Grid Guess

[PaulWAyers]

When generating a grid for the grid-based selection, we need to construct an appropriate guess for the number of bins.

If we assume that the data is uniformly distributed (multi-dimensional-Poisson process), and there are N data points in the volume of the data, Vol, then the density of points is density = N/Vol. If we divide into n_bins bins of equal size, then the volume of a bin is v_bin = Vol/n_bins. The probability that a bin is empty is, assuming a Poisson process, p(empty) = exp(-1*N/n_bins).

Choosing n_bins < N/3 would correspond to roughly 5% of bins being empty.
Choosing n_bins < N/5 would correspond to roughtly 1% (~0.6%) of bins being empty.
Choosing n_bins < N/6 would correspond to roughly 1e-4% (ppm) of bins being empty.

I'm not sure what the default should be. One could ask the user to specify the probability of an empty bin or select something else.