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Bayesian Monte Carlo Simulation

Bayesian Monte Carlo Simulation integrates Bayesian statistical inference with Monte Carlo sampling to propagate uncertainty through complex models. Instead of drawing samples from arbitrary distributions, it conditions sampling on observed data and expert prior knowledge via Bayes' theorem, yielding posterior-based uncertainty estimates that are both statistically coherent and interpretable in probabilistic terms.

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Bayesian Monte Carlo Simulation — Prior-informed stochastic sampling for uncertainty quantification

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O'Hagan, A., Buck, C. E., Daneshkhah, A., Eiser, J. R., Garthwaite, P. H., Jenkinson, D. J., Oakley, J. E., & Rakow, T. (2006). Uncertain Judgements: Eliciting Experts' Probabilities. Wiley. · ISBN 9780470029992
O'Hagan, A. (1987). Monte Carlo is fundamentally unsound. The Statistician, 36(2-3), 247-249. · DOI 10.2307/2348519

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