Explanation of Corner Plot Histograms

[Gaurav17Joshi]

Hi, @Joshuaalbert , I wanted to understand the Histograms made in the corner plot after the sampling run. The Histograms are not made of all the samples of the run. How and why are we taking selected weighted samples?

[Joshuaalbert]

Hi @Gaurav17Joshi the reason is because in nested sampling, the samples produced are not of equal weight, unlike MCMC. Instead they are weighted by how much they contribute to the evidence, Z = sum_i dP_i. Or, dP_i = L_i * w_i, where w_i is the amount of shrinkage between likelihood contours. These weights, dP_i allow you to take expectations, e.g. E_posterior[f] = sum_i f(x_i) * dP_i. When you have weights of equal weight, e.g. with MCMC, dP_i=1. Anyways, you can resample the weighted samples to produce equally weighted samples, by selecting a sample with replacement proportionally to dP_i. And that is what we do before doing any type of statistic that relies of equally weighted samples, such as the histogram. Hope that help! Let me know.

[Gaurav17Joshi]

Thanks for the explaination.