Contents
What is MCMC convergence?
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 integrated autocorrelation time?
Description. The IAT function estimates integrated autocorrelation time, which is the computational inefficiency of a continuous chain or MCMC sampler. IAT is also called the IACT, ACT, autocorrelation time, autocovariance time, correlation time, or inefficiency factor. A lower value of IAT is better.
Why is autocorrelation a problem with MCMC sampling?
The problem however with MCMC is that the resulting samples are correlated. This is because each subsequent sample is drawn by using the current sample. There are two main MCMC sampling methods: Gibbs sampling and Metropolis-Hastings (MH) algorithm. Autocorrelation in the samples is affected by a lot of things.
What is the correlation of autocorrelation in Monte Carlo?
A correlation of 1. With the first lag, a value of the chain has a correlation a little higher than 0.5. And as we go further along the chain, the values become less correlated. We can also look at the values of the auto correlation themselves with autocorr.diag. We run that and we look at those values.
How are MCMC diagnostics used in Markov chain Monte Carlo?
Markov Chain Monte Carlo (MCMC) diagnostics are tools that can be used to check whether the quality of a sample generated with an MCMC algorithm is sufficient to provide an accurate approximation of the target distribution. In particular, MCMC diagnostics are used to check:
How does the starting value of the Markov chain affect autocorrelation?
The autocorrelation is also affected by starting values of the Markov chain. There is generally an (unknown) optimum starting value that leads to the comparatively less autocorrelation. Multi-modality of the target distribution can also greatly affect the autocorrelation of the samples.