Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
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<strong>Metropolis</strong>-<strong>Hastings</strong> <strong>algorithm</strong><br />
• Imagine a politician visiting a string of islands:<br />
– Wants to visit each island a number of times proportional to its<br />
population.<br />
– Doesn’t know how many islands there are.<br />
– Each day: might move to a new neighboring island, or stay on current<br />
island.<br />
• Develops simple heuristic to decide which way to move:<br />
– Flips a fair coin to decide whether to move to east or west.<br />
– If the proposed island has a larger population than the current island,<br />
moves there.<br />
– If the proposed island has a smaller population than the current island,<br />
moves there probabilistically, based on uniform spinner:<br />
• Probability of moving depends on relative population sizes:<br />
P<br />
proposed<br />
pmove<br />
<br />
P<br />
current<br />
• End result: probability that politician is on any one of the islands<br />
exactly matches the relative proportion of the island.
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