Home page for EEB 581:
Advanced Topics in Biological Statistics

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Lecture schedule --- R --- Info on students ---- Problem Sets --- a few statistics links (under construction) -- selected references (under construction)

Course information

This course is designed as a lecture course covering various topics in Statistical analysis (see below). I assume students have some modest background in statistics and we build on this by discussing a number of topics. The goal of this course is to provide students with a better feel for statistics and to be much less intimidated by methods of statistical analysis.

Course Objectives: We will introduce statistical distributions and computing the statistical power of various designs, matrix algebra useful for statistics and the general linear model, maximum likelihood estimation and testing, Bayesian Statistics, and various resampling and randomization methods. The focus is obtaining a general understanding of these statistical tools rather than which computer programs to use. Thus, the course will be somewhat more theoretical than applied, but the student will leave with a much broader understanding than a course concerned with running various statistical packages.

Math/Stats background required: Some knowledge of Calculus and a previous stats course (which introduced covariance, regression and ANOVA) is desirable.

Computer Programs: While the course focus is in basic statistical concepts, we will also introduce the R computing language. R: The most powerful and flexible statistical program, with a very large (and growing) library. Bad news: a little hard to get started on. good news: FREE!! (This is essentially S+, for those of you who have heard of this). More details are given below.

Text While the bulk of the material is introduce via class notes, we will also use Michael Crawley's book Statistical Computing

Meeting time and Place: Tuesday and Thursday, 9:30 a.m. -10:45 a.m. LSS 240

Instructor: Bruce Walsh:

The R Statistical Programming Language

The R Project for statistical Computing website

UA R users group website

US Mirror site for downloading R. Current versions for

An Introduction of R (Walsh notes)

  1. R as a basic statistical calculator for obtaining p values and plotting probability distributions (6 page pdf file).
  2. Power Calculations in R (4 page pdf file).
  3. Matrix Calculations in R (3 page pdf file).
  4. Bootstrap and jackknife in R (5 page pdf file).
  5. The Metropolis-Hastings Sampler in R (4 page pdf file).

pdf files of The official R Manuals

Lecture schedule

(VERY tentative, topics may be added/deleted per wishes of class)

/td> /td>
DATE Day Lect. # Topic Handouts
15 Jan Thursday 1 Overview: Probabilities and Probability Distributions Univariate Distributions
20 Jan Tuesday 2 Overview: Bivariate distributions Bivariate Distributions
22 Jan Thursday 3 Normal, t, Chi-square, F distributions (1): Distributions of functions of normals,

(2): R as a basic statistical calculator

27 Jan Tuesday 4 Power of tests 1: Normals (1): Power,

(2): Simple power calculations in R

29 Jan Thursday 5 Power of tests 2: Fixed Effects ANOVAs  
3 Feb Tuesday 6 Power of tests 3: Random Effects ANOVAs  
5 Feb Thursday   No class, Walsh at UAB  
10 Feb Tuesday 7 Matrix algebra 1: addition, multiplication Intro to Matrix Algebra and linear models
12 Feb Thursday 8 Matrix algebra 2: Inversion and the Multivariate Normal Matrix Calculations in R
17 Feb Tuesday 9 General linear model (GLM) 1: OLS General linear models
19 Feb Thursday 10 GLM 2: Generalized inverses  
24 Feb Tuesday 11 GLM 3: Generalized Least Squares (GLS) and Hypothesis testing  
26 Feb Thursday 12 ANOVA ANOVA
2 March Tuesday 13 Matrix algebra 3: Eigenstructure. Principal Components Eigenstructure Notes
4 March Thursday 14 Mixed Models Mixed Linear Models
9 March Tuesday 15 Generalized Linear Models Generalized Linear Models
11 March Thursday 16 Maximum Likelihood (ML) 1: Introduction MLE and Likelihood ratio tests
16 march Tuesday   Spring Break  
18 March Thursday   Spring Break  
23 March Tuesday 17 ML 2: likelihood ratio tests and asymptotics  
25 March Thursday 18 ML 3: Numerical Methods: Newton, EM  
30 March Tuesday 19 Resampling methods 1: Randomization and the Jackknife Resampling methods
1 April Thursday 20 Resampling methods 2: The Bootstrap Bootstrap and Jackknife in R
6 April Tuesday 21 Bayesian methods: 1: Introduction Bayesian methods  
8 April Thursday 22 Bayesian methods: 2 Posterior information  
13 April Tuesday   No Class (Walsh of out town)  
15 April Thursday   No Class (Walsh of out town)  
20 April Tuesday 23 Bayesian methods: 3: Estimation and hypothesis testing  
22 April Thursday 24 MCMC Methods 1 MCMC and Gibbs Sampler
27 April Tuesday 25 MCMC Methods 2 The Metropolis-Hastings Sampler in R
29 April Thursday 26 Multiple comparisons 1: Bonferroni and sequential Bonferroni corrections [ final version posted 15 May 2004 ] Multiple comparisons and the False Discovery Rate -- additional references
4 May Tuesday 27 Multiple comparisons 2: The False Discovery Rate  

Problem Sets

Problem set Topic Due date Solutions
1 Simple Regressions 22 Jan PS 1 Solutions
2 Power 3 Feb PS 2 Solutions
3 Power in Fixed and Random Effects ANOVA 10 Feb PS 3 Solutions
4 Multivariate Normal 19 Feb PS 4 Solutions
5 GLM 1 - quadratic regressions 23 Feb PS 5 Solutions
6 Generalized Inverses 2 March PS 6 Solutions  
7 Maximum Likelihood 30 March PS 7 Solutions
9 Jackknife, bootstrap 20 April PS 8 Solutions
9 Gibbs Sampler 4 May PS 9 Solutions

Selected Statistics Links

The StatLib site at the Department of Statistics, Carnegie Mellon University.

A collection of fun data sets for analysis can be found in the Journal of Statistics Education Data Archive

Home page for RNR613: , Applied Biostatistics.

Selected Statistics References

  1. Randomization, Boostrap and Monte Carlo methods in biology (2nd ed). Bryan F. J. Manly (1997).

  2. Bayesian Hierarchical Modeling David Draper. You can download a postscript file of the draft version from Draper's website

  3. Generalized, Linear, and Mixed Models. Charles E. McCullock and Shayle R. Searle. (2001).

  4. Categorical Data Analysis, (2nd Ed.). Alan Agresti. (2002).

  5. Multivaraite Statistics: A Practical Approach. Berhard Flury and Hans Riedwyl. (1988)

  6. Applied Nonparametric Statistical methods. P. Sprent. (1989)

  7. Experiments: Planning, Analysis, and Parameter Design Optimization. C. F. Jeff Wu and Michael Hamada. (2000)

  8. Statistical Analysis with Missing Data. Roderick J. A. Little and Donald B. Rubin. (2002).

  9. Bayesian Statistics: An Introduction (2nd ed). Peter M. Lee (1997).

  10. Applying Generalized Linear Models. James K. Lindsey (1997).

  11. Tools for Statistical Inference: Methods for exploration of posterior distributions and likelihood functions (3rd ed). Martin Tanner (1996).

  12. Statistical Principles in Experimental Design (3rd ed). B. J. Winer, Donald R. Brown, and Kenneth M. Michels (1991).

  13. Intutive Biostatistics. Harvey Motulsky.

  14. Statistics as Principled Argument. Robert Abelson.

  15. Markov chain Monte Carlo: Stochastic simulation for Bayesian inference.Dani Gamerman (1997).

  16. The Ecological Detective.Ray Hilborn and Marc Mangel (1997).

  17. Mathematical and Statistical Methods for Genetic Analysis Keenth Lange (1997).

  18. Statistical Data Analysis. Glen Cowan (1998).

  19. Design and Analysis of Ecological Experiments. Samuel Scheiner and Jessice Gurevitch, Eds (1993).

  20. Regression Modeling Strategies. Frank E. Harrell, Jr. (2001).