What computational method catalyzed the rise of Bayesian analysis by making previously intractable posteriors solvable?

Answer

Markov Chain Monte Carlo (MCMC)

The adoption and popularization of Markov Chain Monte Carlo (MCMC) methods were the key catalysts that enabled the practical solving of complex, previously intractable posterior distributions.

What computational method catalyzed the rise of Bayesian analysis by making previously intractable posteriors solvable?
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