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Course Outline
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Introductory Lecture
[1] Jan 8, 2001, one hour only
- Introduction to the course, including overview and selection of topics, grading scheme, and assignments.
- Briefly review reading list to be discussed next week.
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- Handout summarizing basic elements used in Bayesian analysis
- Selected pages from A. Gelman, J. Carlin, H. Stern and D. Rubin, Bayesian Data Analysis, (1995, Chapman and Hall), pages 3 to 10.
- Selected pages from D. Berry and D. Stangl, Bayesian Biostatistics (1996, Dekker), pages 1 to 20.
- Selected pages from J. Berger, Statistical decision theory and Bayesian analysis, (1985), Springer Verlag, pages 20-35.
- J. Berger and D. Berry. Statistical analysis and the illusion of objectivity, (1988), American Scientist, 159--165
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Introduction to the Bayesian Approach to Statistical Analysis
[2] Jan 15, 2001
Discussion based on the readings, focussing on the following topics:
- Review of the correct interpretations of frequentist p-values and confidence intervals
- Problems with frequentist analysis
- Bayes Theorem
- Subjective or objective analyses
- The likelihood principle
- Inferential or decision theoretic Bayesian analysis
- Problems with Bayesian analysis and possible solutions
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Conjugate Bayesian Inference for Proportions and Means
[3] Jan 22, 2001
- Prior distributions (various choices and discussion)
- One sample problem for one proportion
- One sample problem for one mean, variance known
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- Selected pages from A. Gelman, J. Carlin, H. Stern and D. Rubin, Bayesian Data Analysis, (1995), pages 28 to 58.
- Notes from course pack.
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Practical Implementation I
[4] Jan 29, 2001
- Numerical methods, Monte Carlo integration and the Gibbs sampler for simple problems, such as normal means with and without known variance, difference between two proportions.
- Introduction to BUGS software ( Bayesian analysis Using Gibbs Sampling)
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Clinical trials
[5] Feb 5, 2001
- Design issues in clinical trials.
- Decision making during the course of a clinical trial.
- Interim analyses in clinical trials.
- Reporting Bayesian analyses in clinical trials.
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- Notes from course pack.
- D. Spiegelhalter, L. Freedman and M. Parmer. (1995). Bayesian approaches to randomized trials. Journal of the Royal Statistical Society, Series A 157:387-416.
- M. Hughes, Reporting Bayesian analyses of clinical trials, (1993), Statistics In Medicine, 1651--1663
- P. Fayers, D. Ashby, and M. Parmar, Tutorial in Biostatistics: Bayesian Data Monitoring in Clinical Trials, (1997), Statistics in Medicine 16, 1413-30.
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Practical Implementation II
[6] Feb 12, 2001
- Bayesian inference using the Gibbs sampler for linear and logistic regression.
- Missing covariate data
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- G. Casella and E. George, Explaining the Gibbs Sampler, (1992), American Statistician, 167--174
- Notes from course pack.
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Special Topics
[7] Feb 26, 2001
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