This is the teaching material for a short course (4~5 hours) on Bayesian inference and Markov chain Monte Carlo (MCMC). The course focuses on concepts of Bayesian statistics and fundamental ideas of MCMC. The aimed audience is final-year undergraduate students or first-year graduate students in math/stats/engineering departments. R code snippets are provided for the key parts of Monte Carlo algorithms.
The course consists of two parts: the first part introduces basic Bayesian inference and the second part MCMC algorithms. In the end, we discuss Bayesian inference for state space models in finance for a comprehenstive application of conjugate priors, Metropolis-Hastings algorithm, and Gibbs sampler.
- What is Bayesian inference and why?
- One-parameter models
- Binomial model
- Poisson model
- Exponential family and conjugate priors
- Normal model
- Infer mean with known variance
- Jointly infer mean and variance
- Baisc Monte Carlo
- Monte Carlo integration
- Random variable generation
- Markov chain Monte Carlo
- Slice sampler
- Metropolis-Hastings algorithms
- Gibbs sampler
- An Application to State Space Models in Finance