Lawrence Joseph
Bayesian statistics


Please Note: Prof. Joseph has retired.
These pages are left up in case they prove
useful, but the pages and software will
no longer be updated. All material and
software is "as is" with no guarantees
of functionality or correctness.
Course Outline
Introduction
[1] Sept 5
  • course description and evaluation
  • introduction to statistical analysis in medicine
  • math background
  • Colton
    • Chapter 1 pp 1--7
  • Moore and McCabe
    • Not covered.
  • Armitage and Berry
    • Chapter 1 pp 1--4
Data Summaries and Descriptive Statistics
[2] Sept 7 - Sept 12
  • types of data
  • histograms
  • stemplots
  • boxplots
  • means
  • medians
  • variance
  • relocating/rescaling
  • Colton
    • Chapter 2 pp 11--44
    • Boxplots and stemplots not covered.
  • Moore and McCabe
    • Chapter 1 pp 1--58
    • Chapter 2 pp 106--107
  • Armitage and Berry
    • Chapter 1 pp 4--40
    • Boxplots, stemplots not covered
Probability and Probability Distributions
[3] Sept 14 - Sept 21
  • laws of probability
  • discrete and continuous random variables
  • expectation and variance of r.v.'s
  • diagnostic tests and conditional probabilities
  • Bayes Theorem
  • Normal distribution
  • area under Normal curve
  • binomial distribution
  • Normal approximation to the binomial
  • Poisson distribution
  • Colton
    • Chapter 3 pp 63--92
  • Moore and McCabe
    • Chapter 1 pp 64--79
    • Chapter 3 pp 267--275
    • Chapter 4 pp 287--357
    • Chapter 5 pp 374--390
    • Diagnostic tests not covered
  • Armitage and Berry
    • Chapter 2 pp 41--77
    • Chapter 16 pp 522--525
Inference Concerning Means
[4] Sept 26 - Oct 19
  • random sampling
  • hypothesis testing for means
  • type I and type II errors
  • p-values
  • confidence intervals for means
  • t distribution
  • paired and unpaired samples
  • Bayesian inference
  • sample size calculations and power
  • Colton
    • Chapter 4 pp 99--146
    • Bayes not covered
  • Moore and McCabe
    • Chapter 5 pp 397--405
    • Chapter 6 pp 432--493
    • Chapter 7 pp 502--555
    • Bayes not covered
  • Armitage and Berry
    • Chapter 3 pp 78--84
    • Chapter 4 pp 93--114, 146--149
Midterm Exam
Tuesday October 24, 2000, 9:00 am - 11:00 am
  • Room N2/D2, Stewart Biology Building
Inference concerning proportions and counts
[5] Oct 26 - Nov 9
  • hypothesis testing for proportions
  • sample size calculations and power
  • paired and unpaired samples
  • chi_2-test to compare 2 or more proportions
  • Fishers exact test
  • Bayesian inference
  • Mantel-Haenzel to combine 2 x 2 tables
  • relative risk and odds ratios
  • inference for count data
  • Colton
    • Chapter 5 pp 151--183
    • Bayes, Mantel- Haenzel, relative risk and odds ratio not covered
  • Moore and McCabe
    • Chapter 8 pp 584--609
    • Fishers exact test, Bayes, Mantel-Haenzel, relative risk, odds ratios and counts not covered
  • Armitage and Berry
    • Chapter 3 pp 84--85
    • Chapter 4 pp 118--152
    • Chapter 16 pp 508-519
    • Bayes not covered
Nonparametric Statistics
[6] Nov 14 - Nov 16
  • sign test
  • Rank sum test
  • Wilcoxon signed rank test
  • CI for median
  • Colton
    • Chapter 7 pp 219--226
    • Sign test and CI not covered
  • Moore and McCabe
    • Chapter 14 (0n CDROM only)
  • Armitage and Berry
    • Chapter 13 pp 448--460
    • CI not covered
Regression and Correlation
[7] Nov 21 - Dec 5
  • difference between regression and correlation
  • scatter plots
  • linear regression
  • least squares method
  • estimation of parameters in regression
  • Bayesian inference in regression
  • basic design in regression
  • other types of regression
  • Pearson's correlation
  • Spearman's correlation
  • Colton
    • Chapter 6 pp 189--214
    • Bayes not covered
  • Moore and McCabe
    • Chapter 2 pp 126--168
    • Chapter 10 pp 660--694
    • Bayes not covered
  • Armitage and Berry
    • Chapter 5 pp 154--171
    • Bayes not covered
Final Exam
Thursday December 7, 2000, 9:00 am - 12:00 pm
  • Room 129, Education Building