Docente
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TARDELLA LUCA
(programma)
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, INLA[possibly]). There will be some emphasis on the specific detailed theoretical aspects of Bayesian computational tools.
**List of topics**:
Introduction to Bayesian Thinking.
This section covers basic definitions, Bayesian model, Bayes’ theorem. Subjective prior elicitation and asome noninformative or default prior choices (Jeffreys’ Rule). Conjugate analysis. Techniques and tools for characterizing and summarizing posterior distributions.
Multiparameter Inference.
This section covers 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. This section covers 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. General algorithms for Markov chain simulation with a prescribed invariant distribution: Gibbs sampling & Metropolis Hastings. Hhybrid methods: kernel composition, kernel mixtures. Approximate Bayesian Computation.
Course Material and Reference Books
• Course lecture notes (slide available at the https://elearning2.uniroma1.it/course/view.php?id=4460)
• Peter Hoff, A First Course in Bayesian Statistical Methods. Springer-Verlag Inc, 2009.
• Jean-Michel Marin and Christian P. Robert, Bayesian Core: A Practical Approach to Computational
Bayesian Statistics, Springer, 2007
• Ioannis Ntzoufras, Bayesian Modeling Using WinBUGS. Wiley, 2009.
• Peter Congdon. Bayesian Statistical Modelling (2nd ed.). Wiley, 2006
• Christian P. Robert and George Casella. Monte Carlo statistical methods (2nd ed.. Springer-Verlag
Inc, 2004.
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