10.8 Effective Sample Size (ESS)

MCMC samples can be correlated. The reason is that we use the current position to generate a new position and we accept or reject the next position taking into account the old position. This dependency is usually lower for well-tuned modern methods, such as Hamiltonian Monte Carlo, but it can be high. We can compute and plot the autocorrelation with az.plot_autocorrelation. But usually, a more useful metric is to compute the Effective Sample Size (ESS). We can think of this number as the number of useful draws we have in our sample. Due to autocorrelation, this number is usually going to be lower than the actual number of samples. We can compute it using the az.ess function (see Table 10.2). The ESS diagnostic is also computed by default with the az.summary function and optionally with az.plot_forest (using the ess=True argument).

	a	b0	b1	b2	b3	b4	b5	b6	b7	b8	b9
model_cm	14	339	3893	5187	4025	5588	4448	4576	4025	4249	4973
model_ncm	2918	4100	4089...