Contents
What is Gelman Rubin diagnostic?
The Gelman–Rubin diagnostic evaluates MCMC convergence by analyzing the difference between multiple Markov chains. The convergence is assessed by comparing the estimated between-chains and within-chain variances for each model parameter. Large differences between these variances indicate nonconvergence.
What is R Hat value?
What is R-hat? R-hat, or the potential scale reduction factor, is a diagnostic that attempts to measure whether or not an MCMC algorithm1 has converged flag situations where the MCMC algorithm has failed converge.
What is burn in period in MCMC?
What is Burn-In? Burn-in is a colloquial term that describes the practice of throwing away some iterations at the beginning of an MCMC run.
What is the Gelman-Rubin statistic?
The Gelman-Rubin statistic is a ratio, and hence unit free, making it a simple summary for any MCMC sampler. The result is that the uncertainty of any parameter being estimated with a MCMC sampler will be greater than that estimated using MC standard errors.
When to use the Gelman and Rubin diagnostic?
The Gelman and Rubin diagnostic is used to check the convergence of multiple mcmc chains run in parallel. It compares the within-chain variance to the between-chain variance, the exposition is below:
How does Gelman-Rubin diagnostic evaluate MCMC convergence?
The Gelman–Rubin diagnostic evaluates MCMC convergence by analyzing the difference between multiple Markov chains. The convergence is assessed by comparing the estimated between-chains and within-chain variances for each model parameter.
What is the potential scale reduction factor of Gelman and Rubin?
The between-chains and within-chain variances are given by is an unbiased estimator of the marginal posterior variance of (Gelman and Rubin 1992). The potential scale reduction factor (PSRF) is defined to be the ratio of and .
How to deduce convergence from Brooks and Gelman?
To deduce convergence, it is then required that all PSRFs are close to 1. It does not matter that your parameters are interpreted as random vectors, their components are scalars for which you can compute PSRFs. Brooks & Gelman [3] have proposed a multivariate extension of the PSRF, which I review in the next section of this answer.