model_bayes_factor_n: Computes the Bayes factor between two models from samples from their posterior distributions.
Description
The likelihood of a graph can be computed by integrating over all the graph parameters (with appropriate priors).
Doing this by sampling from priors is very inefficient, so we use samples from the posteriors to importance
sample the likelihood. Given two graphs, and samples from their posteriors, we can estimate the Bayes factor
between them.
Samples of log likelihoods from the posterior distribution of the first graph.
logL2
Samples of log likelihoods from the posterior distribution of the second graph.
no_samples
Number of permutations to sample when computing the result.
Value
The Bayes factor between the two graphs given as the mean and standard
deviation over no_samples different permutations of the input.
Details
The numerical issues with adding a lot of numbers in log space is unstable
so we get a better estimate by doing it several times on different permutations
of the data. This function calculates the mean of the Bayes factors over different permutations of the
input and estimates the standard deviation.