Issues in Biostatistical Analysis

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since 13 August 1999 |

Lecture schedule --- Info on students ---- Homework --- 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.

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

**Instructor:** Bruce Walsh:

- office: LSS 327A
- phone: 621-1915
- Office hours -- by appointment
- Home page
- e-mail (jbwalsh@u.arizona.edu)

This is the lecture schedule from the last time the course was taught. WHile all of the below topics will be covered, I also plan to add some news ones, such as logistic regression, and generalized linear models.

DATE | DAY | LECT# | TOPICS | HANDOUTS |

14-Jan | Th | 1 | Overview: Probabilities, Variances, Covariances | Univariate Distributions, Bivariate Distributions |

18-Jan | Tu | 2 | Normal, t, Chi-square, F distributions | Distributions of functions of normals |

20-Jan | Th | 3 | Power of tests | Power |

25-Jan | Tu | 4 | Hypothesis testing | |

27-Jan | Th | 5 | Matrix algebra 1: addition, multiplication | Intro. to matrix algebra and linear models |

1-Feb | Tu | 6 | NO CLASS (in Washington DC) | |

3-Feb | Th | 7 | Matrix algebra 2: Inversion and the Multivariate Normal | |

8-Feb | Tu | 8 | Matrix algebra 3: Eigenstructure. Principal Components | Eigenstructure Notes |

10-Feb | Th | 9 | General linear model (GLM)1: OLS | General linear models |

15-Feb | Tu | 10 | GLM 2: GLS | |

17-Feb | Th | 11 | GLM 3: hypothesis testing | |

22-Feb | Tu | 12 | GLM 4: ANOVA | ANOVA |

24-Feb | Th | 13 | GLM 5: Mixed Models | Mixed Models, BLUP |

29-Feb | Tu | 14 | Maximum Likelihood (ML) 1: Introduction | MLE and Likelihood ratio tests |

2-Mar | Th | 15 | NO CLASS (Meeting in DC) | |

7-Mar | Tu | 16 | ML 2: likelihood ratio tests and asymptotics | |

9-Mar | Th | 17 | ML 3: Mixture models | Mixture Models |

14-Mar | Tu | SPRING BREAK! | ||

16-Mar | Th | SPRING BREAK! | ||

21-Mar | Tu | 18 | ML 4: Variance component models | REML |

23-Mar | Th | 19 | Resampling methods 1: Randomization and the Jackknife | Resampling methods |

28-Mar | Tu | 20 | Resampling methods 2: The Bootstrap | |

30-Mar | Th | 21 | Bayesian methods: 1: Introduction | Bayesian methods |

4-Apr | Tu | NO CLASS (Seminar in Florida) | ||

6-Apr | Th | NO CLASS (Seminar in Florida) | ||

11-Apr | Tu | 22 | Bayesian methods: 2 Posterior information | |

12-Apr | Th | 23 | Bayesian methods: 3: Estimation and hypothesis testing | |

18-Apr | Tu | 24 | Expectation-maximum (EM) methods 1: Introduction | EM methods |

20-Apr | Th | 25 | EM methods 2: Treating missing data | |

25-Apr | Tu | 26 | Gibbs sampler 1: Bayesian applications | MCMC and Gibbs |

27-Apr | Th | 27 | Gibbs sampler 2: ML | |

2-May | Tu | 28 | Generalized linear models |

Problem set |
Topic |
Due date |
Solutions |

1 |
Simple Regressions | 25 Jan | PS 1 Solutions |

2 |
Power of Normal tests | 3-Feb | PS 2 Solutions |

3 |
Power and Non-central Fs | 3-Feb | PS 3 Solutions |

4 |
Multivariate Normal | 8-Feb | PS 4 Solutions |

5 |
General linear Model | 24-Feb | PS 5 Solutions |

6 |
Random-Effects ANOVA | 7 March | PS 6 Solutions |

7 |
Resampling Methods
Data: csv file |
11 April |

Patch for JMP IN 3.1.5 for Power Mac (Stuffit file, place both files in extensions folder)

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

Comprehensive list of power analysis software for microcomputers

A collection of fun data sets for analysis can be found in the Journal of Statistics Education Data Archive

Home page for RNR613:Ê , Applied Biostatistics.

. Bryan F. J. Manly (1997).**Randomization, Boostrap and Monte Carlo methods in biology (2nd ed)**David Draper. You can download a postscript file of the draft version from Draper's website**Bayesian Hierarchical Modeling**Peter M. Lee (1997).**Bayesian Statistics: An Introduction (2nd ed).**James K. Lindsey (1997).**Applying Generalized Linear Models.**Martin Tanner (1996).**Tools for Statistical Inference: Methods for exploration of posterior distributions and likelihood functions (3rd ed).**B. J. Winer, Donald R. Brown, and Kenneth M. Michels (1991).**Statistical Principles in Experimental Design (3rd ed).**Harvey Motulsky.**Intutive Biostatistics.**Robert Abelson.**Statistics as Principled Argument.**James K. Lindsey (1997).**Applying Generalized Linear Models.**Dani Gamerman (1997).**Markov chain Monte Carlo: Stochastic simulation for Bayesian inference.**Ray Hilborn and Marc Mangel (1997).**The Ecological Detective**Keenth Lange (1997).**Mathematical and Statistical Methods for Genetic Analysis**Glen Cowan (1998).**Statistical Data Analysis.**Samuel Scheiner and Jessice Gurevitch, Eds (1993).**Design and Analysis of Ecological Experiments.**