Computational Bayesian Statistics
Course Description: “Compared with Bayesian methods, standard [frequentist] statistical techniques use only a small fraction of the available information about a research hypothesis (how well it predicts some observation), so naturally they will struggle when that limited information proves inadequate. Using standard statistical methods is like driving a car at night on a poorly lit highway: to keep from going in a ditch, we could build an elaborate system of bumpers and guardrails and equip the car with lane departure warnings and sophisticated navigation systems, and even then we could at best only drive to a few destinations. Or we could turn on the headlights.”—Aubrey Clayton, Bernoulli’s Fallacy In this course, we will “turn on the headlights”. That is, we will study Bayesian statistical inference methods, and we will regularly compare Bayesian methods to standard, frequentist methods (the methods covered, for example, in STAT 4520/5520 Introduction to Mathematical Statistics). Our goal will be to gain an extensive Bayesian toolkit, to understand what justifies the use of these tools, and compare and contrast them with frequentist methods. Specific topics may include: an introduction to Bayesian inference, conjugate, improper, and “objective” prior distributions; Bayesian estimation; an introduction to Bayesian statistical modeling, e.g., linear regression, generalized linear models; Bayes’ factors; multinormal and non-normal approximation to likelihood and posteriors; the EM algorithm; data augmentation; and Markov Chain Monte Carlo (MCMC) methods.
Learning Objectives: By the end of this course, students should be able to:
- Articulate the logic of Bayesian inference and compare and contrast it with frequentist inference
- Utilizeconjugate,improper,andobjectivepriorstofindposteriordistributions
- ArticulatetheneedforcomputationalapproachestoBayesianinferenceandimplementvarious computational approaches to find posterior distributions
- Assess the decision-theoretic and frequentist properties of Bayesian estimators
- DevelopandapplyBayesiantechniquesinthecontextoflinearandgeneralizedlinearmodels
- Evaluate the ethical consequences of the use (or misuse) of statistical methods
Required Text: Bayesian Statistical Methods by Brian Reich and Sujit K Ghosh (https://bit.ly/3EojOUQ)