Does MCMC always converge?

Under certain conditions, MCMC algorithms will draw a sample from the target posterior distribution after it has converged to equilibrium. However, since in practice, any sample is finite, there is no guarantee about whether its converged, or is close enough to the posterior distribution.

What is convergence in MCMC?

We can safely assume convergence of an MCMC algorithm when we are certain that the sample generated from the algorithm is indeed from the posterior distribution of interest. Technically, convergence occurs when the generated Markov chain converges in distribution to the posterior distribution of interest.

What is effective sample size in MCMC?

The Effective Sample Size (ESS) in the context of MCMC, measures the information content, or effectiveness of a sample chain. For example, 1,000 samples with an ESS of 200 have a higher information content than 2,000 samples with an ESS of 100.

Are MCMC samples independent?

In MCMC the samples are not independent, and so things are not so simple. We should not use the samples generated during this burn-in period in our estimate of the mean we want to compute.

Why is MCMC Bayesian?

MCMC can be used in Bayesian inference in order to generate, directly from the “not normalised part” of the posterior, samples to work with instead of dealing with intractable computations.

What is r-hat in MCMC?

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 MCMC used for?

MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals, for example in Bayesian statistics, computational physics, computational biology and computational linguistics.

What is r hat in MCMC?

How many effective sample size is enough?

A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000. This exceeds 1000, so in this case the maximum would be 1000.

Is Monte Carlo a frequentist?

On the correspondence between frequentist and bayesian tests. Monte Carlo procedures are useful tools for such cases, and that is why Monte Carlo has been extensively used in both, frequentist and Bayesian analysis.