Menù principale
B027523 - BAYESIAN STATISTICAL INFERENCE
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2019-20
Coorte 2018 - Second Cycle Degree in COMPUTER SCIENCE
Course year
Second year - First Semester
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
SECS-S/01 - STATISTICS
Credits
9
Teaching Hours
72
Teaching Term
16/09/2019 ⇒ 20/12/2019
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B004652 - INFERENZA STATISTICA BAYESIANA
Second Cycle Degree in STATISTICS, ACTUARIAL AND FINANCIAL SCIENCE
Curriculum STATISTICO
B004652 - INFERENZA STATISTICA BAYESIANA
Second Cycle Degree in STATISTICS, ACTUARIAL AND FINANCIAL SCIENCE
Curriculum STATISTICO
Teaching Language
Italian
Course Content
Main aims of Bayesian Statistics. Parametric inference, predictive inference. Observation processes, exchangeability. Univariate parametric models. Monte Carlo approximations. The normal model. Posterior approximation with the Gibbs sampler. The multivariate normal model. Group comparison and hierarchical modeling. Linear regression. Nonconjugate priors and Metropolis-Hastings algorithms. Linear and generalized mixed effect models. Methods for ordinal data. Bayesian networks (time permitting).
Suggested readings (Search our library's catalogue)
Peter D. Hoff A First Course in Bayesian Statistical Methods, 2009 Springer
Learning Objectives
KNOWLEDGE: Deep understanding of Bayesian inference techniques. Use of parametric models defining parameters as random variablesEXPERTISE: Students will be trained to solve complex problems involving the treatment of missing data, the selection of models among possible competitors, the capability to derive complex conditional distribution.ACHIEVED ABILITIES AT THE END OF THE COURSE: Students will be able to develop and implement a Bayesian statistical model involving simple and hierarchical relations
Prerequisites
Preparatory courses: Statistical inference, Probability and mathematics for statistics
Teaching Methods
Oral lectures and sessions of exercises
Further information
Some knowledge of the R software is required
Type of Assessment
There will be a written examination (2/3 of the final mark); homeworks will be also graded (1/3 of the final mark).
Course program
Law of total probability and Bayes rule. Bayesian inference: notation. main differences between Bayesian and frequentist inference. Observation processes. Different hypotheses of dependence. Gaussian process, mixture processes: Exchangeability.
Binomial model, HPD regions. predictive inference Conjugate families. No informative priors, Jeffreys priors, Monte Carlo methods, AR and importance sampling. MCMC, Normal multivariate analysis, Regression methods and variables selection. G-priors. Hierarchical models, linear hierarchical models Bayesian generalized linear models. Bayesian networks, definitions, usage and learning (time permitting).
Binomial model, HPD regions. predictive inference Conjugate families. No informative priors, Jeffreys priors, Monte Carlo methods, AR and importance sampling. MCMC, Normal multivariate analysis, Regression methods and variables selection. G-priors. Hierarchical models, linear hierarchical models Bayesian generalized linear models. Bayesian networks, definitions, usage and learning (time permitting).