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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?
The basic idea of an MCMC algorithm is to create a Markov process that has a stationary distribution the same as a posterior distribution of interest. Technically, convergence occurs when the generated Markov chain converges in distribution to the posterior distribution of interest.
What is convergence in Bayesian analysis?
The standard convergence theorems in Bayesian statistics show that the posterior converges weakly to the true parameter, defined operationally through the law-of-large numbers. It is less common to refer to a “true distribution” of the parameter, as something apart from the prior or posterior.
What is effective sample size 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.
What is the most effective sample size?
A good maximum sample size is usually 10% as long as it does not exceed 1000. 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.
Why does MCMC converge very slowly when not well chosen?
• Standard MCMC converges extremely slowly if the proposal distribution is not well chosen –It’s hard to find a good proposal distribution for complex problems (e.g., many parameters) –Want a way to automatically choose good proposal distribution • Standard MCMC evaluates 1 model at a time
Is there a coda package for MCMC in R?
This is supported in the coda package in R (for “Output analysis and diagnostics for Markov Chain Monte Carlo simulations”). coda also includes other functions (such as the Geweke’s convergence diagnostic). You can also have a look at “boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference”.
How to use BOA for MCMC output convergence assessment?
You can also have a look at “boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference”. Rather than using the Gelman-Rubin statistic, which is a nice aid but not perfect (as with all convergence diagnostics), I simply use the same idea and plot the results for a visual graphical assessment.
Which is the Gelman-Rubin diagnostic for MCMC?
Gelman-Rubin diagnostic ( ) • Compute mindependent Markov chains • Compares variance of each chain to pooled variance • If initial states (θ 1j ) are overdispersed, then approaches unity from above • Provides estimate of how much variance could be reduced by running chains longer • It is an estimate!