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likelihood_atm.py
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likelihood_atm.py
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import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import pandas as pd
class FullLikelihood(object):
def __init__(self, like_type):
self.like = like_type
self.corr = []
def ln_like(self):
return self.like.ln_like(self.corr)
# Mass/abundance priors
class BrogiLikelihood(object):
def ln_like(self,corr):
like = np.zeros(len(corr["data"]))
for i in range(len(corr["data"])):
N = len(corr["data"][i])
sf = np.sqrt(np.var(corr["data"][i]))
sg = np.sqrt(np.var(corr["model"][i]))
corrcoeff = np.corrcoef(corr["data"][i],corr["model"][i])[0,1]
like[i]= -N/2.*((np.log(sf*sg)+np.log(sf/sg+sg/sf-2.0*corrcoeff))+1)
return np.sum(like)
class GibsonLikelihood(object):
def ln_like(self,corr):
like = np.zeros(len(corr["data"]))
for i in range(len(corr["data"])):
N = len(corr["data"][i])
like[i]= -N/2.*np.sum((corr["data"][i]-corr["model"][i])**2/corr["std"][i]**2)
return np.sum(like)
class GaussianMassAbundanceLikelihood(object):
def ln_like(self, rdict):
return -0.5 * (rdict["mass"] ** 2 + rdict["abundance"] ** 2)
class StudentMassAbundanceLikelihood(object):
def __init__(self, nu):
assert nu > 2.0
self.nu = nu
def ln_like(self, rdict):
return np.sum(stats.t.logpdf([rdict["mass"], rdict["abundance"]], df=self.nu))
# J priors
class CorrelatedMomentsLikelihoodBase(object):
def __init__(self, corr_matrix, Jmax):
self.Jmax = Jmax
J_keep = ["J_{}".format(i) for i in range(Jmax + 1)]
self.J_list = [j for j in corr_matrix.index if j in J_keep]
self.corr_matrix = corr_matrix
assert np.all(np.diag(corr_matrix) == 1.0) and np.all(
np.abs(corr_matrix) <= 1.0
)
assert np.all(corr_matrix.T == corr_matrix)
assert not np.any(corr_matrix.isna())
self.C = self.corr_matrix.loc[self.J_list, self.J_list].values
self.inv_C = np.linalg.inv(self.C)
self.p = self.C.shape[0]
def resid_dict_to_J_vector(self, rdict):
return np.array([rdict[j] for j in self.J_list])
def resid_corr_norm2(self, rdict):
rvec = self.resid_dict_to_J_vector(rdict)
return (rvec).dot(self.inv_C).dot(rvec)
class MultigaussianMomentsLikelihood(CorrelatedMomentsLikelihoodBase):
def __init__(self, corr_matrix, Jmax):
super().__init__(corr_matrix, Jmax)
def ln_like(self, rdict):
return -0.5 * self.resid_corr_norm2(rdict)
class MultistudentMomentsLikelihood(CorrelatedMomentsLikelihoodBase):
def __init__(self, corr_matrix, Jmax, nu):
super().__init__(corr_matrix, Jmax)
self.nu = nu
def ln_like(self, rdict):
return (
-(self.nu + self.p)
/ 2.0
* np.log(1.0 + 1.0 / (self.nu - 2.0) * self.resid_corr_norm2(rdict))
)
# Correlation matrix functions
def make_corr_matrix_identity(Jmax=12, even_only=True):
J_orders = range(2, Jmax + 1, (2 if even_only else 1))
values = np.eye(len(J_orders))
labels = ["J_{}".format(j) for j in J_orders]
return pd.DataFrame(values, index=labels, columns=labels)
def make_corr_matrix_from_csv(fname):
corrmat_unnorm = pd.read_csv(fname).set_index("Unnamed: 0")
# Symmetrize any missing values
corrmat_unnorm[corrmat_unnorm.isna()] = corrmat_unnorm.T
# Check diagonal is a constant
diag = np.diag(corrmat_unnorm.values)
assert np.all(diag == diag[0])
# Normalize to diago
return corrmat_unnorm / diag[0]