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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: 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
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
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, | PS 1 Solutions |
26 Jan | Thursday | 5 | F distributions | PS 2 | |
31 Jan | Tuesday | 6 | Power of tests 1: Normals | (1): Power, | 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 | 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 | 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 |
Problem set | Topic | Due date | Solutions |
1 | Regressions, covariances | 24 Jan | PS 1 Solutions |
2 | Confidence Intervals | 31 Jan | PS 2 Solutions |
3 | Power with z and t tests | 14 Feb | PS 3 Solutions |
4 | Power with F tests | 16 Feb | PS 4 Solutions |
5 | Basic Matrices, MVN | 28 Feb | PS 5 Solutions |
6 | Intro to GLM | 7 March | PS 6 Solutions |
7 | Generalized Inverses | 9 March | PS 7 Solutions |
8 | More GLM fun | 23 March | PS 8 Solutions |
9 | Matrix Eigenstructure | 4 April | PS 9 Solutions |
10 | Resampling Approaches | 20 April | PS 10 Solutions |
10 | MCMC | PS 11 Solutions |
data <- c(8.26, 6.33, 10.4, 5.27, 5.35, 5.61, 6.12, 6.19, 5.2, 7.01, 8.74, 7.78 , 7.02, 6, 6.5, 5.8, 5.12, 7.41, 6.52, 6.21, 12.28, 5.6, 5.38, 6.6, 8.74)