Bayesian Data Analysis

Objectie: This course will provide an overview of basic ideas in Bayesian data anlysis. The objective is to understand how Bayes probability models are used to handle the complex problems. The stress will be on understanding the construction of the models and implementation.

  • Introduction

    1. Objective vs Subjective Definition of Probability
    2. Axiomatic Definition of Probability
    3. Bayes Theorem
    4. Applications of Bayes Theorem
  • Decision Theoretic framework and major concepts of Bayesian Analysis

    1. Likelihood, prior and posterior
    2. Loss function
    3. Bayes rule
    4. Conjugate prior and other priors
    5. Sensitivity Analysis
    6. Posterior Convergence
  • One-parameter Bayesian models
    1. Poisson Model for Count data
    2. Binomial Model for Count data

  • Multi-parameter Bayesian models
    1. Univariate Gaussian Model
    2. Multivariate Gaussian Model
    3. Covariance Matrix with Wishart Distribution
    4. Bayesian solution for high-dimensional problem in Covariance matrix - Application: Efficient Portfolio in Finance
    5. Multinomial-Dirichlet Allocation Models- Application: Topic Models
  • Bayesian Machine Learning
    1. Hierarchical Bayesian Model
    2. Regression with Ridge prior, LASSO prior
    3. Classification with Bayesian Logistic Regression
    4. Discriminant Analysis

  • Bayesian Computation with stan
    1. Estimation of Posterior Mode with Optimization
    2. Estimation of Posterior Mean and other summary with Monte Carlo Simulation
    3. Accept-Rejection Sampling
    4. Importance Sampling
    5. Markov-Chain Monte Carlo
    6. Metropolis Hastings
    7. Hamiltonian Monte Carlo method

  • Gaussian Process Regression
    1. Introduction
    2. Gaussian Process Regression for Big Data

  • Bayesian Optimization