This repository consist of a compendium of assignments and their respective solutions for an advanced course in Applied Bayesian Statistics. It imparts a comprehensive understanding of theoretical, computational, and practical aspects of the Bayesian statistics. Throughout the course, the following topics are covered in-depth:
- A contrastive examination of Bayesian and frequentist methodologies
- Bayesian learning paradigms
- Commonly employed prior distributions
- Techniques for succinctly summarizing posterior distributions
Furthermore, the course delves into modern Bayesian computational algorithms, primarily Markov Chain Monte Carlo (MCMC) techniques, executed through the Python/R programming languages. The central subjects covered in this segment include:
- Monte Carlo approximations
- Gibbs sampling
- Diagnostics for convergence evaluation
- Just Another Gibbs Sampler (JAGS)
Armed with these computational tools, participants will engage in the application of Bayesian methodologies to a variety of data analysis problems, including but not limited to:
- Multivariate linear regression
- Generalized linear models
- Hierarchical modeling
- Surrogate models
- Gaussian Proccess
Throughout the course, comparative model evaluation and model adequacy testing are emphasized as fundamental components of Bayesian statistics. Through this course, one will attain a comprehensive understanding of these concepts and the ability to implement them in real-world scenarios.