#### 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.itA 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).

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, Bayesâ€™ theorem. Subjective

prior elicitation and some noninformative or default prior choices (e.g.

Jeffreysâ€™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.

- Teacher: Cristina Mollica
- Teacher: Luca Tardella