This review of #MCMC convergence diagnostics is really good
https://www.annualreviews.org/content/journals/10.1146/annurev-statistics-031219-041300
and pairs very well with this article discussing convergence of #MonteCarlo in #GPU friendly samplers
https://arxiv.org/abs/2110.13017
Only for the serious #Bayesians who refuse to do sloppy numerical work.
#statistics
Convergence Diagnostics for Markov Chain Monte Carlo | Annual Reviews
Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use, and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical questions that MCMC practitioners need to address are where to start and when to stop the simulation. Although a great amount of research has gone into establishing convergence criteria and stopping rules with sound theoretical foundation, in practice, MCMC users often decide convergence by applying empirical diagnostic tools. This review article discusses the most widely used MCMC convergence diagnostic tools. Some recently proposed stopping rules with firm theoretical footing are also presented. The convergence diagnostics and stopping rules are illustrated using three detailed examples.
