The Traceplot Thickens: MCMC Diagnostics for Non-Euclidean Spaces

Abstract: MCMC algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample size, are used to visualize mixing and determine how long to run the sampler. However, these classic diagnostics can be ineffective when the sample space of the algorithm is highly discretized (eg. Bayesian Networks or Dirichlet Process Mixture Models) or the sampler uses frequent non-Euclidean moves. In this article, we develop novel generalized convergence diagnostics produced by mapping the original space to the real-line while respecting a relevant distance function and then evaluating the convergence diagnostics on the mapped values. Simulated examples are provided that demonstrate the success of this method in identifying failures to converge that are missed or unavailable by other methods.