STAT443 Bayesian Statistics
| First Semester |
Bayesian methods provide an approach to statistics that a rapidly-growing number of scientists are starting to use. The key difference between Bayesian and classical statistics is that Bayesian inference makes direct use of probability to represent all uncertainty. In this course we examine the underpinnings of Bayesian inference and familiarize students with computer-based methods used in the Bayesian approach to statistics.
PLEASE NOTE: The contents of this page are meant only as a guideline of what to expect during the paper. The lecturer reserves the right to adjust some details of the paper during the year, as is deemed appropriate.
Paper details
We begin by comparing and contrasting Bayesian inference with its classical counterpart. We then follow with an introduction to Bayes’ theorem, definitions of probability, prior distributions and posterior inference. Students will work towards developing a Bayesian analysis of their own with real data, which will be submitted as a publication-style report document.
Potential students
Post-graduate students in statistics.
Prerequisites
STAT 362. Students should also be familiar with using the R programming language. Those unfamiliar should contact the lecturer to obtain additional support materials.
Main topics
- Subjective probability, belief, and exchangeability
- Random variables
- Exponential family of distributions and conjugacy
- Monte Carlo approximation
- Inference under the normal model
- Gibbs sampling
- Hierarchical modeling
- Bayesian regression
- Metropolis-Hastings sampling
- Linear mixed effects models
- Latent variable methods
- Model checking
Suggested texts
Gelman, A., Carlin, J., Stern, H., and Rubin, D.B. (2003) Bayesian Data Analysis. Second Edition
Robert, C. P. (2007) The Bayesian Choice. Second edition
Gelman, A. and Hill, J. (2006) Data Analysis Using Regression and Multilevel/Hierarchical Models
Albert, J. (2009) Bayesian Computation with R
Link, W. A. and Barker, R. J. (2010) Bayesian Inference with Ecological Applications
Computing Resources
Editors
TeXnicCenter (Free LaTeX editor for Windows)
TeXShop (Free LaTeX editor for Macintosh
TextMate (Code editor for Macintosh)
TextWrangler (Free code editor for Macintosh)
GNU Emacs (Free code editor for all platforms)
LaTeX Distributions
R
The Comprehensive R Archive Network
Lecturer
Matthew Schofield, Room 237
Peter Dillingham
Lectures
Two hours of lecture per week, in Room B21 (Science III). Time and location to be arranged.
Tutorial
One per week at a time to be arranged
Internal Assessment
The internal assessment is made up of 6 bi-weekly homework assignments.
All assignments and projects must be submitted in electronic format, preferably using the ;http://en.wikipedia.org/wiki/LaTeX">LaTeX document preparation language;. See the course resource page for downloadable documents for learning LaTeX.
Exam format
Two-hour exam covering all aspects of the course.
Final mark
Your final mark F in the paper will be calculated according to this formula:
F = max(E, (2E + A)/3)
where:
- E is the Exam mark
- A is the Assignments mark
and all quantities are expressed as percentages.
Students must abide by the University’s Academic Integrity Policy
Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.
The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.
Academic misconduct: Plagiarism
Plagiarism is defined as:
- Copying or paraphrasing another person’s work and presenting it as your own.
- Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
- Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
- Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.
All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.
Academic misconduct: Unauthorised Collaboration
Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.
Thomas Bayes, 1702-1761, who followed his father into the Ministry in England. He was intensely interested in mathematics at a time when calculus was in its infancy. His theory of probability was published in Essay towards solving a problem in the doctrine of chances by the Royal Society of London in 1764 — three years after his death, being submitted by a friend who recognised its value.
His conclusions were accepted by Laplace in 1781, rediscovered by Condorcet, and remained unchallenged until Boole questioned them. Since then Bayes’ techniques have been subject to controversy.
Some quotable quotes
“...everyone is, should be, or will soon be a Bayesian” (H. Chernoff)“Every statistician would be a Bayesian if he took the trouble to read the literature thoroughly...” (D. V. Lindley)
“Probability does not exist” (B. De Finetti (1974) in Theory of Probability)
