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I am new to the Metropolis-Hastings algorithm and am trying to wrap my head around the key points of it. I understand that it uses a Markov Chain Monte Carlo simulation to sample points throughout a region and then calculates a value which is either greater or less than one, which in turn decides whether the chain moves on or not.

If one was to create a proposal density that is very small width-wise, would that lead to the Markov Chain converging quickly to the true pdf value or would it simply restrict the accepted values of the Markov Chain to continue moving to a small set of values?

Thanks for any help :)

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