https://at-ceu.studyguide.timeedit.net/modules/CDCR6031?type=COREThis course will provide an introduction to practical methods for making inferences fromdata using probabilistic models for observed and missing data. This approach is analternative to frequentist statistics, the presently dominant inference technique insciences, and it supports a common-sense interpretation of statistical conclusions byusing probabilities explicitly to quantify uncertainty of inferences. The course willintroduce Bayesian inference starting from first principles using basic probability andstatistics, elementary calculus and linear algebra. We will progress by first discussing thefundamental Bayesian principle of treating all unknowns as random variables, and byintroducing the basic concepts (e. g. conjugate, noninformative priors) and the standardprobability models (normal, binomial, Poisson) through some examples. Next, we willdiscuss multi-parameter problems, and large-sample asymptotic results leading to normalapproximations to posterior distributions. We will continue with hierarchical models,model construction and checking, sensitivity analysis and model comparison. We willconclude the course with explicitly contrasting frequentist and Bayesian treatment of nullhypothesis testing and Bayesian formulation of classical statistical tests. Students in thecourse will use the software packages R and JAGS, which will allow them to fit complexBayesian models with minimal programming expertise. Familiarity with R, Matlab orC++ programming is required.