PHASE RANDOMIZATION: A CONVERGENCE DIAGNOSTIC TEST FOR MCMC

Most Markov chain Monte Carlo (MCMC) users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. Potentially useful diagnostics can be borrowed from diverse areas such as time series. One such method is phase randomization. This paper describes this method in the context of MCMC, summarizes its characteristics, and contrasts its performance with those of the more common diagnostic tests for MCMC. It is observed that the new tool contributes information about third‐ and higher‐order cumulant behaviour which is important in characterizing certain forms of nonlinearity and non‐stationarity.