Statistical Inference II

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

Autore/Autrice
Affiliazione

Ascari Roberto

Università degli Studi di Milano-Bicocca

Statistical Inference II provides an introduction to Bayesian data analysis, covering prior and posterior distributions, classical one-parameter models, prior elicitation, posterior-based inference, MCMC methods, and Bayesian approaches to linear and generalized linear models.

Syllabus

  • Introduction to Bayesian data analysis: prior and posterior distributions for inference.
  • One-parameter models: Binomial-Beta, Poisson-Gamma, Exponential-Gamma, and Normal-Normal.
  • Methods for prior elicitation.
  • Inference based on the posterior distribution (point and interval estimates; hypotheses testing).
  • Simulation-based inference: MCMC methods.
  • Linear and generalized linear models from a Bayesian perspective.

Scripts

  • The Bernoulli-Beta model: Code.
  • Normal approximation and Monte Carlo: Code.
  • MCMC - Gibbs sampling: Code.
  • MCMC - Metropolis Hasting: Code.
  • MCMC - Stan: Code.

Textbooks

  • Hoff, P. (2009). A first course in Bayesian Statistical Methods. Springer.

  • Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A., and Rubin, D. (2013). Bayesian Data Analysis. Chapman & Hall/CRC Texts in Statistical Science.

  • Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods. Springer.