Metropolis-Hastings algorithm

Efficiency, “burn-in”, and convergence
• If proposal ldistribution ib i is narrow relative to target distribution ib i ,
will take a long time for random walk to cover the distribution.
– Algorithm will not be efficient: takes too many steps to accumulate
a representative sample.
– Particular problem if initial position of random walk is in region of
target distribution that is flat and low.
• Random walk moves only slowly away from starting position
into denser region.
– Unrepresentative starting gposition can lead to low efficiency even
if proposal distribution isn’t narrow.
• Solution: early steps of random walk are excluded from portion
of Markov chain considered to be representative of target
distribution.
– Excluded initial steps: burn-in period.