This document discusses using replica exchange Markov chain Monte Carlo (MCMC) with Stan and R to sample from multimodal posterior distributions. It provides an example model with two parameters, samples from the joint distribution using replica exchange MCMC with 10 replicas at different temperatures, and shows trace plots and energy trajectories that indicate good mixing and exchange between replicas. Some discussion points are raised at the end regarding reusing warmup results in Stan and appropriate settings for iteration and warmup lengths in the short MCMC sampling runs between exchange attempts.
This document discusses using replica exchange Markov chain Monte Carlo (MCMC) with Stan and R to sample from multimodal posterior distributions. It provides an example model with two parameters, samples from the joint distribution using replica exchange MCMC with 10 replicas at different temperatures, and shows trace plots and energy trajectories that indicate good mixing and exchange between replicas. Some discussion points are raised at the end regarding reusing warmup results in Stan and appropriate settings for iteration and warmup lengths in the short MCMC sampling runs between exchange attempts.