Home page for EEB 581:
Advanced Topics in Biological Statistics

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since 13 October 2003

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

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:

• office: BSW 322
• phone: 621-1915
• Office hours -- by appointment
• Home page
• e-mail (jbwalsh@u.arizona.edu)

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

• Alpha Unix (OSF/Tru64)
• Linux
• MacOS (System 8.6 to 9.1 and MacOS X)
• MacOS X (Darwin/X11)
• Windows (95 and later) Alpha Unix (OSF/Tru64)

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

• An Introduction to R (approx. 100 pages, 650kB), based on the former "Notes on R", gives an introduction to the language and how to use R for doing statistical analysis and graphics.
• Quick reference card (1 page, 60kB)
• A draft of the R language definition (approx. 60 pages, 380kB) which document the language per se. That is, the objects that it works on, and the details of the expression evaluation process, which are useful to know when programming R functions.
• Writing R Extensions (approx. 70 pages, 450kB) covers how to create your own packages, write R help files, and the foreign language (C, C++, Fortran, ...) interfaces.
• R Data Import/Export (approx. 30 pages, 270kB) describes the import and export facilities available either in R itself or via packages which are available from CRAN.
• R Installation and Administration (approx. 30 pages, 200kB)
• The R Reference Index (approx. 2145 pages, 10.5MB) contains all help files of the R base packages in printable form.

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

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.

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).