Monte Carlo Casino

Collection of Monte Carlo methods with examples in Julia.

Contents

1. Introduction:
   • Estimating $\pi$
   • Monte Carlo Integration
   • Pseudo-random numbers
2. Transformaion, rejection and reweighting methods
   • The inversion method
   • Box-Muller method for generating std. normal variables
   • The rejection sampling algorithm
   • The importance sampling algorithm
3. The Gibbs sampler
   • The Gibbs sampler for bivariate normal distribution
   • The Poisson change-point model
4. The Metropolis-Hastings
   • Metropolis-Hastings Random Walk
   • Bayesian probit model
5. Data augmentation strategies
   • Gaussian mixture model
   • The Ising model
6. The Reversible Jump algorithm
   • Gaussian mixture model (revisited)