Department of Statistics

STAT 907 Syllabus, Fall 2015

BAYESIAN STATISTICAL INFERENCE

Instructor: Nora M. Bello, DVM, PhD

002 Dickens Hall
Department of Statistics
Kansas State University

Phone #: (785) 532-0523
Email: nbello@ksu.edu
http://www.k-state.edu/stats/people/bello.html

The Bayesian approach to statistical inference and computing is of mainstream importance and utility for today’s complex data analysis. This approach represents one of two fundamental modes of statistical thought, the other being the frequency approach (unbiased estimators, hypothesis tests and confidence intervals) with likelihood-based methods. The Bayesian philosophy is innately probabilistic in its inference, making for intuitive interpretation of results. Furthermore, hierarchical modeling within the Bayesian paradigm leverages the flexibility of conditional specifications to accommodate general models required by the inherent complexity of most current datasets and problems. This makes Bayesian data analysis a very effective and practical tool for statisticians and subject-matter scientists alike. This course will be suitable for graduate students and practitioners from many disciplines, provided a basic background in frequentist statistics. This course will also prepare students in Statistics to conduct methodological research in the fundamental area of Bayesian statistical inference.

COURSE OBJECTIVE:

  • To provide fundamental knowledge of Bayesian statistics and its implementation in data-driven research problems.
  • To train students in implementation of Bayesian statistics through Monte Carlo methods with emphasis in problem-driven applications and data analysis.

CLASS TIME: Tuesdays and Thursdays, 1:00 to 2:15 pm

CLASS LOCATION: 302 Dickens Hall, Kansas State University

CREDITS: 3

COURSE TOPICS:

Specific course topics include, but are not limited to:

  • Simple probability computations and general form of Bayes rule
  • Principles of Bayesian inference.
  • Bayesian perspective on statistical models: Linear regression, ANOVA, logistic regression, mixed models
  • Integration vs. simulation in Bayesian inference
  • Choice of prior distributions
  • Posterior computations using simulations
    • Traditional Monte Carlo methods
    • Markov Chain Monte Carlo (MCMC), including Gibbs sampling, Metropolis-Hastings algorithm, slice sampler, hybrid forms and alternative algorithms.
    • Convergence monitoring and diagnosis
  • Hierarchical models: General and Generalized Linear Mixed models
    • The empirical Bayes approach
  • Model checking and selection
  • Applications in the sciences using computer software

REQUISITES:

  • STAT 720: Design of Experiments or equivalent (required)
  • STAT 713: Applied Linear Statistical Models or equivalent, including STAT 705 (required)
  • STAT 770: Theory of Statistics I or equivalent (highly encouraged)
  • STAT 771: Theory of Statistics II or equivalent (preferred)
  • Basic statistical computing skills (e.g. equivalent to STAT 725, STAT 726)

REFERENCE BIBLIOGRAPHY:

Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians, 1stedition. 2010. R. Christensen, W. Johnson, A. Branscum and T. E. Hanson. Chapman & Hall/CRC Press.

Bayesian Data Analysis, 3nd Edition. 2013. A. Gelman, J. B. Carlin, H. S. Stern and D. B. Rubin. Chapman & Hall/CRC Press.

Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. 2010. D. Sorensen and D. Gianola. Springer.

Bayesian Methods for Data Analysis. 2009. B. P. Carlin and T. A. Louis. Chapman & Hall/CRC Press.

Assigned readings from the scientific literature. Students are required to make themselves acquainted with PubMed (www.pubmed.com) and Web of Knowledge (http://apps.webofknowledge.com).

COURSE IMPLEMENTATION:

Twice-a-week course meetings will include lecture recitation and practical computational work.

The softwares R (http://cran.r-project.org/) and WinBUGS (http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/contents.shtml) will be used as main implementation platforms for Bayesian inference. Both softwares are freely available. Students are required to download and install both softwares in their computers.