Bayesian Computations

Ph.D. in Economics, Statistics, and Data Science

Author
Affiliation

Riccardo Corradin

Università degli Studi di Milano-Bicocca

In this page, you can find teaching materials, examples, case studies and information related to the Bayesian Computations module of the PhD course in Bayesian statistics.

I gently acknowledge Tommaso Rigon, who has initially developed the material of this module. The previous version of the module material is available at the following link

https://tommasorigon.github.io/CompStat/

All credit goes to him, all mistakes are mine.

Prerequisites

It is assumed the knowledge of the following topics:

  • Fundamentals of Bayesian statistics. Refer to Chapters 1-5 of Hoff (2009).

  • Monte Carlo integration. Refer to Chapter 3 of Robert and Casella (2009), or Chapter 4 of Hoff (2009).

Teaching material

Here you can find slides, examples and case studies.

Topic Slides Further material
Introduction slides introduction code introduction
Adaptive and dynamic-based methods slides ad&dyn

code ad&dyn

Rcpp RWMH
Importance sampling slide IS code IS
TBD slide approximate code approximate

Material is subject to changes during the module.

Main references

  1. Blei, D. M., Kucukelbirb A., and McAuliffe, J. D. (2017). Variational inference: a review for statisticians. Journal of the American Statistical Association, 112(518), 859–877.

  2. Chopin, N., Papaspiliopoulos, O. (2020). An Introduction to Sequential Monte Carlo. Springer Cham.

  3. Chopin, N. and Ridgway, J. (2017). Leave Pima indians alone: binary regression as a benchmark for Bayesian computation. Statistical Science, 32(1), 64–87.

  4. Durante, D. and Rigon, T. (2019). Conditionally conjugate mean-field variational Bayes for logistic models. Statistical Science, 34(3), 472–485.

  5. Eddelbuettel, D. and Balamuta, J. J. (2018). Extending R with C++: a brief introduction to Rcpp. The American Statistician, 72(1), 28–36.

  6. Hunter, D. R., and Lange, K. (2004). A Tutorial on MM Algorithms. The American Statistician, 58(1), 30–37.

  7. Kloek, T., van Dijk, H. K. (1978). Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo. Econometrica, 46(1), 1-19.

  8. Neal, R. M. (2011). MCMC using Hamiltonian dynamics. CRC press.

  9. Polson, N. G., Scott, J. G. and Windle J. (2013). Bayesian inference for logistic models using Pólya–Gamma latent variables. Journal of the American Statistical Association, 108(504), 1339–1349.

  10. Roberts, G. O. and Rosenthal, J. S. (2001). Optimal scaling for various Metropolis-Hastings algorithms. Statistical Science, 16(4), 351–367.

  11. Roberts, G. O. and Rosenthal, J. S. (2009). Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18(2), 349–367.