1Department of Mathematics, Institute of Chemical Technology, Mumbai
Bayesian statistical methods have become increasingly integral across all branches of science. With the rapid development of statistical software, Bayesian computation is now accessible to researchers in diverse domains, and these methods are widely used in both industry and academia. However, the availability of ready-made software can sometimes overshadow the fundamental principles behind Bayesian estimation.
This document aims to bridge that gap by offering a clear understanding of Bayesian principles through practical examples and case studies. By simulating data and comparing Bayesian estimators with likelihood-based estimators, the material highlights the core concept of bias–variance decomposition of the mean square error (MSE) in evaluating estimators.
This work is based on a series of lectures delivered by Dr. Amiya Ranjan Bhowmick in the course
Advanced Statistical Computing (SEM IV), M.Sc. Engineering Mathematics, during the academic year 2024–2025 at the Institute of Chemical Technology (ICT), Mumbai).
An earlier version of this material was developed in R by Ms. Dipali Vasudev Mestry.
This version has been fully redeveloped in Julia, leveraging its speed, flexibility, and increasing adoption in scientific computing.
The development of this content has been inspired by two exceptional books:
- Statistical Inference — Casella and Berger (2002)
- All of Statistics — Larry Wasserman (2004)
Many examples and exercises from these texts have been studied and adapted for this work.
I am sincerely grateful to Dr. Amiya Ranjan Bhowmick for providing me the opportunity to attend the course, which formed the foundation and motivation for creating this material.
Despite my best efforts, mistakes may remain. Readers are kindly encouraged to report any errors or suggestions for improvement.