Abstract

ROMAN PADILLA, Lizbeth. A quick look at Bayesian Inference. Revista Varianza [online]. 2021, n.18, pp. 63-71. ISSN 9876-6789.

Abstract The Bayesian approach to statistics should be considered as an additional alternative to the classical approach, both approaches being complementary but not exclusive. Bayesian statistics offers a great variety of statistical methods similar in number to those provided by the classical approach. The origin of the term 'Bayesian Statistics' is due to the repeated use of the Bayes Theorem: the final or posterior distribution is the result of applying the Bayes Theorem to the information provided by data (likelihood function) and initial information about the parameter of interest (distribution initial). Posterior distribution is ideal for making any kind of inferences about the parameter of interest, whether it can be a point estímate or by interval, since it includes all the information available about θ after data has been observed together with initial information. The objective of this article is to illustrate how to get a Bayesian point estimator and credible region for the mean (θ) of Cauchy data Cau(θ, 1). For this purpose, annual rainfall data of Tabasco (Mexican state) will be used. Additionally, random variable simulation techniques and numerical integration are employed. The results obtained through Bayesian inference provides us with an approximation to the trae mean of precipitation (θ) since the classical estimator becomes unstable as the sample size increases. This simple exercise is intended to show some advantages of applying Bayesian methods

Keywords : Acceptance-Rejection algorithm; Bayesian estimation; Non-Informative Priors; Bayesian Inference; HPD regions; Simulation.