Bayesian Statistics and Applications
( 25 Modules )

Module #1
Introduction to Bayesian Statistics
Overview of Bayesian statistics, its importance, and applications

Module #2
Bayes Theorem
Understanding Bayes theorem, conditional probability, and its role in Bayesian inference

Module #3
Prior Distributions
Introduction to prior distributions, types, and importance in Bayesian analysis

Module #4
Likelihood Functions
Understanding likelihood functions, their role in Bayesian inference, and examples

Module #5
Posterior Distributions
Calculating and interpreting posterior distributions, summarization, and visualization

Module #6
Bayesian Estimation
Introduction to Bayesian estimation, point estimation, and interval estimation

Module #7
Bayesian Hypothesis Testing
Bayesian approach to hypothesis testing, Bayes factors, and decision-making

Module #8
Bayesian Model Selection
Model selection using Bayesian methods, including Bayes factors and cross-validation

Module #9
Markov Chain Monte Carlo (MCMC) Methods
Introduction to MCMC methods, algorithms, and convergence diagnostics

Module #10
Gibbs Sampling
Gibbs sampling, implementation, and examples

Module #11
Metropolis-Hastings Algorithm
Metropolis-Hastings algorithm, implementation, and examples

Module #12
Bayesian Linear Regression
Bayesian approach to linear regression, model specification, and inference

Module #13
Bayesian Generalized Linear Models
Bayesian generalized linear models, including logistic regression and Poisson regression

Module #14
Bayesian Hierarchical Models
Bayesian hierarchical models, including multilevel and longitudinal data analysis

Module #15
Bayesian Model Averaging
Bayesian model averaging, including BMA and Bayesian stacking

Module #16
Applications in Finance
Bayesian methods in finance, including option pricing and credit risk analysis

Module #17
Applications in Machine Learning
Bayesian methods in machine learning, including Bayesian neural networks and Gaussian processes

Module #18
Applications in Healthcare
Bayesian methods in healthcare, including clinical trials and epidemiology

Module #19
Applications in Environmental Sciences
Bayesian methods in environmental sciences, including climate modeling and ecological inference

Module #20
Introduction to Bayesian Computation
Introduction to Bayesian computation using R, Python, and Stan

Module #21
Using R for Bayesian Analysis
Using R for Bayesian analysis, including rstan and rstanarm

Module #22
Using Python for Bayesian Analysis
Using Python for Bayesian analysis, including PyMC3 and scikit-bayes

Module #23
Using Stan for Bayesian Analysis
Using Stan for Bayesian analysis, including model specification and inference

Module #24
Bayesian Model Validation and Criticism
Bayesian model validation, criticism, and diagnosis

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Bayesian Statistics and Applications career

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