetXA3FPGIIp0gtU82GJD3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teXuuy29yYgiHrXBbP95htznHeOImtDnmEAE0WYMMRneTmuKH/smTDGhAEmCMr5vC+P3RjAbM5n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\nos4fy76h4CUiIiIie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       "text": [
        "<matplotlib.figure.Figure at 0x1108406d0>"
       ]
      }
     ],
     "prompt_number": 142
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Basic Probability Theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Probability theory provides the basis for manipulating probabilities. It has its roots in measure theory, but only a few key concepts are required to understand the basis of probability calculus. Note that these concepts are independent of your preferred *interpretation* of probability; they are universally valid. Below, we outline the basic ideas for how to thing about probability, and provide an interactive figure that illustrates many of these concepts.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Set Theory Stuff"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "   "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Conditional Probabilities"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A conditional probability expresses the probability of an event occuring *given* that another event has already occurred. For example, one may want to compute the probability of rain in the next hour given that it is cloudy, which should differ from the probability of rain in the next hour given that it is sunny. Formally, this is expressed as \n",
      "\n",
      "P(A|B) .\n",
      "\n",
      "The conditional probability of event A given another event $B$ is defined as the intersection between A and B divided by the probability of B [**ADD EQUATION**]. Imagine a space of all possible outcomes (say, rain, wind, hail, sun, thunderstorms, ...). Both P(A) (e.g. the probability of rain, where rain could be a number of possible outcomes, such as drizzle, sheeting rain etc.) and P(B) (e.g. the probability of thunderstorms) occupy a subset of this space. We now wish to compute P(A|B), the probability that it's raining given that there is a thunderstorm. For this, we need to find all possible outcomes that obey both restrictions: this is the intersection between A and B. However, the probability of the intersection is computed with respect to the entire space of possible outcomes; but we already know that most of this space is irrelevant: since there is a thunderstorm, sunny weather is no longer in out space of possible outcomes. Thus, the probability of the intersection must be renormalised to the relevant space of outcomes, i.e. thunderstorms only. This is P(B). \n",
      "\n",
      "Note that the probability of A given B is **not** the same as the probability of B given A: P(A|B) $\\neq$ P(B|A)! This can easily be unerstood: the probability that it is raining given that it is cloudy is not the same as the probability that it is cloudy given that it is raining. It can be cloudy without raining (P(A|B) < 1), however, as soon as we know that it is raining, we also know it must be cloudy (P(B|A) = 1)! Thus, the two are not the same.\n",
      "\n",
      "Below, we provide an interactive figure to visualise key concepts of probability theory. We show a possible space of outcomes in yellow, and two subsets of outcomes (A and B) in red and blue. Think of this as a collection of outcomes (they can be discrete, such as in the weather example above, but they need not be): A could be all possible types of rainy weather you can think of, B could be storms (including, say, thunderstorms, hurricanes, tornados, ...). As you change the number of outcomes in B, and change their position relative to the outcomes in A, observe how the probabilities change. \n",
      "\n",
      "#### Exercises\n",
      "- \n",
      "- [to be written]\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def circle_intersection(r1, r2, d):\n",
      "    tinner_left = (d**2. + r2**2. - r1**2.)/(2.*d*r2)\n",
      "    tinner_right = (d**2. + r1**2. - r2**2.)/(2.*d*r1)\n",
      "\n",
      "    if d >= (r1 + r2):\n",
      "        area = 0.0   \n",
      "    elif r2 <= (r1+d):\n",
      "        area = (r2**2.)*np.arccos(tinner_left) + (r1**2.)*np.arccos(tinner_right) \\\n",
      "            - 0.5*np.sqrt((-d+r2+r1)*(d+r2-r1)*(d+r1-r2)*(d+r1+r2))\n",
      "    else:\n",
      "        area = np.pi*r1**2.\n",
      "            \n",
      "    return area"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.testing as npt\n",
      "\n",
      "def check_circle(r1):\n",
      "    r2 = 0.5*r1\n",
      "    npt.assert_allclose(circle_intersection(r1,r2,r1+r2), 0.0)\n",
      "    npt.assert_allclose(circle_intersection(r1,r2, r1-r2), np.pi*r2**2.)\n",
      "    return"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 144
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_circle():\n",
      "    for r in (1,2,3):\n",
      "        check_circle(r)\n",
      "        \n",
      "test_circle()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 145
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import display, HTML\n",
      "\n",
      "\n",
      "def html_figure(fig):\n",
      "    \"\"\"Return an HTML <img> tag with the data for a matplotlib figure embedded\"\"\"\n",
      "    \n",
      "    from IPython.core.pylabtools import print_figure\n",
      "    import base64\n",
      "\n",
      "    fdata64 = base64.b64encode(print_figure(fig))\n",
      "    html_tpl = '<img alt=\"Figure\" src=\"data:image/png;base64,{}\">'\n",
      "    return html_tpl.format(fdata64)\n",
      "\n",
      "\n",
      "def html_table(dct, title=None, fmt=\"{:.4f}\"):\n",
      "    \"\"\"Produce an HTML table from a dict, with an optional title.\n",
      "    \"\"\"\n",
      "    import html as H\n",
      "    \n",
      "    h = H.HTML()\n",
      "    if title:\n",
      "        h.h2(title)\n",
      "        \n",
      "    t = h.table(border='1')\n",
      "    for k, v in dct.items():\n",
      "      r = t.tr\n",
      "      r.td(str(k))\n",
      "      r.td(fmt.format(v))\n",
      "    return str(h)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 146
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from collections import OrderedDict\n",
      "\n",
      "def probabilities(ra, rb, offset):\n",
      "    square_area = 1\n",
      "\n",
      "    aa = np.pi*ra**2.\n",
      "    ab = np.pi*rb**2.\n",
      "    ab_complement = 1.0 - ab\n",
      "    \n",
      "    intersection = circle_intersection(ra, rb, offset)\n",
      "    union = aa + ab - intersection\n",
      "\n",
      "    agivenb = intersection/ab\n",
      "    bgivena = intersection/aa\n",
      "    \n",
      "    od = OrderedDict()\n",
      "    od[\"P(A)\"] = aa\n",
      "    od[\"P(B)\"] = ab\n",
      "    od[\"P(A^c)\"] = ab_complement\n",
      "    od[\"P(A and B)\"] = intersection\n",
      "    od[\"P(A or B)\"] = union\n",
      "    od[\"P(A|B)\"] = agivenb\n",
      "    od[\"P(B|A)\"] = bgivena\n",
      "    return od\n",
      "\n",
      "\n",
      "def draw_circles(r2):\n",
      "    xlim = (-0.25,.75)\n",
      "    ylim = (-0.5,.5)\n",
      "\n",
      "    a1 = 0.05\n",
      "    r1 = np.sqrt(a1/np.pi)\n",
      "\n",
      "    offset = 0.25\n",
      "    d = 2.*offset\n",
      "\n",
      "    colors = sns.color_palette()\n",
      "    fig, ax = plt.subplots(figsize=(6,6), subplot_kw=dict(axisbg=colors[5]))\n",
      "\n",
      "    ax.set_xlim(xlim)\n",
      "    ax.set_ylim(ylim)\n",
      "    ax.set_xticks([])\n",
      "    ax.set_yticks([])\n",
      "    ax.set_aspect('equal')\n",
      "\n",
      "\n",
      "    c1 = plt.Circle((0, 0), r1, facecolor=colors[2], fill=True, alpha=0.8)\n",
      "    ax.text(0-0.02,0-0.02, \"A\", color='black', fontsize=20)\n",
      "    c2 = plt.Circle((offset, 0), r2, facecolor=colors[1], fill=True, alpha=0.8 )\n",
      "    ax.text(offset-0.01,0-0.02, \"B\", color='black', fontsize=20)\n",
      "\n",
      "    ax.add_artist(c1)\n",
      "    ax.add_artist(c2)\n",
      "    plt.close(fig)\n",
      "    \n",
      "    probtab = probabilities(r1, r2, offset)\n",
      "    \n",
      "    # Produce HTML side-by-side display\n",
      "    fh = html_figure(fig)\n",
      "    h = html_table(probtab, title=\"Probabilities\")\n",
      "    html = HTML(\"\"\"\n",
      "    <div style=\"float:left;width=50%\">\n",
      "    {fh}\n",
      "    </div>\n",
      "\n",
      "    <div style=\"width=50%\">\n",
      "    {h}\n",
      "    </div>\n",
      "    \"\"\".format(**locals()))\n",
      "    display(html)    \n",
      "    \n",
      "    return \n",
      "\n",
      "#draw_circles(0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 147
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(draw_circles, r2=(0.001,0.5, 0.01));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ImportError",
       "evalue": "No module named html",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-147-b444e3d7159f>\u001b[0m in \u001b[0;36mdraw_circles\u001b[0;34m(r2)\u001b[0m\n\u001b[1;32m     58\u001b[0m     \u001b[0;31m# Produce HTML side-by-side display\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     59\u001b[0m     \u001b[0mfh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhtml_figure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 60\u001b[0;31m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhtml_table\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprobtab\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"Probabilities\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     61\u001b[0m     html = HTML(\"\"\"\n\u001b[1;32m     62\u001b[0m     \u001b[0;34m<\u001b[0m\u001b[0mdiv\u001b[0m \u001b[0mstyle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"float:left;width=50%\"\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m<ipython-input-146-e39db9587ad5>\u001b[0m in \u001b[0;36mhtml_table\u001b[0;34m(dct, title, fmt)\u001b[0m\n\u001b[1;32m     16\u001b[0m     \"\"\"Produce an HTML table from a dict, with an optional title.\n\u001b[1;32m     17\u001b[0m     \"\"\"\n\u001b[0;32m---> 18\u001b[0;31m     \u001b[0;32mimport\u001b[0m \u001b[0mhtml\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mH\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m     \u001b[0mh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mH\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mHTML\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mImportError\u001b[0m: No module named html"
       ]
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The bar toggles the radius of circle $B$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Statistical Distributions in Numpy and Scipy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Both numpy and scipy have many of the most useful standard distributions already in their code base. You've already seen above how to quickly and easily make random numbers in numpy. If that's all you want (and this can be incredibly powerful for producing simulated data), you're good to go. \n",
      "\n",
      "However, scipy can do more. In scipy.stats, there are classes for many distributions, which have methods that can do a whole lot more than just produce random numbers for you! \n",
      "For example, to produce an instance of a normal distribution with \"frozen\" parameters (mean=2, standard deviation=2 here), goes like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats\n",
      "n = scipy.stats.norm(2, 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can now use this distribution in various ways. For example, to plot the pdf and cdf, you can do this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## define some x coordinates\n",
      "x = np.linspace(-10, 20, 2000)\n",
      "\n",
      "## make a figure\n",
      "fig, (ax,ax2) = plt.subplots(1,2,figsize=(12,6))\n",
      "ax.plot(x, n.pdf(x))\n",
      "ax.set_title(\"PDF\")\n",
      "\n",
      "ax2.plot(x, n.cdf(x))\n",
      "ax2.set_title(\"CDF\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 607,
       "text": [
        "<matplotlib.text.Text at 0xb497390>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lTM3Mc/xSLxUlOSm9VaskHhXTKSx0SMkIlaU5ZGem2Y4TF2oqCxgZn2VwdMZ2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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcb14910>"
       ]
      }
     ],
     "prompt_number": 607
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly, it allows you to play around with the mean, median, standard deviation and other moments. \n",
      "\n",
      "Something else that might be useful is the capability of fitting a distribution to a data sample:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## let's make another sample\n",
      "sample = np.random.normal(2,2,size=1000)\n",
      "\n",
      "## now fit a normal distribution to the sample with the \n",
      "## fit method of the norm class\n",
      "f = scipy.stats.norm.fit(sample)\n",
      "\n",
      "print(\"The fit parameter for the mean of the distribution is: %.4f\"%f[0])\n",
      "print(\"The fit parameter for the standard deviation of the distribution is: %.4f\"%f[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The fit parameter for the mean of the distribution is: 2.0043\n",
        "The fit parameter for the standard deviation of the distribution is: 1.9015\n"
       ]
      }
     ],
     "prompt_number": 608
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Normal Distributions\n",
      "\n",
      "This is an explanation of the normal distribution!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_dist(x,n, continuous=True, distname=\"\"):\n",
      "    fig, (ax1,ax2) = plt.subplots(1,2,figsize=(12,6))\n",
      "    if continuous:\n",
      "        density = n.pdf\n",
      "        title = \"Probability Density Function\"\n",
      "        plot_symbol = '-'\n",
      "    else:\n",
      "        density = n.pmf\n",
      "        title = \"Probability Mass Function\"\n",
      "        plot_symbol = 'bo'\n",
      "        \n",
      "    distribution = density(x)\n",
      "    ax1.plot(x, distribution, plot_symbol, color=\"blue\", label=distname)\n",
      "    if continuous:\n",
      "        ax1.fill_between(x, 0, distribution, color=\"blue\", alpha=0.6)\n",
      "    else:\n",
      "        ax1.vlines(x, 0, distribution, colors='b', lw=5, alpha=0.5)\n",
      "    ax1.set_title(title)\n",
      "\n",
      "    cdf = n.cdf(x)\n",
      "    ax2.plot(x, cdf, lw=1, color=\"blue\", label=distname)\n",
      "    ax2.fill_between(x, 0, cdf, color=\"blue\", alpha=0.6)\n",
      "    ax2.set_title(\"CDF\")\n",
      "    return ax1, ax2\n",
      "\n",
      "def normal(m,s):\n",
      "    x = np.linspace(-10, 20, 2000)\n",
      "    n = scipy.stats.norm(m, s)\n",
      "    plot_dist(x,n)\n",
      "    return\n",
      "\n",
      "interact(normal, m=(-5.,10.), s=(0.001, 10.0));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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856Ww2kWpUzEtJWnyZL+83ZgxfnJGewwfDu96Fzz/PPzud4XJJyIiAvDKK/Cxj/mlW/v1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\nwSWXxAGW5uas04jIqVBnegB1dcGtt8KGDTBmDFx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       "text": [
        "<matplotlib.figure.Figure at 0x10f5e6e50>"
       ]
      }
     ],
     "prompt_number": 157
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Poisson Distribution \n",
      "\n",
      "This is an explanation of the Poisson distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def poisson(m):\n",
      "    d = scipy.stats.poisson(m)\n",
      "    x = np.arange(d.ppf(0.01), d.ppf(0.99))\n",
      "    plot_dist(x, d, continuous=False)\n",
      "    return\n",
      "\n",
      "interact(poisson, m=(1,200,1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7OyxeXP1YGk1bW5Zot7Rk25Kk4XHppdk0gKWFDqm/dio6AEn9N358VtWWJA2f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\nV5WU+s7pMqW+27wZ3vEOOOYY2HXXoqO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       "text": [
        "<matplotlib.figure.Figure at 0x10f4a8b90>"
       ]
      }
     ],
     "prompt_number": 158
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Binomial Distribution\n",
      "\n",
      "Some information about the Binomial distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#def binomial(sample, success):\n",
      "#    d = scipy.stats.binom(samples, success)\n",
      "#    x = d.ppf(0.01), d.ppf(0.99)\n",
      "#    plot_dist(x, d, continuous=False)\n",
      "#    return\n",
      "#\n",
      "#interact(binomial, sample=(1,200,1), success=(1,200,1));\n",
      "d = scipy.stats.binom(100, 10)\n",
      "x = np.arange(scipy.stats.binom(0.01, 100, 10), scipy.stats.binom(0.99, 100, 10))\n",
      "\n",
      "#x = np.arange(d.ppf(0.01), d.ppf(0.99))\n",
      "print(x)\n",
      "print(d.pmf(x))\n",
      "plt.plot(x, d.pmf(x), \"o\", color=\"blue\", label=\"Binomial Distribution\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "unsupported operand type(s) for -: 'rv_frozen' and 'rv_frozen'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-184-9fa355dad5ed>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;31m#interact(binomial, sample=(1,200,1), success=(1,200,1));\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbinom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbinom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbinom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.99\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0;31m#x = np.arange(d.ppf(0.01), d.ppf(0.99))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'rv_frozen' and 'rv_frozen'"
       ]
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Chi-Square Distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Central Limit Theorem\n",
      "\n",
      "[two iterations: \n",
      "- in the limit of large numbers, the Poisson distribution goes to a Gaussian. Plot Poisson distribution again, make drop-down menu such that one can overplot the Gaussian distribution\n",
      "- In the limit of many (averaged) observations, the averaged data points go to a Gaussian distribution, which gets narrower; plot (averaged) data points on left side, histogram of distribution on right side]\n",
      "\n",
      "Let's go back to the Poisson distribution. \n",
      "Below is a plot of the distribution where, again, you can adjust the scale parameter. \n",
      "The drop-down menu allows you to overplot a Gaussian distribution. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def poisson2(m):\n",
      "    d = scipy.stats.poisson(m)\n",
      "    x = np.arange(d.ppf(0.01), d.ppf(0.99))\n",
      "    ax1, ax2 = plot_dist(x, d, continuous=False, distname=\"Poisson distribution\")\n",
      "    ax1, ax2 = overplot_gaussian(ax1, ax2, d)\n",
      "    \n",
      "    ax2.legend(loc=\"upper left\")\n",
      "    return\n",
      "\n",
      "def overplot_gaussian(ax1, ax2, d):\n",
      "    x = np.arange(d.ppf(0.01), d.ppf(0.99))\n",
      "    n = scipy.stats.norm(d.args[0], np.sqrt(d.args[0]))\n",
      "    ax1.plot(x, n.pdf(x), lw=3, color=\"red\")\n",
      "    ax2.plot(x, n.cdf(x), lw=3, color=\"red\",label=\"Normal distribution\")\n",
      "    return ax1, ax2\n",
      "\n",
      "interact(poisson2, m=(1,200,1));\n",
      "#from IPython.html.widgets import fixed, interact, interactive\n",
      "\n",
      "#from collections import OrderedDict\n",
      "\n",
      "#functions = OrderedDict()\n",
      "#for func in (poisson2, overplot_gaussian):\n",
      "#    functions[func.__name__] = func\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "global name 'plot_dist' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-156-13f146c68ea7>\u001b[0m in \u001b[0;36mpoisson2\u001b[0;34m(m)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpoisson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mppf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mppf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.99\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0max1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplot_dist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcontinuous\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdistname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"Poisson distribution\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0max1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moverplot_gaussian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0max1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mNameError\u001b[0m: global name 'plot_dist' is not defined"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 156,
       "text": [
        "<function __main__.poisson2>"
       ]
      }
     ],
     "prompt_number": 156
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#from IPython.display import display\n",
      "\n",
      "# Create a plotter that takes a function to plot and displays the plot\n",
      "#def p(x, function):\n",
      "#    p.ax.plot(x, function(x))\n",
      "#    display(p.fig)\n",
      "\n",
      "# Little hack to attach a persistent figure to the function object\n",
      "# so we can overplot.  Note that we close the figure to avoid \n",
      "# IPython's auto-display of figures that would create a duplicate\n",
      "#p.fig, p.ax = plt.subplots()\n",
      "#plt.close(p.fig)\n",
      "\n",
      "\n",
      "#from IPython.html.widgets import fixed, interactive\n",
      "\n",
      "#interactive(p, x=fixed(x), function=functions)\n",
      "#interact(poisson2, m=(1,100,1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**NOTE** Add explanation and illustration on how, in the limit of large $\\mu$, the Poisson distribution approaches the Normal."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "averaging data makes a Gaussian distribution, too!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0,1000, 1000)\n",
      "\n",
      "def sine_data(x, period, amplitude):\n",
      "    y = amplitude*np.sin(2.*np.pi*x/period)\n",
      "    return y\n",
      "\n",
      "def compute_error(y, sigma):\n",
      "    return np.random.normal(0, sigma, size=len(y))\n",
      "    \n",
      "\n",
      "#y = sine_data(x, 200, 10)\n",
      "#plt.plot(x,add_error(y, 30))\n",
      "\n",
      "\n",
      "def average_sims(nsims):\n",
      "    period=200\n",
      "    amplitude = 10\n",
      "    noise = 30\n",
      "\n",
      "    x = np.linspace(0,1000, 1000)\n",
      "    y = sine_data(x, period, amplitude)\n",
      "\n",
      "    yall, yerr_all = [], []\n",
      "    for n in xrange(nsims):\n",
      "        yerr = compute_error(y, noise)\n",
      "        yall.append(y+yerr)\n",
      "        \n",
      "    yall = np.array(yall)\n",
      "    ymean = np.mean(yall, axis=0)\n",
      "    yres = ymean - amplitude*np.sin(2.*np.pi*x/period)\n",
      "    yerr_res = np.mean(yerr_all, axis=0)\n",
      "    \n",
      "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,7))\n",
      "    #ax1.plot(x, yres, lw=2, color=\"blue\", linestyle='steps-mid')\n",
      "    ax1.plot(x, ymean, lw=2, color=\"black\", linestyle='steps-mid')\n",
      "\n",
      "    ax1.set_ylim(-100, 100)\n",
      "    ax2.hist(yres, bins=100, range=[-100,100], color=\"blue\", histtype=\"stepfilled\", alpha=0.6)\n",
      "    ax2.set_xlim(-100, 100)\n",
      "    return\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 615
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "interact(average_sims, nsims=(1,500,1));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GqAxJRERqeMQdpUuXLqFFixYAgNjYWNSsWbPY844ePYpJkyZh0KBBeOSRR+44/sMPPyA6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\n9NHXefzxnS94/8u/3MJf//VEAJ5//g1++tOdL4A78cSPuOK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       "text": [
        "<matplotlib.figure.Figure at 0xb15d1d0>"
       ]
      }
     ],
     "prompt_number": 356
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Likelihood Functions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Estimating the best-fit parameters of a distribution is one of the standard problems in astronomy. Numpy and scipy have many different tools for this available already. In the following, we're going to play around with a Poisson likelihood for a while. The Poisson distribution is useful anywhere where you have discrete, rare events. These can be, for example, particle in a detector, car accidents, or other data sets like these. \n",
      "\n",
      "Because likelihood functions can have quite large and small values, we'll work with the log-likelihood without loss of any capabilities in inferring from the data. \n",
      "\n",
      "First, we define the log-likelihood. Then we make some Poisson sample data, with a rate parameter of 5. This could be, for example, a count rate in a photon detector detecting of the order of 5 photons per second. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def poisson_loglike(rate, data):\n",
      "    ## make rate parameter into array of same length as data:\n",
      "    r = np.ones(len(data))*rate\n",
      "    ## now we can compute the log-likelihood:\n",
      "    llike = -np.sum(r) + np.sum(data*np.log(r))-np.sum(scipy.special.gammaln(data + 1))\n",
      "    return llike\n",
      "\n",
      "\n",
      "sample = np.random.poisson(10, size=10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 616
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I'll leave it to you to verify that the expression in the definition of the likelihood function is indeed that of the Poisson likelihood for N samples. \n",
      "\n",
      "Now, let's have a look at the shape of the likelihood. We'll use the first 100 events from our sample:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "## return likelihood for sample s for a bunch of guesses\n",
      "def guess_like(s):\n",
      "    guesses = np.arange(100)\n",
      "    like_all = [poisson_loglike(g, s) for g in guesses]\n",
      "    return like_all\n",
      "\n",
      "def plot_like(nsamples):\n",
      "    np.random.poisson(10, size=10000)\n",
      "    fig = plt.figure(figsize=(12,12))\n",
      "    plt.plot(np.arange(100), np.array(guess_like(sample[:nsamples])), color=\"black\", label=\"%i samples\"%nsamples)\n",
      "\n",
      "interact(plot_like, nsamples=(10,10000));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dPn3adCwAAHIUxf0mKO6A63I4HJo0aZL+/ve/67vvvlNoaKh++eUX07EAAMgx\nFPebuFbcy5YtazgJgBtxOByaPHmyunXrpi1btqh58+b67bffTMcCACBHUNxvgivugOvz8fHRtGnT\nFBERofXr16tVq1a6cOGC6VgAAGQ7ivtNUNwB95AnTx5FRUWpdevWWr16tcLDw3X58mXTsQAAyFYU\n95tISkqSv7+/7r33XtNRANyCr6+v5s2bp9DQUC1dulQdO3ZUamqq6VgAAGQbivtNHDp0SKVLl5aP\nD78mwB34+/srJiZGDRo0UExMjLp06aK0tDTTsQAAyBY00j9x4cIFnThxgmUygJvJnz+/vvjiC9Wu\nXVtz585Vr169lJ6ebjoWAAB3jOL+Jw4fPiyJ9e2AO7rnnnsUHx+vxx9/XNOnT9eAAQOUkZFhOhYA\nAHeE4v4nAgICVLRoUTVs2NB0FABZEBAQoOXLl+uhhx7SBx98oKFDh5qOBADAHclrOoCrKlq0qI4d\nOyaHw2E6CoAsCgoK0sqVK1W3bl2NGTNG99xzj4YMGWI6FgAAWcIV95ugtAPur3jx4lq9erXKli2r\noUOH6r333jMdCQCALKG4A/B4pUuX1qpVq1SiRAm9+OKL+uSTT0xHAgAg0yjuALxC+fLltWrVKhUp\nUkTPPfec5syZYzoSAACZQnEH4DUqV66sFStWqGDBgurSpYsWL15sOhIAALeN4g7Aqzz66KNatmyZ\n8uXLpw4dOmjlypWmIwEAcFso7gC8Ts2aNbVkyRI5HA61bt1aiYmJpiMBAHBLFHcAXik4OFjR0dG6\ndOmSmjVrpu3bt5uOBADATVHcAXitli1bavbs2Tp37pwaN26sPXv2mI4EAMCforgD8GodO3bUxx9/\nrJMnT6pRo0Y6cOCA6UgAANwQxR2A1+vZs6cmTJigI0eOKCQkREePHjUdCQCA/0FxBwBJL730kkaM\nGKEff/xRjRo10smTJ01HAgDgv1DcAcBpxIgRevHFF7V79241bdpUv/zyi+lIAAD8juIOAE4Oh0MT\nJkxQ9+7d9e233yosLEwXLlwwHQsAAEkUdwD4Lw6HQ1OnTlW7du301VdfqX379rpy5YrpWAAAUNwB\n4I/y5s2rzz77TI0bN1ZcXJy6du2qtLQ007EAAF6O4g4AN+Dv76+YmBjVqlVLc+fOVZ8+fZSRkWE6\nFgDAi1HcAeBP3H333YqPj1fVqlX10UcfaciQIaYjAQC8GMUdAG6iUKFCSkhIUIUKFTR27FiNGzfO\ndCQAgJdevDw6AAAgAElEQVSiuAPALRQrVkyrVq1SqVKl9Nprr+mTTz4xHQkA4IUo7gBwG8qUKaOV\nK1eqSJEieu6557RgwQLTkQAAXobiDgC3qWLFilq+fLnuuecede7cWQkJCaYjAQC8CMUdADKhWrVq\nio2NlY+Pj9q2basNGzaYjgQA8BIUdwDIpHr16ik6OlqXLl1S8+bN9f3335uOBADwAhR3AMiCli1b\nasaMGTpz5oyaNGmiH374wXQkAICHo7gDQBZFRkbq/fff17Fjx9SoUSMdPXrUdCQAgAejuAPAHejX\nr59GjhypAwcOqEmTJjp9+rTpSAAAD0VxB4A7NHz4cPXt21c7d+5UixYt9Ntvv5mOBADwQHmzOtGy\nrKckjZRUUdLfbNvedt1jgyU9IylNUj/btlc4x6tJmikpn6Sltm33d477S4qS9JikFEkdbNs+5Hys\nq6ShzlOPtm07yjn+gKR5kgpL2iop0rbtK1l9PQCQVQ6HQ++9955SUlI0Z84chYeHa8mSJfLz8zMd\nDQDgQe7kivu/JbWRtO76QcuyKkvqIKmypFBJH1qW5XA+PEVSD9u2K0iqYFlWqHO8h6QU5/gkSeOc\n5yosabikJ5xfIyzLCnDOGSdpgnPOaec5AMAIHx8fzZw5U02bNtXy5cvVrVs3paenm44FAPAgWS7u\ntm3vtW173w0eaiVprm3bV2zbPihpv6TqlmWVkFTAtu0tzudFSWrtPA6TNMt5vFBSsPO4iaQVtm2f\nsW37jKSVkpo6/yLQQNLnzufNuu5cAGCEr6+vPv/8c9WuXVtz585V//79lZGRYToWAMBD5MQa95KS\nDl/3/WFJ991g/IhzXM4/kyXJtu1USWctywq6ybkKSzpj23b6Dc4FAMbcddddio2NVZUqVTR58mSN\nGjXKdCQAgIe46Rp3y7JWSip+g4eG2LYdmzORbinLl68syxopaUT2RQGA/xUYGKiEhATVrl1bI0eO\nVFBQkPr06WM6FgDAdRywLOuPY2/Ytj3yZpNuWtxt226UhSBHJJW+7vtSunql/Ijz+I/j1+aUkXTU\nsqy8kgJs206xLOuIpPrXzSktaY2kU5IKWZbl47zqXsp5jpty/jJGXj9mWdb9kg7c3ksDgNtTokQJ\nrVixQnXq1FHfvn0VFBSkjh07mo4FAHANDziXlGdKdi2VcVx3/IWkCMuy/Jw7v1SQtMW27WOSfrEs\nq7pzjXqkpCXXzenqPA6XtNp5vEJSY8uyClmWFSipkaQE27YzJK2V9JTzeV0lLc6m1wIA2aJ8+fJK\nSEhQwYIF1aVLFyUkJJiOBABwY1ku7pZltbEsK1lSDUnxlmUtkyTbtndLWiBpt6Rlkno7i7Yk9ZY0\nTdJ/JO23bXu5c/xTSUGWZf1H0gBJrznPdUrSm5K+kbRFV/8J4YxzzquSXnLOCXSeAwBcStWqVRUb\nG6s8efKoXbt22rx5s+lIAAA35fD2HQ+uLZVZvXq1SpUqdaunA0CWLFmyRG3btlVgYKC+/vprVapU\nyXQkAEAuO3z4sIKDgyXDS2UAADfRqlUrffLJJ0pJSVGTJk2UnJxsOhIAwM1Q3AEglzzzzDMaO3as\nkpOT1aRJE6WkpJiOBABwIxR3AMhFr7zyil566SXt2bNHzZs316+//mo6EgDATVDcASAXORwOjR8/\nXpGRkdq8ebPCw8N1+fJl07EAAG6A4g4AuczHx0effvqpmjdvroSEBD3zzDNKT0+/9UQAgFejuAOA\nAb6+vlqwYIFq1Kihzz77TC+//LK8fZcvAMDNUdwBwJC77rpLcXFxqlSpkiZNmqTx48ebjgQAcGEU\ndwAwKCgoSAkJCSpVqpReffVVzZw503QkAICLorgDgGGlS5dWQkKCChcurGeffVZxcXGmIwEAXBDF\nHQBcQOXKlRUXFyc/Pz+1b99eGzZsMB0JAOBiKO4A4CJq1qyp6OhoXb58WS1atNCuXbtMRwIAuBCK\nOwC4kObNm2v69Ok6ffq0QkNDlZycbDoSAMBFUNwBwMV06dJF48aN0+HDh9WkSROdOnXKdCQAgAug\nuAOACxo0aJAGDBigPXv2qGXLljp//rzpSAAAwyjuAOCCHA6HJkyYoI4dO2rDhg2KiIhQamqq6VgA\nAIMo7gDgonx8fDRz5kyFhIQoNjZWzz//PJ+uCgBejOIOAC7Mz89PMTExqlatmj799FMNHz7cdCQA\ngCEUdwBwcQUKFNDSpUtVrlw5jR49Wh9++KHpSAAAAyjuAOAGihYtqoSEBBUtWlR9+vTRwoULTUcC\nAOQyijsAuIly5cpp2bJluvvuu/X0009r3bp1piMBAHIRxR0A3Mhjjz2mmJgYpaWlKSwsTDt37jQd\nCQCQSyjuAOBmGjVqpJkzZ+rs2bN8uioAeBGKOwC4oaefflrjx4/XkSNHFBoayqerAoAXoLgDgJsa\nOHCgBgwYoN27d6tVq1a6cOGC6UgAgBxEcQcAN3Xt01U7dOig9evXq1OnTkpLSzMdCwCQQyjuAODG\nfHx8NGvWLDVo0ECLFy9W3759+XRVAPBQFHcAcHP+/v5atGiRqlatqilTpmjMmDGmIwEAcgDFHQA8\nQEBAgJYuXaoyZcpo6NChmjlzpulIAIBsRnEHAA9RsmRJLV++XIGBgXr22We1fPly05EAANmI4g4A\nHqRSpUqKjY2Vr6+vwsPD9e2335qOBADIJhR3APAwtWvX1pw5c3T+/Hk1b95cP/zwg+lIAIBsQHEH\nAA/Upk0bTZ48WSdOnFBoaKh+/vln05EAAHeI4g4AHqp3794aMmSI9u/frxYtWui3334zHQkAcAco\n7gDgwUaPHq0uXbpoy5Yt6tChg1JTU01HAgBkEcUdADyYw+HQtGnT1LhxY8XHx6t37958QBMAuCmK\nOwB4OF9fX33++ed69NFH9cknn2j06NGmIwEAsoDiDgBeoECBAoqPj1fZsmU1fPhwzZgxw3QkAEAm\nUdwBwEuUKFFCy5cvV+HChdWzZ08lJCSYjgQAyASKOwB4kYoVK+qLL76Qr6+v2rVrp23btpmOBAC4\nTRR3APAytWvX1meffabz58+rWbNmOnDggOlIAIDbQHEHAC/Utm1bvf/++zp+/LhCQ0OVkpJiOhIA\n4BYo7gDgpfr27atBgwZp3759CgsL04ULF0xHAgDcBMUdALzY2LFj1bFjR23YsEGRkZFKS0szHQkA\n8Cco7gDgxXx8fDRjxgzVr19fCxcu1Msvv2w6EgDgT1DcAcDL+fv7a9GiRXrwwQf13nvvadKkSaYj\nAQBugOIOAFChQoW0dOlSlSxZUgMHDlR0dLTpSACAP6C4AwAkSWXKlFF8fLzuueceRUZGav369aYj\nAQCuQ3EHAPzukUce0cKFC5WWlqawsDDt3bvXdCQAgBPFHQDwXxo1aqRp06bp9OnTatq0qY4dO2Y6\nEgBAFHcAwA107dpVo0aN0sGDB9WiRQv9+uuvpiMBgNejuAMAbmjYsGHq0aOHtm7dqoiICKWmppqO\nBABejeIOALghh8OhKVOmqEmTJoqPj1efPn2UkZFhOhYAeC2KOwDgT/n6+io6OlqPPPKIPv74Y40b\nN850JADwWhR3AMBNFShQQPHx8SpdurQGDx6sOXPmmI4EAF6J4g4AuKWSJUtq2bJlCggIULdu3bR2\n7VrTkQDA61DcAQC35cEHH9SiRYskSW3atNGuXbsMJwIA70JxBwDctgYNGmjGjBk6e/asmjVrpp9+\n+sl0JADwGhR3AECmPP300xo9erSSkpLY4x0AchHFHQCQaUOGDNGzzz6rbdu2qUOHDuzxDgC5gOIO\nAMg0h8OhDz/8UE2aNNHSpUvVt29f9ngHgBxGcQcAZMm1Pd6rVq2qjz76SOPHjzcdCQA8GsUdAJBl\n1/Z4L1WqlF599VXNmzfPdCQA8FgUdwDAHbnvvvsUHx+vAgUKqGvXrvr6669NRwIAj0RxBwDcsYcf\nflgLFy5Uenq6WrVqJdu2TUcCAI9DcQcAZItGjRpp6tSpOn36tJo1a6YTJ06YjgQAHoXiDgDINt27\nd9frr7+uH3/8UWFhYTp//rzpSADgMSjuAIBs9cYbbygyMlKbN29W586dlZaWZjoSAHgEijsAIFs5\nHA5NmzZN9evX16JFi/TKK6+YjgQAHoHiDgDIdn5+foqJiVHFihU1ceJETZ482XQkAHB7FHcAQI4I\nDAzU0qVLVbRoUfXv31+xsbGmIwGAW6O4AwByzAMPPKC4uDj5+/srIiJCW7duNR0JANwWxR0AkKP+\n9re/ae7cubpw4YKaN2+uQ4cOmY4EAG6J4g4AyHGtWrXSe++9p+PHj6t58+Y6e/as6UgA4HYo7gCA\nXNGvXz/169dPu3btUnh4uK5cuWI6EgC4FYo7ACDXTJw4UWFhYVq1apWef/55ZWRkmI4EAG6D4g4A\nyDV58uTRnDlzVK1aNU2fPl1jxowxHQkA3AbFHQCQq+6++27FxsaqTJkyGjp0qObOnWs6EgC4BYo7\nACDXlShRQkuXLlXBggXVrVs3ff3116YjAYDLo7gDAIx48MEHtXDhQqWnp6t169bat2+f6UgA4NIo\n7gAAY0JCQvTxxx/r1KlTatasmU6ePGk6EgC4LIo7AMCoZ555RkOGDNEPP/yg1q1b6+LFi6YjAYBL\norgDAIx788031aFDByUmJqp79+5KT083HQkAXA7FHQBgnI+Pj2bOnKlatWpp3rx5GjFihOlIAOBy\nKO4AAJeQL18+LV68WOXKldPo0aM1Y8YM05EAwKVQ3AEALuPee+9VfHy8AgMD1atXL61Zs8Z0JABw\nGRR3AIBLsSxLixcvlsPhUNu2bbVnzx7TkQDAJeTN6kTLsp6SNFJSRUl/s217m3P8fkl7JO11PnWj\nbdu9nY9VkzRTUj5JS23b7u8c95cUJekxSSmSOti2fcj5WFdJQ53nGm3bdpRz/AFJ8yQVlrRVUqRt\n21ey+noAAK6jbt26mj59uiIjI9WsWTNt2rRJxYoVMx0LAIy6kyvu/5bURtK6Gzy237btR51fva8b\nnyKph23bFSRVsCwr1DneQ1KKc3ySpHGSZFlWYUnDJT3h/BphWVaAc844SROcc047zwEA8BCdO3fW\nyJEjdfDgQbVq1UoXLlwwHQkAjMpycbdte69t27f9MXeWZZWQVMC27S3OoShJrZ3HYZJmOY8XSgp2\nHjeRtMK27TO2bZ+RtFJSU8uyHJIaSPrc+bxZ150LAOAhhg8frs6dO2vz5s3q2rUr20QC8Go5tcb9\nAcuytluW9aVlWXWcY/dJOnzdc444x649lixJtm2nSjprWVaQpJJ/mHPY+dzCks7Ytp1+g3MBADyE\nw+HQtGnTVLduXUVHR2vo0KG3ngQAHuqma9wty1opqfgNHhpi23bsn0w7Kqm0bdunLct6TNJiy7Ie\nvMOc18vI6kTLskZKYnNgAHAj/v7+iomJUc2aNTV27FhVqFBBzzzzjOlYAHAnDliW9cexN2zbHnmz\nSTct7rZtN8psCtu2L0u67DzeZlnWD5Iq6OpV8VLXPbWU/v9q+hFJZSQdtSwrr6QA27ZTLMs6Iqn+\ndXNKS1oj6ZSkQpZl+TivupdynuNW2Ubq6g21v3PeTHsgUy8SAJCrgoKCFB8frxo1aui5555T2bJl\nFRwcfOuJAOCaHrBt+2BmJ2XXUhnHtQPLsopYlpXHefwXXS3tP9q2/ZOkXyzLqu5cox4paYlz2heS\nujqPwyWtdh6vkNTYsqxClmUFSmokKcG27QxJayU95XxeV0mLs+m1AABcUIUKFbR48WL5+PioXbt2\nbBMJwOtkubhbltXGsqxkSTUkxVuWtcz5UD1JOyzL2i4pWtJzzhtLJam3pGmS/qOrO88sd45/KinI\nsqz/SBog6TVJsm37lKQ3JX0jaYuu/hPCtXO9Kukl55xA5zkAAB7sySef1KeffqqzZ8+qefPmOnHi\nhOlIAJBrHBkZWV4y7hGuLZVZvXq1SpUqdaunAwBcwMiRI/XGG2+oZs2aWr16tfLnz286EgDc0uHD\nh68t8zO6VAYAgFwzYsQIde7cWRs3blT37t3ZJhKAV6C4AwDczrVtIuvUqaP58+drxAg2DAPg+Sju\nAAC35O/vr0WLFqlcuXIaPXq0Zs2adetJAODGKO4AALdVpEgRxcfHKzAwUD179tRXX31lOhIA5BiK\nOwDArVmWpZiYGGVkZKhNmzbat2+f6UgAkCMo7gAAt1e/fn1NnTpVp0+fVvPmzXXy5EnTkQAg21Hc\nAQAeoXv37ho8eLD279+vtm3b6tKlS6YjAUC2orgDADzG6NGj9dRTT+nrr79Wz5495e2fVQLAs1Dc\nAQAew8fHR7NmzVL16tU1e/ZsvfXWW6YjAUC2obgDADxK/vz5tWTJEpUtW1avv/665s+fbzoSAGQL\nijsAwOMUK1ZMcXFxKlCggLp27aqNGzeajgQAd4ziDgDwSA899JAWLFigK1euqFWrVjp48KDpSABw\nRyjuAACPFRoaqn/84x/6+eef1aJFC509e9Z0JADIMoo7AMCjvfDCC+rXr5927dql9u3bKzU11XQk\nAMgSijsAwONNnDhRzZo104oVK9SvXz+2iQTglijuAACPlydPHs2bN09VqlTRlClT9I9//MN0JADI\nNIo7AMArFChQQHFxcSpevLheeuklxcfHm44EAJlCcQcAeI0yZcpoyZIl8vPzU0REhL7//nvTkQDg\ntlHcAQBe5YknnlBUVJR+/fVXtWjRQseOHTMdCQBuC8UdAOB1nnrqKY0ePVrJyclq1aqVLly4YDoS\nANwSxR0A4JWGDBmiLl26aMuWLeratavS09NNRwKAm6K4AwC8ksPh0NSpU1WnTh1FR0drxIgRpiMB\nwE1R3AEAXsvf31+LFi3SX/7yF40ePVqzZ882HQkA/hTFHQDg1YoUKaL4+HgFBATo2Wef1fr1601H\nAoAborgDALxexYoV9fnnnystLU1t2rTRjz/+aDoSAPwPijsAAJJCQkI0efJknTx5Ui1atNDZs2dN\nRwKA/0JxBwDA6fnnn9eAAQO0Z88etW/fXqmpqaYjAcDvKO4AAFzn3XffVfPmzbVixQoNGDDAdBwA\n+B3FHQCA6+TJk0dz585VlSpV9M9//lOTJ082HQkAJFHcAQD4HwUKFFBsbKyKFi2q/v37a/ny5aYj\nAQDFHQCAGylbtqyWLFkiX19ftW/fXrt27TIdCYCXo7gDAPAnatSooZkzZ+rcuXNq0aKFTpw4YToS\nAC9GcQcA4CYiIiI0cuRIHTx4UG3bttWlS5dMRwLgpSjuAADcwvDhwxUREaHExET17NlTGRkZpiMB\n8EIUdwAAbsHhcGj69OmqXr26Zs+erbFjx5qOBMALUdwBALgN+fPn1+LFi1W6dGkNGTJEMTExpiMB\n8DIUdwAAblPx4sUVFxenu+++W507d9bWrVtNRwLgRSjuAABkwsMPP6y5c+fq4sWLCgsL05EjR0xH\nAuAlKO4AAGRSy5Yt9c477+jo0aNq1aqVzp8/bzoSAC9AcQcAIAsGDhyoZ555Rlu3blWXLl2Unp5u\nOhIAD0dxBwAgCxwOh6ZMmaJ69epp4cKFGjFihOlIADwcxR0AgCzy8/PTwoULVa5cOY0ePVqfffaZ\n6UgAPBjFHQCAOxAUFKS4uDgFBASoR48e2rhxo+lIADwUxR0AgDtUsWJFLViwQKmpqWrdurUOHTpk\nOhIAD0RxBwAgGzRu3Fjvv/++Tpw4oZYtW+rcuXOmIwHwMBR3AACyyQsvvKDevXvr3//+tzp16qS0\ntDTTkQB4EIo7AADZ6P3331dISIji4uL02muvmY4DwINQ3AEAyEZ58+ZVdHS0LMvSu+++q+nTp5uO\nBMBDUNwBAMhmhQoVUlxcnAoXLqznn39e69atMx0JgAeguAMAkAPKly+vzz//XBkZGWrbtq1+/PFH\n05EAuDmKOwAAOaRBgwb68MMPlZKSopYtW+qXX34xHQmAG6O4AwCQg3r27KkBAwZo9+7dioiIYKcZ\nAFlGcQcAIIeNHz9eoaGhWrZsmQYNGmQ6DgA3RXEHACCH5c2bV/PmzVOlSpU0adIkffLJJ6YjAXBD\nFHcAAHJBQECAYmNjFRQUpN69e+vLL780HQmAm6G4AwCQS8qVK6eYmBg5HA61a9dO+/fvNx0JgBuh\nuAMAkIvq1q2rKVOm6NSpUwoLC9PZs2dNRwLgJijuAADksh49eujFF1/Unj171KFDB6WmppqOBMAN\nUNwBADBg/Pjxatq0qRISEvTyyy+bjgPADVDcAQAwIE+ePJo7d64qVaqk999/n51mANwSxR0AAEPY\naQZAZlDcAQAwqFy5clq4cKEkqV27dvrhhx8MJwLgqijuAAAYVq9evd93mmnZsiU7zQC4IYo7AAAu\n4Nlnn9WAAQO0Z88eRUREKC0tzXQkAC6G4g4AgIsYP368QkNDtXz5cg0aNMh0HAAuhuIOAICLyJs3\nr+bNm6eKFStq0qRJ+vTTT01HAuBCKO4AALiQazvNFC5cWH//+9/19ddfm44EwEVQ3AEAcDHly5fX\n559/royMDLVt21YHDhwwHQmAC6C4AwDggho0aKAPPvhAJ0+eVFhYmM6dO2c6EgDDKO4AALio559/\nXn369NHOnTv19NNPs9MM4OUo7gAAuLBJkyYpJCREsbGxGjp0qOk4AAyiuAMA4MLy5s2rBQsWqEKF\nCho3bpxmz55tOhIAQyjuAAC4uMDAQMXGxiogIEDPPvusNm3aZDoSAAMo7gAAuAHLsrRgwQKlpqaq\ndevWSk5ONh0JQC6juAMA4CYaN26sSZMm6fjx42rVqpV+++0305EA5CKKOwAAbqRv377q2bOntm/f\nrm7duik9Pd10JAC5hOIOAIAbcTgcmjx5surWravPP/9cb775pulIAHIJxR0AADfj5+enhQsX6v77\n79fIkSMVHR1tOhKAXEBxBwDADRUpUkSxsbG655571LVrV23bts10JAA5jOIOAICbeuihhzRnzhxd\nvHhRYWFh+umnn0xHApCDKO4AALixli1bauzYsTpy5IjatGmjixcvmo4EIIdQ3AEAcHODBg1SZGSk\nNm/erF69eikjI8N0JAA5gOIOAICbczgcmjp1qqpXr67Zs2fr3XffNR0JQA6guAMA4AHy5cunRYsW\n6b777tOrr76quLg405EAZDOKOwAAHqJEiRJasmSJ8uXLp06dOmnXrl2mIwHIRhR3AAA8SLVq1TRj\nxgydO3dOYWFhSklJMR0JQDahuAMA4GE6dOigYcOG6ccff1R4eLiuXLliOhKAbJA3qxMtyxovqYWk\ny5J+kNTdtu2zzscGS3pGUpqkfrZtr3COV5M0U1I+SUtt2+7vHPeXFCXpMUkpkjrYtn3I+VhXSUOd\nP3a0bdtRzvEHJM2TVFjSVkmRtm3zfyYAACS98cYb2rVrlxYtWqT+/fvrww8/NB0JwB26kyvuKyQ9\naNt2VUn7JA2WJMuyKkvqIKmypFBJH1qW5XDOmSKph23bFSRVsCwr1DneQ1KKc3ySpHHOcxWWNFzS\nE86vEZZlBTjnjJM0wTnntPMcAABAko+Pj6KiovTwww9rypQpmjJliulIAO7Q/7V351FWVIfaxp8D\nyKAMggMO4MVxGxI1qFHudbh4iVGJAXoQZFAU1ICKiIKiaEDjiBrAKIgiKJOM3YBZzl5FE41E9IuJ\nw1aJU4NiRFCcGPv7o0vT8SJDQ3f16fP81mJZZ1ftOm+zdsLb1VWnK1zcY4yPxxg3JC9fAFok252A\nB2KMa2OM7wJvA0eHEPYEGsUYFybHTQI6J9sdgfuT7TlA+2T7JOCxGOPKGONK4HHglOQbgROA2clx\n95c7lyRJAho2bMi8efPYdddd6d+/P0899VTakSRtg+11j3tv4KFkey+gpNy+EmDvjYwvScZJ/vsB\nQIxxHfBZCGGXTZyrGbCy3DcO5c8lSZISrVq1oqioiFq1alFYWMjixYvTjiSpgjZ5j3sI4XFgj43s\nujLG+GByzFBgTYxxWiXk25gK/zq4EMJwYNj2iyJJUvV33HHHMWbMGM4991w6duzI888/T+PGjdOO\nJeWyd0II3x+7JsY4fFOTNlncY4wnbmp/COEsoAP/urUFyq5+tyz3ugVlV8qX8K/bacqPfztnH2Bp\nCKEO0CTGuDyEsARoV25OS+B/gU+BnUMItZKr7i2Sc2xS8pcx/HtfQyvgnc3NlSQpm51zzjn87W9/\n4/bbb6dnz54UFxdTu3bttGNJuWrf5JbyrVLhW2WSB0sHA51ijN+U2zUfOD2EUDf55JcDgYUxxo+A\nz0MIRyf3qJ8BzCs3p1eyXQg8mWw/BvwihLBzCKEpcCLwaIyxFHgKOC05rhcwt6JfiyRJueC2227j\n5z//OQ8++CBXXXVV2nEkbaVtucf990BD4PEQwsshhDEAMcbXgJnAa8DDwPlJ0QY4HxgPvAW8HWN8\nJBm/F9glhPAWcDEwJDnXp8Bvgb8ACyn7EcLKZM7lwCXJnKbJOSRJ0g+oU6cOM2bM4IADDuCmm25i\n6tSpaUeStBUypaUVvmW8Rvj2Vpknn3ySFi1abO5wSZKy3htvvMHRRx/N6tWreeaZZzjqqKPSjiTl\nhJKSEtq3bw9VfauMJEnKTgcffDDTp09n7dq15OXlsXTp0rQjSdoCFndJknLQKaecws0338zSpUvJ\ny8vjm2++2fwkSamyuEuSlKMuvfRSzjzzTBYuXMi5555Lrt8+K1V3FndJknJUJpNh3LhxHH300UyZ\nMoVbb7017UiSNsHiLklSDqtfvz7FxcXstddeXH755Tz00EObnyQpFRZ3SZJy3J577sm8efOoV68e\n3bp14/XXX087kqSNsLhLkiSOPPJIJkyYwOeff07Hjh1ZsWJF2pEkfY/FXZIkAdCtWzeuuOIK3n77\nbbp27cq6devSjiSpHIu7JEn6znXXXcevfvUrHn/8cQYPHpx2HEnlWNwlSdJ3atWqxZQpU2jdujWj\nRn4jSqUAACAASURBVI1iwoQJaUeSlLC4S5Kkf9O4cWPmz59P06ZN6du3L88991zakSRhcZckSRux\n//77M2vWLDZs2EB+fj4ffPBB2pGknGdxlyRJG9W+fXtGjhzJsmXL6Ny5M1999VXakaScZnGXJEk/\n6MILL6RPnz689NJL9O7dm9LS0rQjSTnL4i5Jkn5QJpPhzjvv5JhjjmHGjBncdNNNaUeScpbFXZIk\nbVK9evWYM2cOLVu2ZOjQocyfPz/tSFJOsrhLkqTNat68OfPmzaN+/fr06NGDV199Ne1IUs6xuEuS\npC3Spk0b7rvvPr744gs6derEp59+mnYkKadY3CVJ0hbr0qULQ4cOZfHixXTt2pV169alHUnKGRZ3\nSZK0Va699lo6duzIE088waBBg9KOI+UMi7skSdoqtWrVYvLkybRu3ZrRo0czceLEtCNJOcHiLkmS\ntlrjxo2ZP38+TZs2pW/fvjz//PNpR5JqPIu7JEmqkP3335+ZM2eyfv168vLyKCkpSTuSVKNZ3CVJ\nUoX9/Oc/57bbbmPZsmV07tyZr7/+Ou1IUo1lcZckSdvkoosuonfv3ixatIg+ffpQWlqadiSpRrK4\nS5KkbZLJZBgzZgz/+Z//yQMPPMAtt9ySdiSpRrK4S5KkbVavXj2KiorYe++9GTJkCA899FDakaQa\nx+IuSZK2iz322IO5c+dSr149unfvTowx7UhSjWJxlyRJ282RRx7J+PHj+eyzz+jYsSMrV65MO5JU\nY1jcJUnSdtWjRw8GDx7Mm2++Sffu3Vm/fn3akaQaweIuSZK2uxtvvJFTTjmFhx9+mCuvvDLtOFKN\nYHGXJEnbXe3atZk2bRoHHXQQI0aMYNq0aWlHkrKexV2SJFWKnXfemfnz59O4cWP69OnDokWL0o4k\nZTWLuyRJqjQhBB544AFWr15N586d+eijj9KOJGUti7skSapUHTp04MYbb6SkpISCggJWr16ddiQp\nK1ncJUlSpbvsssvo1q0bzz33HBdeeCGlpaVpR5KyjsVdkiRVukwmw/jx4zn88MMZP348Y8aMSTuS\nlHUs7pIkqUrsuOOOFBcXs/vuuzNgwACefvrptCNJWcXiLkmSqsw+++zDnDlzqFWrFoWFhbz77rtp\nR5KyhsVdkiRVqWOPPZY77riD5cuX06lTJ7788su0I0lZweIuSZKq3HnnnUe/fv145ZVXOOuss3xY\nVdoCFndJkpSKUaNGcfzxxzN79mxuuOGGtONI1Z7FXZIkpaJu3brMmjWLffbZh6uuuor58+enHUmq\n1izukiQpNbvvvjtz586lQYMG9OzZk9dffz3tSFK1ZXGXJEmpatOmDRMnTmTVqlV06tSJFStWpB1J\nqpYs7pIkKXVdu3ZlyJAhvPXWW3Tr1o3169enHUmqdizukiSpWrjuuuvo0KEDjz76KFdccUXacaRq\nx+IuSZKqhdq1azNt2jQOOuggbrnlFqZNm5Z2JKlasbhLkqRqo0mTJsybN4/GjRvTp08fFi1alHYk\nqdqwuEuSpGrl4IMPZtq0aaxevZrOnTuzbNmytCNJ1YLFXZIkVTu//OUvuf766ykpKaGwsJA1a9ak\nHUlKncVdkiRVS0OGDKFLly788Y9/ZMCAAWnHkVJncZckSdVSJpNhwoQJHHbYYdx1113cfffdaUeS\nUmVxlyRJ1dZOO+3E3Llz2WWXXbjwwgv505/+lHYkKTUWd0mSVK21atWK2bNns2HDBgoKCvjggw/S\njiSlwuIuSZKqvXbt2jFy5EiWLVtGXl4eX3/9ddqRpCpncZckSVnhwgsv5Oyzz2bRokWcd955lJaW\nph1JqlIWd0mSlBUymQxjx46lbdu2TJkyhZEjR6YdSapSFndJkpQ16tWrR1FREXvuuSeDBw/m8ccf\nTzuSVGUs7pIkKavsueeeFBUVUadOHbp27crixYvTjiRVCYu7JEnKOm3btmXs2LGsWLGCzp0788UX\nX6QdSap0FndJkpSVevfuzYUXXsjf//53evXqxYYNG9KOJFUqi7skScpav/vd72jXrh1FRUXccMMN\naceRKpXFXZIkZa0ddtiBmTNn8h//8R9cffXVPPjgg2lHkiqNxV2SJGW13XbbjeLiYho0aECPHj14\n/fXX044kVQqLuyRJynpt2rTh3nvvZdWqVXTq1ImVK1emHUna7izukiSpRujWrRuXXXYZb731Ft27\nd2f9+vVpR5K2K4u7JEmqMW644QZOOukkHn74Ya6++uq040jblcVdkiTVGLVr1+aBBx5g//3358Yb\nb2TmzJlpR5K2G4u7JEmqUZo2bcq8efNo2LAhZ599Nq+88krakaTtwuIuSZJqnB//+MdMmjSJr776\nis6dO7N8+fK0I0nbzOIuSZJqpLy8PH7zm9/wzjvv0LVrV9atW5d2JGmbWNwlSVKNNWzYMDp27MiT\nTz7JZZddlnYcaZtY3CVJUo1Vq1YtJk+ezMEHH8zIkSOZPHly2pGkCrO4S5KkGq1x48bMmzePJk2a\ncO655/Liiy+mHUmqEIu7JEmq8Q466CCmTZvGmjVryMvLY9myZWlHkraaxV2SJOWEDh06cP3111NS\nUsJpp53G2rVr044kbRWLuyRJyhlDhgyhsLCQZ599loEDB6YdR9oqFndJkpQzMpkMEydO5Cc/+Ql3\n3nknEyZMSDuStMUs7pIkKac0bNiQuXPn0rRpU/r168cLL7yQdiRpi1jcJUlSztl///2ZPn0669at\nIz8/nw8//DDtSNJmWdwlSVJO+sUvfsHNN9/M0qVLKSgoYPXq1WlHkjbJ4i5JknLWpZdeSrdu3Xj+\n+efp379/2nGkTbK4S5KknJXJZBg/fjw//elPueeeexg3blzakaQfZHGXJEk5bccdd6S4uJhddtmF\n/v3786c//SntSNJGWdwlSVLOa9WqFTNnzmTDhg0UFBSwZMmStCNJ/0edik4MIdwCnAqsARYDZ8cY\nPwshtAJeB95IDn0+xnh+MucI4D6gPvBQjHFAMl4PmAQcDiwHusYY30v29QKGJue6LsY4KRnfF5gO\nNAMWAWfEGP0VaJIkqUL+53/+h1tvvZWBAweSn5/PggULqF+/ftqxpO9syxX3x4AfxxgPA94Erii3\n7+0YY5vkz/nlxscCfWKMBwIHhhBOTsb7AMuT8ZHAzQAhhGbAb4Cjkj/DQghNkjk3A7clc1Yk55Ak\nSaqwAQMGcMYZZ7Bw4UIuuOACSktL044kfafCxT3G+HiMcUPy8gWgxaaODyHsCTSKMS5MhiYBnZPt\njsD9yfYcoH2yfRLwWIxxZYxxJfA4cEoIIQOcAMxOjru/3LkkSZIqJJPJMG7cOI444ggmTJjAmDFj\n0o4kfWd73ePeG3io3Ot9QwgvhxCeDiEcm4ztDZSUO2ZJMvbtvg8AYozrgM9CCLsAe31vTklybDNg\nZblvHMqfS5IkqcIaNGhAcXExu+22GxdffDHPPPNM2pEkYDP3uIcQHgf22MiuK2OMDybHDAXWxBin\nJfuWAi1jjCtCCIcDc0MIP96OmSv8M6sQwnBg2PaLIkmSaqKWLVsye/Zs2rdvT2FhIS+++CL77LNP\n2rFUc7wTQvj+2DUxxuGbmrTJ4h5jPHFT+0MIZwEd+NetLcQY11D2wCoxxpdCCIuBAym7Kl7+dpoW\n/Otq+hJgH2BpCKEO0CTGuDyEsARoV25OS+B/gU+BnUMItZKr7i2Sc2xS8pcx/HtfQyvgnc3NlSRJ\nueX4449n5MiR9O/fn/z8fJ599lkaNGiQdizVDPvGGN/d2kkVvlUmebB0MNApxvhNufFdQwi1k+39\nKCvt/4gxfgh8HkI4OrlH/QxgXjJtPtAr2S4Enky2HwN+EULYOYTQFDgReDTGWAo8BZyWHNcLmFvR\nr0WSJGljLrjgAs466ywWLVpE3759fVhVqdqWe9x/DzQEHk/uZ//26Y3/Bv4aQngZmAX8OnmwFOB8\nYDzwFmWfPPNIMn4vsEsI4S3gYmAIQIzxU+C3wF+AhZT9COHbc10OXJLMaZqcQ5IkabvJZDKMHTuW\nn/3sZ0yaNInf//73aUdSDsvk+neO394q8+STT9KixSY/GEeSJOWokpISjjjiCJYvX84TTzxBu3bt\n0o6kLFRSUkL79u2hqm+VkSRJyhUtWrRg9uzZZDIZTjvtNN5///20IykHWdwlSZK2wHHHHcfo0aP5\n5JNPyMvL4+uvv047knKMxV2SJGkL9evXj969e/PSSy/x61//2odVVaUs7pIkSVsok8lw5513ctRR\nRzF58mRGjx6ddiTlEIu7JEnSVqhfvz5FRUU0b96cQYMG8dRTT6UdSTnC4i5JkrSV9t577+8eVu3S\npQvvvfde2pGUAyzukiRJFXDsscdy++2388knn5Cfn+/Dqqp0FndJkqQK6tu3L3369OGll17ivPPO\n82FVVSqLuyRJUgV9+7Dq0UcfzZQpU7j99tvTjqQazOIuSZK0DerVq8ecOXPYY489uPTSS31YVZXG\n4i5JkrSNfFhVVcHiLkmStB0cc8wxPqyqSmVxlyRJ2k58WFWVyeIuSZK0nfiwqiqTxV2SJGk7+vZh\n1ebNm3PppZfy9NNPpx1JNYTFXZIkaTsr/7Dqaaedxvvvv592JNUAFndJkqRKcOyxxzJ69GgfVtV2\nY3GXJEmqJP369aN3794sWrSIvn37+rCqtonFXZIkqZJ8+7Dqz372MyZNmsTvf//7tCMpi1ncJUmS\nKlH9+vUpKipi991355JLLmHBggVpR1KWsrhLkiRVshYtWjBr1qzvHlb94IMP0o6kLGRxlyRJqgLH\nH388I0eO5J///Cf5+fl88803aUdSlrG4S5IkVZELLriAXr168eKLL9KvXz8fVtVWsbhLkiRVkUwm\nw9ixYzniiCO47777GDt2bNqRlEUs7pIkSVWoQYMGFBcXs9tuuzFgwAD++Mc/ph1JWcLiLkmSVMVa\ntmzJzJkzKS0tpbCwkCVLlqQdSVnA4i5JkpSCdu3acdttt7Fs2TIKCgpYvXp12pFUzVncJUmSUnLR\nRRfRs2dPXnjhBfr37592HFVzFndJkqSUZDIZxo0bR5s2bbjnnnsYN25c2pFUjVncJUmSUrTjjjtS\nVFTELrvsQv/+/Xn++efTjqRqyuIuSZKUslatWjFjxgzWr19PQUEBH374YdqRVA1Z3CVJkqqB9u3b\nM2LECD788EMKCwtZs2ZN2pFUzVjcJUmSqolLLrmE008/neeee46LL7447TiqZizukiRJ1UQmk2H8\n+PEccsghjB07lgkTJqQdSdWIxV2SJKka2WmnnSguLqZp06b069ePhQsXph1J1YTFXZIkqZrZf//9\nmTZtGmvXrqWgoICPP/447UiqBizukiRJ1dDJJ5/M9ddfT0lJCV26dGHt2rVpR1LKLO6SJEnV1JAh\nQygoKGDBggUMGjQo7ThKmcVdkiSpmspkMkycOJHWrVtz++23M2XKlLQjKUUWd0mSpGqsUaNGFBcX\n07hxY84991xefvnltCMpJRZ3SZKkau6ggw5i6tSpfPPNN+Tl5fHJJ5+kHUkpsLhLkiRlgVNPPZXh\nw4fz3nvv0a1bN9atW5d2JFUxi7skSVKWuPrqq/nVr37FE088wdChQ9OOoypmcZckScoStWrVYvLk\nyRx00EGMGDGCmTNnph1JVcjiLkmSlEWaNGlCcXExDRs25Oyzz+Zvf/tb2pFURSzukiRJWaZ169bc\nf//9fPXVV+Tl5bFixYq0I6kKWNwlSZKyUH5+PldeeSWLFy+mZ8+ebNiwIe1IqmQWd0mSpCx17bXX\nctJJJ/HQQw8xfPjwtOOoklncJUmSslTt2rWZNm0a++23H7/97W+ZN29e2pFUiSzukiRJWaxZs2YU\nFRXRoEEDzjjjDN544420I6mSWNwlSZKy3GGHHca9997LqlWryMvL4/PPP087kiqBxV2SJKkG6Nat\nGwMHDuSNN97grLPO8mHVGsjiLkmSVEOMGDGCdu3aUVxczE033ZR2HG1nFndJkqQaok6dOsyYMYMW\nLVpw1VVX8cgjj6QdSduRxV2SJKkG2X333SkqKqJu3bp069aNxYsXpx1J24nFXZIkqYb52c9+xpgx\nY1i5ciX5+fl8+eWXaUfSdmBxlyRJqoF69+5N3759eeWVVzjvvPMoLS1NO5K2kcVdkiSphho9ejRt\n27Zl2rRpjB49Ou042kYWd0mSpBqqbt26zJkzh+bNmzNo0CCefvrptCNpG1jcJUmSarC99tqL2bNn\nk8lk6NKlCyUlJWlHUgVZ3CVJkmq4Y489lpEjR/LPf/6TgoICVq9enXYkVYDFXZIkKQdccMEFnHnm\nmSxcuJALL7ww7TiqAIu7JElSDshkMtx11120adOG8ePHc/fdd6cdSVvJ4i5JkpQjGjRoQFFREbvs\nsgv9+/fnhRdeSDuStoLFXZIkKYe0atWKBx54gHXr1lFQUMCyZcvSjqQtZHGXJEnKMSeeeCI33HAD\nS5YsoWvXrqxduzbtSNoCFndJkqQcdNlll1FQUMCCBQu47LLL0o6jLWBxlyRJykGZTIaJEyfSunVr\nRo0axbRp09KOpM2wuEuSJOWoRo0aUVRUROPGjTnnnHP461//mnYkbYLFXZIkKYeFEJg8eTJff/01\neXl5fPrpp2lH0g+wuEuSJOW4jh07cvXVV/POO+/Qo0cP1q9fn3YkbYTFXZIkSQwbNoxTTjmFRx55\nhOHDh6cdRxthcZckSRK1a9dm6tSp7Lffflx33XXMmzcv7Uj6Hou7JEmSAGjatCnFxcU0aNCAM844\ngxhj2pFUjsVdkiRJ3zn00EMZP348q1atIj8/n1WrVqUdSQmLuyRJkv5N9+7dufjii3nttdfo3bs3\npaWlaUcSFndJkiRtxIgRIzj++OOZPXs2t9xyS9pxhMVdkiRJG7HDDjswc+ZM9tprL6644gqeeOKJ\ntCPlPIu7JEmSNqp58+bMmTOH2rVrc/rpp/Pee++lHSmnWdwlSZL0g9q2bcsdd9zB8uXLyc/P5+uv\nv047Us6yuEuSJGmTzj33XPr06cNLL73E+eef78OqKbG4S5IkaZMymQx33HEHRx55JPfddx/jxo1L\nO1JOsrhLkiRps+rXr8+cOXPYddddueiii3j++efTjpRzLO6SJEnaIvvssw/Tp09n/fr1FBYW8tFH\nH6UdKadY3CVJkrTF2rdvz0033cTSpUvp0qULa9euTTtSzrC4S5IkaasMGjSIwsJCnn32WS677LK0\n4+QMi7skSZK2SiaTYcKECbRu3ZpRo0Yxbdq0tCPlhDoVnRhC+C3QESgFlgNnxRg/SPZdAfQG1gMX\nxRgfS8aPAO4D6gMPxRgHJOP1gEnA4cm5usYY30v29QKGJm97XYxxUjK+LzAdaAYsAs6IMfqzGkmS\npCrQqFEjioqKOOqoozjnnHP4yU9+wqGHHpp2rBptW664j4gxHhZj/CkwFxgGEEJoDXQFWgMnA2NC\nCJlkzligT4zxQODAEMLJyXgfYHkyPhK4OTlXM+A3wFHJn2EhhCbJnJuB25I5K5JzSJIkqYqEEJg0\naRJff/01eXl5rFixIu1INVqFi3uMcVW5lw2BT5LtTsADMca1McZ3gbeBo0MIewKNYowLk+MmAZ2T\n7Y7A/cn2HKB9sn0S8FiMcWWMcSXwOHBK8o3ACcDs5Lj7y51LkiRJVaRTp04MHTqUf/zjH/Ts2ZMN\nGzakHanG2qZ73EMI14cQ3gfOAm5MhvcCSsodVgLsvZHxJck4yX8/AIgxrgM+CyHssolzNQNWxhg3\nbORckiRJqkLXXHMNJ510Eg899BDXXntt2nFqrE3e4x5CeBzYYyO7rowxPhhjHAoMDSEMAUYBZ1dC\nxu+r8O/YDSEMJ7mlR5IkSdtH7dq1mTZtGkcccQTXXHMNRx55JKeeemrasaqzd0II3x+7JsY4fFOT\nNlncY4wnbuGbTwMeSraXAC3L7WtB2ZXyJcn298e/nbMPsDSEUAdoEmNcHkJYArQrN6cl8L/Ap8DO\nIYRayVX3Fsk5Nin5yxhefiyE0Ap4Z3NzJUmS9MOaNWtGUVER//Vf/0XPnj158cUXOeCAA9KOVV3t\nm9xSvlUqfKtMCOHAci87AS8n2/OB00MIdZNPfjkQWBhj/Aj4PIRwdHKP+hnAvHJzeiXbhcCTyfZj\nwC9CCDuHEJoCJwKPxhhLgaeA05LjelH2gKwkSZJS0qZNG8aNG8dnn31GXl4eX375ZdqRapRtucf9\nxhDC30II/4+yq+KXAsQYXwNmAq8BDwPnJ0Ub4HxgPPAW8HaM8ZFk/F5glxDCW8DFwJDkXJ8CvwX+\nAiyk7EcIK5M5lwOXJHOaJueQJElSis4880wuuOAC/v73v3PuuedSWlrhu5z1PZlc/8v89laZJ598\nkhYtWmzucEmSJG3GmjVrOOGEE3juuecYOXIkF198cdqRqoWSkhLat28PVX2rjCRJkrQxdevWZdas\nWTRv3pxBgwaxYMGCtCPVCBZ3SZIkbXd77bUXs2bNIpPJ0KVLF5Ys2ezniGgzLO6SJEmqFMcddxy3\n3XYbH3/8MYWFhaxZsybtSFnN4i5JkqRK079/f7p3786f//xnBg4cmHacrGZxlyRJUqXJZDLcfffd\nHHLIIYwZM4b7778/7UhZy+IuSZKkSrXTTjtRVFREkyZN6Nu3Ly+//PLmJ+n/sLhLkiSp0h1wwAFM\nnTqVb775hvz8fJYvX552pKxjcZckSVKV+OUvf8mwYcN499136d69O+vXr087UlaxuEuSJKnK/OY3\nv6FDhw489thjDBs2LO04WcXiLkmSpCpTq1YtpkyZwn777cf111/PvHnz0o6UNSzukiRJqlJNmzal\nuLiYBg0acOaZZ/Lmm2+mHSkrWNwlSZJU5Q499FDuuecePv/8c/Lz8/niiy/SjlTtWdwlSZKUih49\netC/f39effVVzjnnHEpLS9OOVK1Z3CVJkpSaW2+9lWOOOYYZM2YwatSotONUaxZ3SZIkpaZu3brM\nmjWLPfbYg8GDB7NgwYK0I1VbFndJkiSlas8992TWrFlkMhm6dOnCkiVL0o5ULVncJUmSlLpjjz2W\n2267jY8//pjCwkLWrFmTdqRqx+IuSZKkaqF///50796dP//5zwwcODDtONWOxV2SJEnVQiaT4e67\n7+aQQw5hzJgxTJo0Ke1I1YrFXZIkSdXGTjvtRFFREU2aNOHXv/41L7/8ctqRqg2LuyRJkqqVAw44\ngClTpvDNN99QUFDAp59+mnakasHiLkmSpGrn1FNP5eqrr+add96hZ8+ebNiwIe1IqbO4S5IkqVoa\nNmwYJ598Mg8//DDXXHNN2nFSZ3GXJElStVS7dm2mTp1Kq1atuPbaa/nDH/6QdqRUWdwlSZJUbTVr\n1oyioiLq169Pz549efvtt9OOlBqLuyRJkqq1Nm3acNddd/HZZ59RUFDAV199lXakVFjcJUmSVO31\n6tWLfv368corr3DeeedRWlqadqQqZ3GXJElSVhg5ciRt27Zl6tSp3HnnnWnHqXIWd0mSJGWFevXq\nMWvWLHbbbTcGDhzIc889l3akKmVxlyRJUtZo0aIFM2bMYMOGDRQWFvLRRx+lHanKWNwlSZKUVU44\n4QRuvvlmPvzwQ7p27cratWvTjlQlLO6SJEnKOpdeeimFhYU888wzXH755WnHqRIWd0mSJGWdTCbD\nhAkTOPjggxk5ciQzZsxIO1Kls7hLkiQpKzVq1Iji4mIaNmxInz59ePXVV9OOVKks7pIkScpaBx98\nMPfddx9ffvkleXl5fPbZZ2lHqjQWd0mSJGW1goICBg8ezFtvvcVZZ51VY385k8VdkiRJWe+GG27g\nhBNOYO7cuYwYMSLtOJXC4i5JkqSsV6dOHaZPn87ee+/NlVdeyZNPPpl2pO3O4i5JkqQaYffdd2f2\n7NnUrl2b008/nffffz/tSNuVxV2SJEk1Rtu2bRk9ejSffPIJhYWFrF69Ou1I243FXZIkSTVK3759\nOfPMM/nLX/7CgAED0o6z3VjcJUmSVKNkMhnuuusufvrTnzJu3DgmTpyYdqTtwuIuSZKkGqdBgwbM\nmTOHnXfemX79+vHSSy+lHWmbWdwlSZJUI+23335MnTqVNWvWUFBQwPLly9OOtE0s7pIkSaqxOnTo\nwLBhw3j33Xfp0aMH69evTztShVncJUmSVKNdffXVdOjQgUcffZRrr7027TgVZnGXJElSjVarVi0m\nT57Mvvvuy7XXXssf/vCHtCNViMVdkiRJNV6zZs2YM2cO9evX54wzzmDx4sVpR9pqFndJkiTlhDZt\n2nDXXXexcuVKCgoK+Oqrr9KOtFUs7pIkScoZvXr1om/fvvz1r3+lb9++lJaWph1pi1ncJUmSlFNG\njRrFUUcdxeTJk7nrrrvSjrPFLO6SJEnKKfXq1WP27NnsuuuuDBgwgOeffz7tSFvE4i5JkqSc07Jl\nS6ZPn8769es57bTT+Pjjj9OOtFkWd0mSJOWk9u3bc/3117NkyRJOP/101q1bl3akTbK4S5IkKWdd\nfvnldO7cmaeeeoqhQ4emHWeTLO6SJEnKWZlMhvvuu48DDzyQESNGUFRUlHakH2RxlyRJUk5r0qQJ\nRUVF7Ljjjpx11lnEGNOOtFEWd0mSJOW8n/zkJ4wfP55Vq1aRn5/PF198kXak/8PiLkmSJAHdunXj\noosu4rXXXuOcc86pdr+cyeIuSZIkJW655RaOOeYYZsyYwe233552nH9jcZckSZISdevWZebMmTRv\n3pxBgwbx7LPPph3pOxZ3SZIkqZy99tqLmTNnUlpaSpcuXfjwww/TjgRY3CVJkqT/4/jjj2fEiBF8\n9NFHdO3albVr16YdyeIuSZIkbczAgQMpLCzk2Wef5fLLL087jsVdkiRJ2phMJsOECRM4+OCDGTly\nJDNnzkw1j8VdkiRJ+gGNGjWiqKiIhg0b0rt3b15//fXUsljcJUmSpE340Y9+xIQJE/jyyy/JY6Im\n6gAACLdJREFUz89n1apVqeSwuEuSJEmbcdppp3HJJZfwxhtv0Lt371R+OZPFXZIkSdoCN910E8cf\nfzyzZ8/md7/7XZW/v8VdkiRJ2gI77LADM2bMYM899+Tyyy9nwYIFVfr+FndJkiRpC+2xxx7MmjWL\nTCZD165dWbp0aZW9t8VdkiRJ2grHHHMMt956K8uWLaNLly5V9suZLO6SJEnSVrrooovo2rUrf/rT\nnxg8eHCVvKfFXZIkSdpKmUyG8ePH07p1a0aPHs306dMr/T0t7pIkSVIFNGzYkKKiIho1akSfPn14\n9dVXK/X9LO6SJElSBYUQmDhxIl999RX5+fl8/vnnlfZeFndJkiRpGxQUFDBo0CDefPNNzj777Er7\n5UwWd0mSJGkb3XjjjbRr146ioiLuvPPOSnkPi7skSZK0jerUqcP06dM58MAD+cc//lE571EpZ5Uk\nSZJyTPPmzXnjjTeoVatyro17xV2SJEnaTiqrtIPFXZIkScoKFndJkiQpC1jcJUmSpCxgcZckSZKy\ngMVdkiRJygIWd0mSJCkLVPhz3EMIvwU6AqXAcuCsGOMHIYRWwOvAG8mhz8cYz0/mHAHcB9QHHoox\nDkjG6wGTgMOTc3WNMb6X7OsFDE3OdV2McVIyvi8wHWgGLALOiDGurejXI0mSJFVn23LFfUSM8bAY\n40+BucCwcvvejjG2Sf6cX258LNAnxnggcGAI4eRkvA+wPBkfCdwMEEJoBvwGOCr5MyyE0CSZczNw\nWzJnRXIOSZIkqUaqcHGPMa4q97Ih8Mmmjg8h7Ak0ijEuTIYmAZ2T7Y7A/cn2HKB9sn0S8FiMcWWM\ncSXwOHBKCCEDnADMTo67v9y5JEmSpBqnwrfKAIQQrgfOAL4C2pbbtW8I4WXgM+CqGOMfgb2BknLH\nLEnGSP77AUCMcV0I4bMQwi7AXt+bU5Ic2wxYGWPcsJFzba3aAB999FEFp0uSJEmbV65v1q7I/E0W\n9xDC48AeG9l1ZYzxwRjjUGBoCGEIZbe4nA0sBVrGGFeEEA4H5oYQflyRcD+gtKITQwjD+fdber7T\no0ePip5WkiRJ2hpvhxC+P3ZNjHH4piZtsrjHGE/cwjefBjyUzFkDrEm2XwohLAYOpOyqeItyc1rw\nr6vpS4B9gKUhhDpAkxjj8hDCEqBduTktgf8FPgV2DiHUSq66t0jOsUnJX8bw8mPJg7HfAAcA67fw\n61VueAfYN+0QqnZcF9oY14U2xnWh76sNvA3UjzGu3trJ2/KpMgfGGN9KXnYCXk7GdwVWxBjXhxD2\no6y0/yPGuDKE8HkI4WhgIWW32NyezJ8P9AL+DBQCTybjjwE3hBB2BjLAicDlMcbSEMJTwGnAjGTu\n3Ip8HTHG1SEEYoyLKzJfNVeyLt5NO4eqF9eFNsZ1oY1xXWhjknWx1aUdtu0e9xtD2TX+9cBioF8y\nfjxwbQhhLbAB+HXyYCnA+ZR9HGQDyj4O8pFk/F5gcgjhLco+DvJ0gBjjp8nHTv4lOe6acue6HJge\nQrgOeCk5hyRJklQjZUpLK3zLeI0RQiiNMWbSzqHqxXWhjXFdaGNcF9oY14U2ZlvWhb85VZIkScoC\nFvcy16QdQNWS60Ib47rQxrgutDGuC21MhdeFt8pIkiRJWcAr7pIkSVIWsLhLkiRJWcDiLkmSJGUB\ni7skSZKUBSzukiRJUhawuEuSJElZoE7aAdIUQjgZGAXUBsbHGG9OOZJSEEJoCUwCdgdKgbtjjLeH\nEJoBM4D/AN4FusQYV6YWVKkIIdQGXgRKYoy/cl0ohLAzMB74MWX/n3E28Baui5wWQrgC6AlsAP5G\n2brYCddFTgkhTAB+CXwcYzwkGfvBfzeSddMbWA9cFGN8bFPnz9kr7sk/xncAJwOtgW4hhB+lm0op\nWQsMjDH+GGgLXJCshSHA4zHGg4Ank9fKPQOA1ygraOC6EIwGHoox/gg4FHgD10VOCyG0As4FDk/K\nWm3gdFwXuWgiZd2yvI2ugxBCa6ArZT30ZGBMCGGT3TxniztwFPB2jPHdGONaYDrQKeVMSkGM8aMY\n4/9Ltr8AXgf2BjoC9yeH3Q90Tieh0hJCaAF0oOzqaiYZdl3ksBBCE+C4GOMEgBjjuhjjZ7guct3n\nlF0E2jGEUAfYEViK6yLnxBifBVZ8b/iH1kEn4IEY49oY47vA25T10x+Uy8V9b+CDcq9LkjHlsOSq\nSRvgBaB5jHFZsmsZ0DytXErNSGAwZT/6/pbrIrftC/wzhDAxhPBSCOGeEMJOuC5yWozxU+A24H3K\nCvvKGOPjuC5U5ofWwV6U9c9vbbaL5nJxL938IcolIYSGwBxgQIxxVfl9McZSXDM5JYRwKmX3KL7M\nv662/xvXRU6qAxwOjIkxHg58yfduf3Bd5J4Qwv7AxUAryspYwxBCz/LHuC4EW7QONrlGcrm4LwFa\nlnvdkn//rkc5JISwA2WlfXKMcW4yvCyEsEeyf0/g47TyKRX/BXQMIbwDPAD8TwhhMq6LXFdC2YPK\nf0lez6asyH/kushpRwLPxRiXxxjXAUXAf+K6UJkf+nfj+120RTL2g3K5uL8IHBhCaBVCqEvZwwHz\nU86kFIQQMsC9wGsxxlHlds0HeiXbvYC535+rmivGeGWMsWWMcV/KHjL73xjjGbguclqM8SPggxDC\nQcnQz4FXgQdxXeSyN4C2IYQGyb8pP6fsoXbXheCH/92YD5weQqgbQtgXOBBYuKkTZUpLc/enNiGE\nU/jXx0HeG2O8MeVISkEI4VjgGeAV/vUjqiso+x/PTGAf/BivnBZC+G/g0hhjx+RjvVwXOSyEcBhl\nDyzXBRZT9rF/tXFd5LQQwmWUlbINwEvAOUAjXBc5JYTwAPDfwK6U3c/+G2AeP7AOQghXUvZxkOso\nu1X30U2dP6eLuyRJkpQtcvlWGUmSJClrWNwlSZKkLGBxlyRJkrKAxV2SJEnKAhZ3SZIkKQtY3CVJ\nkqQsYHGXJEmSssD/B88U3rJ/rKW8AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc643e10>"
       ]
      }
     ],
     "prompt_number": 617
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As more data points are included, the values close to that from which the data was drawn (here, a rate parameter of 5).\n",
      "\n",
      "Usually, our models are more complex than a simple distribution with one or two parameters. Say you have a spectrum and want to fit a spectral model. You have pretty good data, so you can approximate it with a Gaussian distribution. \n",
      "scipy already gives you the tools you need to do this. scipy.optimize allows you to find the minimum of a given function.\n",
      "For weighted least squares, scipy.optimize.curve_fit will do the trick:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## define a straight line function:\n",
      "def straight(x, a, b):\n",
      "    return x*a + b\n",
      "\n",
      "## x-coordinate\n",
      "x = np.linspace(0, 10, 1000)\n",
      "\n",
      "## some data\n",
      "a = -2\n",
      "b = 3\n",
      "y = straight(x, a, b)\n",
      "\n",
      "## add some random Gaussian noise:\n",
      "data = np.random.normal(0, 2, size=len(x))+y\n",
      "\n",
      "## fit straight line to data:\n",
      "popt, pcov = scipy.optimize.curve_fit(straight, x, data)\n",
      "\n",
      "print(\"Fit straight line data with a=-2, b=3\")\n",
      "print(\"Fitted parameter a is %.3f\"%popt[0])\n",
      "print(\"Fitted parameter b is %.3f\"%popt[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fit straight line data with a=-2, b=3\n",
        "Fitted parameter a is -1.993\n",
        "Fitted parameter b is 2.924\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "curve_fit also gives you the covariance matrix, which is really handy, because it allows you to estimate the errors on the parameters you've just derived, by taking the square root of the diagonal of the covariance matrix. Taking the square root will give you the estimated standard deviation on the parameter. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "errors = np.sqrt(np.diag(pcov))\n",
      "print(\"Fitted parameter a with error is %.3f +/- %.3f\"%(popt[0], errors[0]))\n",
      "print(\"Fitted parameter b with error is %.3f +/- %.3f\"%(popt[1], errors[1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Fitted parameter a with error is -1.993 +/- 0.023\n",
        "Fitted parameter b with error is 2.924 +/- 0.130\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, it is also possible to use likelihood functions other than Gaussian ones. In this case, define the log-likelihood explicitly and use one of scipy.optimize's many minimisation routines. Be sure to minimise the *negative* log-likelihood!\n",
      "\n",
      "Recall the Poisson likelihood from earlier. Instead of plotting the log-likelihood and finding the maximum on the plot, we can estimate it by minimising the negative log-likelihood:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sample = np.random.poisson(5, size=10000)\n",
      "\n",
      "## define the -log-likelihood\n",
      "neg_poisson = lambda r: -poisson_loglike(r, sample)\n",
      "\n",
      "## minimise using Powell's algorithm, starting value for rate parameter is 10\n",
      "result = scipy.optimize.fmin_powell(neg_poisson, 10, full_output=True)\n",
      "\n",
      "print(\"The fit-parameter for the Poisson rate parameter: %.3f \"%result[0])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 22094.062420\n",
        "         Iterations: 2\n",
        "         Function evaluations: 24\n",
        "The fit-parameter for the Poisson rate parameter: 4.996 \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:5: RuntimeWarning: invalid value encountered in log\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are quite a large range of optimisation routines available in scipy.optimize. All of them have certain strengths and weaknesses. I invite you to have a look in the documentation, and to play around with some of the algorithms to see which works for a given problem. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Significance Tests"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Pearson's Chi-Square Test"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Sigmas"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Hypothesis Tests"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Errors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model Selection "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Monte Carlo Simulations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Literature"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below some literature suggestions. This list is by no means exhaustive; we welcome additional suggestions!\n",
      "Books are marked by **(b)**, papers are marked by a **(p)**\n",
      "\n",
      "Statistics:\n",
      "- Simon Vaughan: Scientific Inference, Cambridge University Press (Sept, 2013) **(b)**\n",
      "- \u017deljko Ivezi\u0107, Andrew J. Connolly, Jacob T. VanderPlas & Alexander Gray: \n",
      "  Statistics, Data Mining and Machine Learning in Astronomy, Princeton University Press (2014) **(b)** \n",
      "- David Hogg (arxiv, 2012): Data analysis recipes: Probability calculus for inference [eprint](http://arxiv.org/abs/1205.4446) **(p)**\n",
      "- Protassov+ (ApJ, 2002): Statistics, Handle with Care: Detecting Multiple Model Components\n",
      "  with the Likelihood Ratio Test [eprint](http://arxiv.org/abs/astro-ph/0201547)  **(p)**\n",
      "- Roberto Trotta (2008): Bayes in the sky: Bayesian inference and model selection in cosmology [eprint](http://arxiv.org/abs/0803.4089)  **(p)**\n",
      "- Andrew Liddle (2007): Information criteria for astrophysical model selection [eprint](http://arxiv.org/abs/astro-ph/0701113)  **(p)**\n",
      "    \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}