Bayesian Statistical Inference
Bayesian inference is a statistical framework using Bayes' theorem to update beliefs about parameters or hypotheses as data accumulate. Published posthumously in 1763, Thomas Bayes' work lay dormant until the 20th century, when computational advances (Gibbs sampling, Markov Chain Monte Carlo) made Bayesian methods practical. Unlike frequentist inference (which treats parameters as fixed unknowns), Bayesian analysis treats parameters as random variables with probability distributions, enabling direct probability statements about parameters, incorporation of prior knowledge, and sequential updating. Essential in precision medicine, adaptive trials, complex hierarchical models, and any context where prior information enriches inference.
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- Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 53, 370–418. · URL
- Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. · DOI 10.1201/b16018
- Kruschke, J. K. (2015). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan (2nd ed.). Academic Press. · DOI 10.1016/b978-0-12-405888-0.00008-8
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