A student runs a Metropolis sampler to estimate the posterior of a binomial proportion, starting the chain at 0.5. The posterior is centred near 0.72, so the starting value sits well out in the lower tail. The student decides not to use any burn-in and keeps every iteration, including the very first ones.
What happens as a result?

Question

A student runs a Metropolis sampler to estimate the posterior of a binomial proportion, starting the chain at 0.5. The posterior is centred near 0.72, so the starting value sits well out in the lower tail. The student decides not to use any burn-in and keeps every iteration, including the very first ones.

What happens as a result?

Answer

The first few draws, which sit near the starting value, are kept and can pull the posterior summaries slightly towards that value.

Answer

The posterior distribution itself changes, because the target depends on how many early iterations the sampler discards.

Answer

The draws become less correlated with each other, because no early iterations are removed from the start of the chain.

Answer

The chain never reaches the high-probability region, so every one of the kept draws is a poor sample from the posterior.

Answer

The sampler stops with an error, because a burn-in period is needed to tune the proposal distribution before sampling can begin.

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A student runs a Metropolis sampler to estimate the posterior of a binomial prop...

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