Discarding chains when Rhat is high

General
1

Hi,

I recently found a preprint that implements a model I’ve been working on implementing in Stan. The authors say they discarded fits when R-hat was high and kept restarting the fitting procedure until R-hat was lower. My intuition is that this could lead to missing regions of the posterior. However, I’m fairly new to Bayesian modeling and not sure whether I’m misunderstanding something. I’d greatly appreciate any input or reading suggestions.

Quote from the preprint:

Samples from individual patient posteriors are obtained using an adaptive Metropolis with adaptive scaling Markov chain Monte Carlo (MCMC) algorithm provided by AdaptiveMCMC in Julia. For each patient, we take 105 samples across four independent chains, initialised independently using samples from the prior distribution. We verify MCMC convergence using the Rˆ convergence diagnostic: in cases for which Rˆ < 1.1 is not satisfied, the chains are discarded and resampled.

2

That’s correct. If what’s happening is that chains are getting stuck when trying to explore regions of high curvature, then throwing them away will underestimate the probability of these high curvature regions in the posterior.

Sometimes it can be OK to discard stuck chains if the chains are getting stuck due to poor initialization/adaptation.

3

Interesting! Initializing this model has definitely been a challenge for me, so that is probably what’s going on. Thank you!