Objectives and Overview

This course introduces advanced Monte Carlo statistical methods that have been a part of standard computational techniques used in Bayesian data analysis and data science. We will cover implementations using C/C++/R/Python/Julia.

Textbooks & References

• Faming Liang, Chuanhai Liu, Raymond Carroll (2010). Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley.
• Christian Robert, George Casella (2005). Monte Carlo Statistical Methods. Springer.
• Steve Brooks, Andrew Gelman, Galin Jones, Xiao-Li Meng (2011). Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC.

Topics

1. Review: Markov Chain Monte Carlo
2. Advanced Markov Chain Monte Carlo I: Data Augmentation, Hit-and-Run Algorithm, Multiple-Try Metropolis
3. Advanced Markov Chain Monte Carlo II: Reversible Jump MCMC, MCMC with Adaptive Proposal, Simulated Annealing
4. Auxiliary Variable MCMC I: Simulated Tempering, Slice Sampler, Swendsen-Wang Algorithm
5. Auxiliary Variable MCMC II: Exchange Sampler, Double MH Sampler, Monte Carlo MH Sampler
6. Approximate Bayesian Computation: ABC with Regression Approach, ABC with MCMC and SMC, ABC with Model Selection
7. Hamiltonian Monte Carlo I: Hamiltonian Monte Carlo, Metropolis-Adjusted Langevin Algorithm (MALA), Riemann Manifold HMC
8. Hamiltonian Monte Carlo II: No U-Turn Sampler (NUTS), Stochastic Gradient MCMC, Stochastic Gradient HMC
9. Population-Based MCMC I: Adaptive Direction Sampling, Conjugate Gradient Monte Carlo, Parallel Tempering
10. Population-Based MCMC II: Sequential Parallel Tempering, Evolutionary Monte Carlo, Equi-Energy Sampler
11. Stochastic Approximation Monte Carlo I: SAMC, Population SAMC, Varying Truncation SAMC
12. Stochastic Approximation Monte Carlo II: Adaptive Exchange Algorithm, Simulated Stochastic Approximation Annealing, Resampling-based SAMC

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