The subject of this document is Bayesian Inference, an inference system based on Bayes’ Formula. In the first chapter we will state this formula and will discuss how to use it. It will be shown that, according to the formula, posterior distributions are proportional to the likelihood function times the prior distribution. This is the essential notion of Bayesian inference. In the second chapter, definitions and results related to Bayesian Analysis will be given in order to accomplish our inference. These mathematical tools will be of great use in the following chapters, where inference on proportions, Poisson distribution and Normal distribution will be studied. Both conjugate and noninformative prior distributions are considered. This documents ends with the transcription of an R code, allowing us to compute posterior distributions.

Universidad de Sevilla. Grado en Matemáticas