Home page for EEB 596Z:
Issues in Biostatistical Analysis

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since 18 December 2001

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

Current student information

Problem Set Five is due 28 march 2002.

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 two programs:

• JMP: A cheap, easy to use graphical stats package that does most of the basics in an easy manner.
• 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.

Meeting time and Place: Tuesday and Thursday, 8:00 am - 9:15 a.m. BSW 237

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

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). [ posted 28 Dec. 2001 ]
2. Power Calculations in R (4 page pdf file). [ posted 18 Jan 2002 ]
3. Matrix Calculations in R (3 page pdf file). [ posted 14 Feb 2002 ]

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

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

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DATE	Day	Lect. #	Topic	misc	handouts
10 Jan	Thursday	1	Overview: Probabilities, Variances, Covariances		(1): Univariate Distributions, (2): Bivariate Distributions
15 Jan	Tuesday	2	Normal, t, Chi-square, F distributions		(1): Distributions of functions of normals, (2): R as a basic statistical calculator
17 Jan	Thursday	3	Power of tests 1: Normals	Problem Set One due	(1): Power, (2): Simple power calculations in R
22 Jan	Tuseday	4	Power of tests 2: ANOVAs
24 Jan	Thursday	5	Matrix algebra 1: addition, multiplication	Problem Set Two due	Intro to Matrix Algebra and linear models
29 Jan	Tuseday	6	Matrix algebra 2: Inversion and the Multivariate Normal	Problem Set Three due	Matrix Calculations in R
31 Jan	Thursday	7	Matrix algebra 3: Eigenstructure. Principal Components		Eigenstructure Notes
5 Feb	Tuseday	8	General linear model (GLM)1: OLS		General linear models
7 Feb	Thursday	9	GLM 2: GLS	Problem Set Four due
12 Feb	Tuesday	10	GLM 3: hypothesis testing
14 Feb	Thursday	11		Walsh at NIH
19 Feb	Tuesday	12	Generalized Linear Models		Generalized Linear Models
21 Feb	Thursday	13	ANOVA		ANOVA
21 Feb	Tuesday	14	Mixed Models		Mixed Linear Models
26 Feb	Thursday	15	Maximum Likelihood (ML) 1: Introduction		MLE and Likelihood ratio tests
28 Feb	Tuesday	16	ML 2: likelihood ratio tests and asymptotics
5 March	Thursday	17	ML 3: Mixture models
12 march	Tuesday		Spring Break
14 March	Thursday		Spring Break
19 March	Tuesday	18	No Class
21 March	Thursday	19	No Class
26 March	Tuesday	20	No Class
28 March	Thursday	21	Resampling methods 1: Randomization and the Jackknife	Problem Set Five due	Resampling methods
2 April	Tuesday	22	Resampling methods 2: The Bootstrap
4 April	Thursday	23	Bayesian methods: 1: Introduction		Bayesian methods
9 April	Tuesday	24	Bayesian methods: 2 Posterior information
11 April	Thursday	25	Bayesian methods: 3: Estimation and hypothesis testing
16 April	Tuesday	26	Gibbs sampler: Bayesian applications		MCMC and Gibbs
18 April	Thursday	27	Bayesian methods: 3: Estimation and hypothesis testing
23 April	Tuesday	28	Gibbs sampler: Bayesian applications
25 April	Thursday	29			MCMC and Gibbs
30 April	Tuesday	30	Expectation-maximum (EM) methods 1: Treating missing data

Homework

Problem set	Topic	Due date	Solutions
1	Simple Regressions	17 Jan 2002	PS 1 Solutions
2	Power of Normal tests	24 Jan 2002	PS 2 Solutions
3	Power and Non-central Fs	29 Jan 2002	PS 3 Solutions
4	Multivariate normal calculations	7 Feb 2002	PS 4 Solutions
5	Univariate Maximum Likelihood	28 March 2002	PS 5 Solutions

On line Statistical tables (from UCLA) -- // -- Other statistical calculators

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

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

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

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

7. Intutive Biostatistics. Harvey Motulsky.

8. Statistics as Principled Argument. Robert Abelson. -+-+--+ +

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

10. The Ecological DetectiveRay Hilborn and Marc Mangel (1997).

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

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

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

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