This is a question from past paper about Stochastic simulation.

Suppose that a 95% equal-tailed credible interval for a parameter 0 was obtained from a sample using MCMC. In each of the following circumstances, is the width of the credible interval for 0 likely to increase noticeably, decrease noticeably or stay roughly the same? Provide justication for your answer. (a) The number of observations in the samples increased from 20 to 100. [2] (b) The length of each Markov chain is increased from 1000 iterations after the burn-in to 5000 iterations after the burn-in. [3]