Home page for EEB 581:
Advanced Topics in Biological Statistics

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since 26 December 2005

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: is one of the most powerful and flexible statistical programs, 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.

Class textbooks/reading There is no formal textbook for the class, although there will be extensive readings for most lectures (posted as pdf files below).

You also might wish to buy one or more of the following textbooks on using R

• An introduction to R (Revised and updated). W. N. Venables, D. M. Smith, etc. 146 pages. ($14.00 on Amazon)
  • This is a very short paperback that essentially lists all of the commands in R. A nice quick reference, but little detail beyond this.
• Introductory Statistics with R . P. Dalgaards.
  • Nice review of basic statistical applications using R. Paperback, 267 pages. ($35.00 on Amazon)
• Using R for Introductory Statistics J. Verzani.
  • More extensive that Dalgaards, with good discussions on programming. Hardback, 414 pages ($41.00 on Amazon)
• Statistical computing: An introduction to Data Analysis using S-plus (S+ is essentially R). M. J. Crawley.
  • A much more comprehensive introduction to R/S+ with lots of examples. Hardback, 760 pages ($87.00 on Amazon)

Meeting time and Place: Tuesday and Thursday, 9:30 a.m. -10:45 a.m. LSS 340

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)

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)

DATE	Day	Lect. #	Topic	Handouts	Problem Sets
12 Jan	Thursday	1	Overview: Probabilities and Probability Distributions	Univariate Distributions
17 Jan	Tuesday	2	Overview: Univariate distributions		PS 1
19 Jan	Thursday	3	Overview: Bivariate distributions	Bivariate Distributions
24 Jan	Tuesday	4	Normal, t, Chi-square distributions	(1): Distributions of functions of normals, (2): R as a basic statistical calculator	PS 1 Solutions
26 Jan	Thursday	5	F distributions		PS 2
31 Jan	Tuesday	6	Power of tests 1: Normals	(1): Power, (2): Simple power calculations in R	PS 2 Solutions
2 Feb	Thursday	7	Power of tests 2: Fixed Effects ANOVAs
7 Feb	Tuesday	8	Power of tests 3: Random Effects ANOVAs		PS 3
9 Feb	Thursday		No class, Walsh at NIH	Central Limit theorem problem	PS 4
14 Feb	Tuesday	9	Matrix algebra 1: addition, multiplication	(1): Intro to Matrix Algebra and linear models (2): Matrix Calculations in R	PS 3 due
16 Feb	Thursday	10	Matrix algebra 2: Inversion and the Multivariate Normal		PS 4 due
21 Feb	Tuesday	11	Matrix algebra 3: The Multivariate Normal
23 Feb	Thursday	12	Matrix algebra 3: The Multivariate Normal		PS 5
28 Feb	Tuesday	13	General linear model (GLM) 1: OLS	General linear Model Summary of GLM results	PS 5 due
2 March	Thursday	14	GLM 2: Generalized inverses, systems of equations	Generalized inverses	PS 6
7 March	Tuesday	15	GLM 3: Geometry of matrices, PC	matrix Eigenstructure	PS 7 PS 6 due
9 March	Thursday	16			PS 7 due
14 March	Thursday		Spring Break
16 March	Thursday		Spring Break
21 March	Tuesday	17
23 March	Thursday	18			PS 8 due
28 March	Tuesday	19	Maximum Likelihood estimation, Likelihood ratio tests	MLEs	PS 9
30 March	Thursday		No class, Walsh at UCSF
4 April	Tuesday	20	Generalized Linear models	Generalized Linear models	PS 9 due
6 April	Thursday		No class, Walsh seminar at University of Florida
11 April	Tuesday	21	Resampling methods 1: Randomization and the Jackknife	Resampling methods
13 April	Thursday	22	Resampling methods 2: The Bootstrap	Bootstrap and Jackknife in R	PS 10
18 April	Tuesday	23	Multiple comparisons: 1: Sequential Bonferroni corrections and the False Discovery Rate	Multiple comparisons
20 April	Thursday	24	Multiple comparisons: 2: the False Discovery Rate		PS 10 due
25 April	Tuesday	25	Bayesian methods: Introduction	Bayesian methods
27 April	Thursday	26	Bayesian methods: Advanced topics
2 May	Tuesday	27	MCMC methods	MCMC and Gibbs Sampler The Metropolis-Hastings Sampler in R

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).