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What is autocorrelation in MCMC?
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. For example, when using MH algorithms, to some extent you can reduce or increase your autocorrelations by adjusting the step size of proposal distribution.
What is autocorrelation time MCMC?
Conceptually, the autocorrelation time is the number of Markov chain transitions equivalent to a single independent draw from the distribution of {Xi}. It can be a useful summary of the efficiency of a Markov chain Monte Carlo (MCMC) sampler.
What are MCMC diagnostics?
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. whether the size of the generated sample is too small.
How much does it cost to thin MCMC?
The parameter thin allows the user to specify if and how much the MCMC chains should be thinned out before storing them. By default thin = 1 is used, which corresponds to keeping all values. A value thin = 10 would result in keeping every 10th value and discarding all other values.
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.
When is the MCMC sample size too small?
When the dependence decays very slowly ( is very large), it easily happens that the effective sample size ( ) of the MCMC sample is too small, in the sense that the limited size of the sample makes its empirical distribution a very noisy/imprecise approximation of the target distribution.
What causes high autocorrelation in a Bayesian analysis?
When running a Bayesian analysis, one thing to check is the autocorrelation of the MCMC samples. But I don’t understand what is causing this autocorrelation. High autocorrelation samples [from MCMC] often are caused by strong correlations among variables.
What kind of problem do MCMC diagnostics try to spot?
When we run an MCMC algorithm for periods, we get an MCMC sample made up of the first realizations of the chain: and then we use the empirical distribution of the sample to approximate the target distribution. What kind of problems do MCMC diagnostics try to spot?