Some basic ideas of Bayesian inference
Miguel A. Martínez‐Beneito, Paloma Botella-Rocamora · 2019
This chapter introduces the basic ideas and concepts of Bayesian inference. It discusses Bayesian hierarchical models and random effects, the main modeling tool used in this book and for disease mapping in general. The chapter examines Markov Chain Monte Carlo as the main tool to carry inference out in hierarchical models, paying particular attention to convergence analysis, the process used to assess the correctness of the inference made. Prior distributions are, by far, the most controversial issue in Bayesian statistics. The need of specifying a prior distribution for any parameter in the model raises lots of criticisms from the non-Bayesian world, blaming Bayesian analyses of being subjective. A basic knowledge of probability distributions is essential for an adequate understanding of Bayesian models. Both the frequentist and Bayesian approaches find their particular mathematical obstacles, maximization and integration respectively, to carry inference out in statistical models.