Project Statistical Reasoning
Faculteit  Science and Engineering 
Jaar  2019/20 
Vakcode  WBMA19010 
Vaknaam  Project Statistical Reasoning 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester II a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Project Statistical Reasoning  
Leerdoelen  At the end of the course, the student is able to: 1) formulate and to model statistical realworld problem in terms of Bayesian probabilistic models. 2) analytically derive posterior distributions for standard Bayesian models with conjugate prior distributions e.g. BernoulliBeta, BinomialBeta, PoissonGamma, NormalNormal, NormalGamma, NormalNormalGamma. 3) compute predictive distributions and full conditional distributions for standard Bayesian models with conjugate prior distributions. 4) design Monte Carlo (MC) approximation algorithms and Markov Chain Monte Carlo (MCMC) sampling algorithms (for probabilities and models which are analytically infeasible). 5) implement those Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) algorithms in the R programming environment. 

Omschrijving  Our knowledge about the world is uncertain and continuously updated by observing data and learning from data. Statistics is the science which deals with the analysis of data, and two conceptually different paradigms can be distinguished: Frequentist and Bayesian Statistics. This course gives an introduction to Bayesian Statistics, while the course unit: 'Statistics' deals with frequentist Statistics. In frequentist Statistics model parameters are assumed to be unknown constants which have to be estimated from data. In Bayesian Statistics model parameters are assumed to be random variables, whose distributions are unknown. The goal is then to infer their distributions. The Bayesian approach is to formulate prior belief about the unknown parameters in terms of prior distributions and to update those prior distributions in light of data, so as to obtain the posterior distributions of the parameters. For more complex Bayesian models computationally expensive Markov Chain Monte Carlo (MCMC) sampling algorithms have to be designed to generated posterior distribution samples. It can be shown that both concepts (Bayesian vs. Frequentist) yield identical results asymptotically, i.e. for large informative data sets. However, in realworld applications the available data are often rather sparse and noisy. Then Bayesian approaches can be beneficial, e.g. when genuine 'preknowledge' is available or when information can be coupled by hierarchical models. The course covers the themes: Bayes theorem, Bayesian models, conjugate priors, various standard conjugate Bayesian models, posterior distributions, marginal likelihoods, predictive distributions, full conditional distributions, Monte Carlo approximations, Markov chains, Markov Chain Monte Carlo (MCMC) simulations, MetropolisHastings MCMC sampling, Gibbs MCMC sampling, Graphical Model representations and Hierarchical Bayesian models. The computer practical will start with an introductory tutorial on R programming. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(Final grade = 0.1 x max(HW1, ET) + 0.1 x max(HW2, ET) + 0.1 x max(HW3, ET) + 0.7 x ET only if ET >=4.5 otherwise Final = ET, where HWi is homework grade for ith homework set, ET final exam grade.) 

Vaksoort  bachelor  
Coördinator  dr. M.A. Grzegorczyk  
Docent(en)  dr. M.A. Grzegorczyk  
Verplichte literatuur 


Entreevoorwaarden  The course assumes prior knowledge of the course 'Probability Theory'  
Opmerkingen  
Opgenomen in 
