This is an introductory course about Bayesian inference and 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, [possible hints on INLA and Stan]). There will be also some emphasis on the specific theoretical aspects of Bayesian computational tools.

List of topics: 

• 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.
• Bayesian computational tools Introduction to Monte Carlo methods as approximation strategy. Monte Carlo
• methods for Bayesian inference. Classical asymptotic theorems and Monte Carlo methods: convergence and
• error control. Importance sampling techniques. Monte Carlo strategies for approximating marginal likelihood and
• Bayes Factor. Introduction to Markov chains on a finite state space and on general state spaces. Markov chains,
• stationarity, invariant measures. Limiting distributions and rate of convergence. Convergence and error control
• for MCMC. General algorithms for Markov chain simulation with a prescribed invariant distribution: Gibbs
• sampling & Metropolis Hastings. Hybrid methods: kernel composition, kernel mixtures. MCMC diagnostics.
• Approximate Bayesian Computation.

You can find out more either on the official webpage corsidilaurea or in a single PDF file available at https://bit.ly/BayesianModelling