LM Statistical Methods and Applications

BAYESIAN MODELLING

Luca Tardella
The registration key will be delivered to all students during the first lecture. If you miss it please send an email to luca.tardella@uniroma1.it
A comprehensive overview as a pdf file can be downloaded from here: BM-2020-2021-Overview.pdf

This
is an introductory course about Bayesian inference and Bayesian
modelling for data analysis. We will balance between theoretical and
analytical tools and practice. In particular for practical
implementation of Bayesian models on real data we will make use of some
software for Bayesian modelling and inference (R, BUGS/JAGS, INLA).
The course will cover:

  • Introduction to Bayesian Thinking
    In this part we will
    cover basic definitions, Bayesian model, Bayes’ theorem. Subjective
    prior elicitation and some noninformative or default prior choices (e.g.
    Jeffreys’Rule). Conjugate analysis. Techniques and tools for
    characterizing and summarizing posterior distributions. Bayes Factor, introduction to multi-model inference and Bayesian model choice.

  • Multiparameter Inference
    In this part we will cover
    multivariate normal and multinomial models and introduces to approximate
    random sampling from a multivariate distribution. Bayesian inference in
    the presence of missing data.

  • Hierarchical Models, Model Checking and Linear Models
    In this last part we will cover
    the Bayesian approach for hierarchical modelling and linear regression.
    Linear and generalized linear mixed effects models. It also considers
    posterior predictive checking, sensitivity analysis, and goodness-of-fit
    statistics.

  • MC & MCMC
    Introduction to Monte Carlo and Monte
    Carlo Markov Chain sampling techniques for approximating expectations
    and distributions: Gibbs Sampling and Metropolis Hastings algorithms.