Bayesian Statistical Methods (POPH90139)

This subject introduces Bayesian statistical concepts and methods, with emphasis on practical applications in biostatistics. We begin with a discussion of subjective probability in quantifying uncertainty in the scientific process. Subsequently, the concept of full probability modelling is introduced and developed through single- and multi-parameter models with conjugate prior distributions. The connection with frequentist approaches is examined in light of the relationship between non-informative and informative prior distributions and their effect on posterior estimates We discuss the specification of appropriate prior distributions, including the concepts of non-informative and weakly informative priors. We consider the frequentist properties of Bayesian procedures. The application of Bayesian methods for fitting hierarchical models to correlated data structures is developed. Computational techniques for use in Bayesian statistics, especially the use of iterative simulation from posterior distributions using Markov chain Monte Carlo techniques (MCMC) will be covered using the Stan software through R.