In this video, we build the Metropolis–Hastings algorithm from scratch using a single concrete problem: locating an earthquake off a coastline from arrival-time recordings. We show how a random walker that only compares two candidate spots at a time recovers exact probabilities without ever computing the intractable normalizing constant. We then explore step-size tuning and examine how multimodal geometry can quietly trap a Markov chain on the wrong side of the coast.

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Chapters:
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0:00 The Earthquake Location Problem
1:50 Computing Probabilities by Hand
3:46 The Curse of Dimensionality
5:35 Walking Without Normalization
7:23 Detailed Balance and Hastings
9:33 Tuning the Step Size
11:10 The Mirror-Image Trap
12:52 Origins and Practical Limits

#MetropolisHastings #MarkovChainMonteCarlo #BayesianInference #Statistics #AppliedMathematics