Detailed_syllabus_03-22-10

Detailed_syllabus_03-22-10 - PUBH 8400 Sec 001 Richly...

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PUBH 8400 Sec 001, Richly Parameterized Models, Spring 2010 Detailed syllabus 3/22/10, Jim Hodges “RWC” is Ruppert, Wand, and Carroll’s book Semiparametric Regression . The book's web site is http://www.stat.tamu.edu/~carroll/semiregbook/ . This web site includes most of their datasets, an errata sheet (5 pages!), and computer code in SAS, WinBUGS, R/S+ and Matlab. Part I. Mixed Linear Models, per RWC Review: Read RWC Chapter 1, 2 (thru section 2.6) A. Mixed linear models in the standard formulation Reading: RWC Chapter 4 (except section 9), Chapter 16 1. The mixed linear model, standard form. Examples. 2. Doing statistics with this model a. Conventional (likelihood-based) analyses b. Bayesian analyses c. Pros and cons of the two approaches 3. A bit about computing Datasets: Pig weight data (RWC); molecular structure of a virus (Peterson et al 2001); rating vocal-fold images B. The constraint-case formulation; Lee & Nelder alternative syntax; measures of complexity Reading: Hodges (1998) sections 1, 2; Cui et al (2010). 1. The constraint-case formulation for richly-parameterized models 2. Lee, Nelder, and Pawitan’s book in 5 minutes 3. Measuring model complexity: degrees of freedom in the whole model fit; degrees of freedom for individual components of the model; residual degrees of freedom; prior distributions on degrees of freedom. C. Smoothing using penalized splines represented as mixed models Reading: RWC Chapter 3; Chapter 4 section 9; Chapter 6 sections 1-4. 1. Basics of smoothing splines: bases, knots, penalized splines, rank of smoothers. 1 3/22/10 PubH 8400/1 Richly Parameterized Models, Detailed Syllabus
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2. Penalized splines as mixed linear models; fitted values, inference, complexity. Datasets: Global mean surface temperature. D. Additive and interaction models represented as mixed models Reading: RWC Chapters 7, 8, 9; Chapter 12 sections 1-3; Hodges et al (2007). 1. Additive models (RWC Chapter 7-9), starting with the simplest such model and building up to more complicated ones by adding spline smooths for effects, curves as random effects. 2. Interactions: categorical-by-continuous (RWC Chapter 12 sections 1-3); categorical-by- categorical (smoothed ANOVA; Hodges et al (2007)) Dataset: Physical properties of pig jawbone. E. Spatial smoothing using mixed linear models Reading: Review Cui et al (2010); RWC Chapter 13 sections 1-4 1. Smoothing on a lattice: conditional autoregressive (CAR) models/priors; using a lattice smoother to smooth a spatial effect in smoothed ANOVA. 2. Two-dimensional splines: naïve x-y smoothing, penalized splines with radial basis functions Dataset: Minnesota counties three-cancer incidence data.
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