Bayesian Models in Biostatistics
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A B S T R A C T
Bayesian models constitute a fundamental theoretical and methodological framework in biostatistics, offering a coherent probabilistic approach for statistical inference under uncertainty. Grounded in probability theory and Bayes’ theorem, Bayesian methods systematically update prior knowledge with observed data and represent uncertainty through posterior distributions. This paper presents a comprehensive theoretical and methodological overview of Bayesian models in biostatistics, with emphasis on their mathematical foundations, inferential principles, and practical applicability in biomedical research. Key concepts discussed include the axiomatic basis of probability, prior and posterior distributions, likelihood functions, credibility intervals, conjugate Bayesian models, and Bayesian parameter estimation. The study further examines the role of numerical methods, particularly Monte Carlo and Markov Chain Monte Carlo (MCMC) algorithms, in approximating posterior distributions when analytical solutions are unavailable. Illustrative examples, including the Poisson-Gamma conjugate model and MCMC-based inference, are used to demonstrate the practical implementation of Bayesian reasoning in biostatistical contexts. The paper highlights the advantages of Bayesian models in handling complex data structures, small sample sizes, uncertainty, and the integration of prior information, while also discussing key methodological challenges such as prior specification and computational demands. In all, the study underscores the relevance and robustness of Bayesian models as a powerful framework for contemporary biostatistical analysis and biomedical decision-making.