In the Metropolis–Hastings algorithm you accept a new sample based on how probable the new proposed sample is with respect to the current sample. But what is wrong with only accepting when the new proposed sample is actually better?
2026-04-17 12:39:19.1776429559
Why accept worse samples in Metropolis–Hastings Algorithm?
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You want to satisfy detailed balance for the Markov chain you're creating in MH, so that you automatically have the right stationary distribution.
Calculate out the stationary distribution if you do as you propose for some small example, and see what happens; you will get a different distribution.