To Bayes or Not To Bayes? That's no longer the question!

TL;DR

This paper reviews the widespread adoption of Bayesian methods across various scientific fields, emphasizing their practical importance and the role of computational tools in making Bayesian inference accessible and central to modern data analysis.

Contribution

It provides a comprehensive account of Bayesian paradigm's evolution, its current dominance, and practical computational tools for Bayesian analysis in R.

Findings

Bayesian methods are now central in many scientific disciplines.

Computational advances have made Bayesian inference more accessible.

Bayesian paradigm offers robust solutions for statistical learning.

Abstract

This paper seeks to provide a thorough account of the ubiquitous nature of the Bayesian paradigm in modern statistics, data science and artificial intelligence. Once maligned, on the one hand by those who philosophically hated the very idea of subjective probability used in prior specification, and on the other hand because of the intractability of the computations needed for Bayesian estimation and inference, the Bayesian school of thought now permeates and pervades virtually all areas of science, applied science, engineering, social science and even liberal arts, often in unsuspected ways. Thanks in part to the availability of powerful computing resources, but also to the literally unavoidable inherent presence of the quintessential building blocks of the Bayesian paradigm in all walks of life, the Bayesian way of handling statistical learning, estimation and inference is not only mainstream but also becoming the most central approach to learning from the data. This paper explores some of the most relevant elements to help to the reader appreciate the pervading power and presence of the Bayesian paradigm in statistics, artificial intelligence and data science, with an emphasis on how the Gospel according to Reverend Thomas Bayes has turned out to be the truly good news, and some cases the amazing saving grace, for all who seek to learn statistically from the data. To further help the reader gain deeper and tangible practical insights into the Bayesian machinery, we point to some computational tools designed for the R Statistical Software Environment to help explore Bayesian statistical learning.