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Explain MCMC and Metropolis-Hastings: why does the chain sample from the posterior?

Bayesian inference needs an intractable normalizing constant, and MCMC sidesteps it. The signal is explaining the acceptance ratio, detailed balance, and why you can skip the constant entirely. Here is the answer.

Updated Aug 2026 · Grounded in real Applied AI Engineer interview loops and written to a senior-engineer editorial bar.

Bayesian inference needs an intractable normalizing constant, and MCMC sidesteps it. The signal is explaining the acceptance ratio, detailed balance, and why you can skip the constant entirely. Here is the answer.

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