Biostat 25OC - UCLA (Spring 2023) - Syllabus.pdf
Schedule of Lectures
(04/03) Introduction - Multivariate Normal Regression - Basic Concepts and Distribution Theory [Lecture.pdf - recording] {Anderson Ch. 8 - Izenman Ch 6}
(04/05) Testing General Linear Hypotheses - [Lecture.pdf - recording] {Anderson Ch. 8 - Seber Ch 8}
(04/10) Inference for MNLM - [Lecture.pdf - recording] {Anderson Ch 8 - Rowe Ch 8}
(04/12) Introduction to Longitudinal Data Analysis - [Lecture.pdf - recording] {Wakefield Ch 8}
(04/17) Inference for Linear Mixed Effects Models - [Lecture.pdf - recording] {Wakefield Ch 8}
(04/19) Generalized Linear Mixed Effects Models - [Lecture.pdf - recording] {Wakefield Ch 9}
(04/24) Hierarchical Bayesian Analysis of Longitudinal Data - [Lecture.Rmd - Lecture.pdf - recording] {Wakefield Ch 9}
(04/26) Review and Examples - [Lab.Rmd]
(05/01) Marginal Models for Longitudinal Data (GEE) - [Lecture.Rmd - Lecture.pdf] {Wakefield Ch 2}
(05/03) Midterm
(05/08) Linear Dimension Reduction (PCA) [Lecture.pdf]
(05/10) Latent Variables and Factor Analysis [Lecture.pdf - recording]
(05/15) Introduction to Discriminant Analysis [Lecture.pdf - recording]
(05/17) Introduction to Clustering [Lecture.pdf - recording]
(05/22) Review of Midterm [Slides.pdf]
(05/24) Conditional Independence and Graphical Models [Slides.pdf - recording]
(05/29) Memorial Day Holiday
(05/31) Parametrization and Inference in Graphical Models [Slides.pdf - recording]
(06/05) Introduction to Copula Modeling [Slides.pdf - recording]
(06/07) Review + Office Hour [Notes.pdf]
Coursework
5 HW Assignments 40%
Midterm (5/03) 30%
Take-Home Final Due (6/13) 30%
Reading List
(Recommended Textbooks)
Anderson T.W., An Introduction to Multivariate Statistical Analysis. Wiley Series in Probability and Statistics.
Izenman A.J., Modern Multivariate Statistical Techniques. Regression, Classification and Manifold Learning. Springer.
Seber G., Multivariate Observations. Wiley Series in Probability and Statistics.
Mardia, Kent and Bibby, Multivariate Analysis. Academic Press.
Rowe, Multivariate Bayesian Statistics. Chapman and Hall.
Diggle, Heagerty, Liang and Zeger, Analysis of Longitudinal Data. Oxford.
Hoff, P., A first Course in Bayesian Statistical Methods. Springer
Drton, M., Sturmfels, B and Sullivant, S. Lectures on Algebraic Statistics. Springer
(Longitudinal Data Analysis Textbooks)
Diggle, PJ, Heagerty, P, Liang KY and Zeger SL (2002). Analysis of Longitudinal Data. Oxford University Press.
Weiss R., Modeling Longitudinal Data. Springer Texts in Statistics.
Fitzmaurice GM, Laird, NM and Ware JH (2004). Applied Longitudinal Analysis. Wiley.
Verbeke, G and Molenberghs, G (2000) Linear Mixed Models for Longitudinal Data. Springer-Verlag.
Wakefield, J. (2012) Bayesian and Frequentist Regression Methods. Springer.
(Journal Articles)
Mixed Effects Models
Sartori, N. and Severini, T.A. (2004). Conditional Likelihood Inference in Generalized Linear Mixed Models. Statistica Sinica, 14, 349-360.
Breslow, N.E. and Clayton, D.G. (1993). Approximate Inference in Generalized Linear Mixed Models. JASA, 88, 125-134.
Liard, N.M. and Ware, F. (1982). Random Effects Models for Longitudinal Data, Biometrics, 38, 963-974.
Lindstrom, M., & Bates, D. (1988). Newton-Raphson and EM algorithms for linear mixed effects models for repeated measures data. JASA, 83,1014 1022.
GEE
Liang, K-Y. and Zeger S.L. (1986). Longitudinal Data Analysis Using Generalized Linear Models. Biometrika, 73, 12-22.
Prentice, R.L. (1988). Correlated binary regression with covariates specific to each binary observation. Biometrics, 44, 1033-1048.
Pepe, M. S. and Anderson, G.L. (1994) A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data. Communications in Statistics - Simulation and Computation, 17, 1155-1171.
Zhao L. P. and Prentice R.L. (1990). Correlated binary regression using a quadratic exponential model. Biometrika, 77, 642-648.
Classic Multivariate Analysis
Eaton, M.L. and Perlman, MD. (1973). Non-Singularity of Generalized Sample Covariance Matrices. Annals of Statistics, 1 (4), 710-717.
Okamoto, M. (1973). Distinctness of Eigenvalues of a Quadratic Form in a Multivariate Sample. Annals of Statistics, 1 (4), 763-765.
Graphical Models
Jordan, M. I. (2004). Graphical Models. Statistical Science, 19 (1), 140-155.
Dawid, P. (1979). Conditional Independence in Statistical Theory. JRSS B, 41, 1, 1-31.
Lauritzen, S.L. and Spiegelhalter, D.J. (1988). Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems. JRSS B, 50, 2, 157 - 224.
Arnold, B.C. and Press, J. (1989). Compatible Conditional Distributions. JASA, 84, 152-156.
Gelman, A. and Meng, XL. (1991). A Note on Bivariate Distributions that Are Conditionally Normal. The American Statistician, 45 (2), 125-126
Besag, J. (1974). Spatial Interaction and the Statistical Analysis of Lattice Systems. JRSS-B, 36, 192-236.
Computing
Recommended computing for Biostat 251 will be based on the R programming language.
For more information please visit (http://cran.r-project.org/).