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Mathematics

Markov Chain Monte Carlo for Bayesian Inverse Problems

Quick fact

The Metropolis-Hastings algorithm, a cornerstone of MCMC, was ranked among the top 10 algorithms of the 20th century, and it allows sampling from distributions known only up to a constant, which is crucial for Bayesian inversion where the normalizing constant is typically intractable.

Why this is interesting

When you can't calculate the answer directly, can you still somehow 'sample' your way to the truth? In Bayesian inverse problems, we often face just that—so how do we draw meaningful conclusions from a distribution we can't write down?