If you have Data ask me. Everything else ask God.

**Introduction**

- Objective vs Subjective Definition of Probability
- Axiomatic Definition of Probability
- Bayes Theorem
- Applications of Bayes Theorem

**Decision Theoretic framework and major concepts of Bayesian Analysis**

- Likelihood, prior and posterior
- Loss function
- Bayes rule
- Conjugate prior and other priors
- Sensitivity Analysis
- Posterior Convergence

**One-parameter Bayesian models**

- Poisson Model for Count data
- Binomial Model for Count data

**Multi-parameter Bayesian models**

- Univariate Gaussian Model
- Multivariate Gaussian Model
- Covariance Matrix with Wishart Distribution
- Bayesian solution for high-dimensional problem in Covariance matrix - Application: Efficient Portfolio in Finance
- Multinomial-Dirichlet Allocation Models- Application: Topic Models

**Bayesian Machine Learning**

- Hierarchical Bayesian Model
- Regression with Ridge prior, LASSO prior
- Classification with Bayesian Logistic Regression
- Discriminant Analysis

**Bayesian Computation with stan**

- Estimation of Posterior Mode with Optimization
- Estimation of Posterior Mean and other summary with Monte Carlo Simulation
- Accept-Rejection Sampling
- Importance Sampling
- Markov-Chain Monte Carlo
- Metropolis Hastings
- Hamiltonian Monte Carlo method

**Gaussian Process Regression**

- Introduction
- Gaussian Process Regression for Big Data

**Bayesian Optimization**