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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
Instructor: Bruce Walsh:
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)
pdf files of The official R Manuals
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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, | |
27 Jan | Tuesday | 4 | Power of tests 1: Normals | (1): Power, | |
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 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 |
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.