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Bayesian Statistics is a captivating field and is used most prominently in data sciences. In this course we will learn about the foundation of Bayesian concepts, how it differs from Classical Statistics including among others Parametrizations, Priors, Likelihood, Monte Carlo methods and computing Bayesian models with the exploration of Multilevel modelling.
This course is divided into two parts i.e. Theoretical and Empirical part of Bayesian Analytics. First three weeks cover the Theoretical part which includes how to form a prior, how to calculate a posterior and several other aspects. Rest of the weeks will cover the empirical part which explains how to compute Bayesian modelling. Completion of this course will provide you with an understanding of the Bayesian approach, the primary difference between Bayesian and Frequentist approaches and experience in data analyses.
Overview
Syllabus
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Week 01: What is Bayesian Statistics and How it is different than Classical Statistics
- Foundations of Bayesian Inference
- Bayes theorem
- Advantages of Bayesian models
- Why Bayesian approach is so important in Analytics
- Major densities and their applications
Week 02: Bayesian analysis of Simple Models
- Likelihood theory and Estimation
- Parametrizations and priors
- Learning from binary models
- Learning from Normal Distribution
Week 03: Monte Carlo Methods
- Basics of Monte carol integration
- Basics of Markov chain Monte Carlo
- Gibs Sampling
Week 04: Computational Bayes
- Examples of Bayesian Analytics
- Introduction to R and OPENBUGS for Bayesian analysis
Week 05: Bayesian Linear Models
- Context for Bayesian Regression Models
- Normal Linear regression
- Logistic regression
Week 06: Bayesian Hierarchical Models
- Introduction to Multilevel models
- Exchangeability
- Computation in Hierarchical Models
