What happens when a chain converges in MCMC?
When the chain converges slowly, a large portion of our MCMC sample might be made up of observations drawn from distributions that are significantly different from the target distribution. If we are able to spot this kind of problem, we can try to fix it by: discarding a large chunk of initial observations (the so-called burn-in sample);
What do you call a Markov chain in MCMC?
Such a sequence is call a Markov chain. Thus MCMC techniques aim to construct cleverly sampled chains which (after a burn in period) draw samples which are progressively more likely realizations of the distribution of interest; the target distribution.
Why is chain 3 slow in MCMC diagnostics?
In the third plot (Chain 3), there is a lot of serial correlation between successive draws. The chain is very slow in exploring the sample space. The sample space has been explored only few times. In other words, there seems to be few independent observations in our sample.
What are the properties of a MCMC algorithm?
Here are some important facts that you need to keep in mind. An MCMC algorithm produces a sequence of random variables (or vectors). The sequence has the following properties: it is a Markov chain ;
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 are MCMC diagnostics used in the real world?
In particular, MCMC diagnostics are used to check: whether a large portion of the MCMC sample has been drawn from distributions that are significantly different from the target distribution; whether the size of the generated sample is too small.
Why does MCMC stand for Markov chain Monte Carlo?
MCMC is simply an algorithm for sampling from a distribution. It’s only one of many algorithms for doing so. The term stands for “Markov Chain Monte Carlo”, because it is a type of “Monte Carlo” (i.e., a random) method that uses “Markov chains” (we’ll discuss these later).
Which is an example of a MCMC sample?
Example Suppose our MCMC sample is made up of draws (with even): where a generic draw is a random vector.