STAT/BOT 5380: Bayesian Data Analysis

Fall 2008

Office

Office hours

Final exam

Software

Classroom

Meeting time

Aven Nelson (AV) 107B

Wed 2:00-3:30 pm and Thur 1:00-2:30 pm or by appointment

Thur, Dec 11, 10:15 am - 12:15 pm

WinBUGS (free software): download & install WinBUGS 1.4.3

Anthropology 335 (new building, north of Engineering, on Lewis St.)

Tues, Thur 11:00 am - 12:15 pm

Week

Lecture and assignment topics

• Course overview
  • Goals, assignments, prerequisites, and expectations
  • PDFs: Syllabus
• Basic overview of probability
  • Review of probability concepts and rules
  • Bayes' rule
  • Conditional, marginal, and joint probability
  • Readings: Bolker (2008) Chapter 4 on "Probability and statistical distributions for ecological modeling"; additional e-chapters can be downloaded from Bolker's Web page (or, your can purchase the book; it's relatively cheap, but not required).
  • PDFs: Lecture 1, Calculus review (for your reference, not to be covered in class)
• Distributions functions
  • Random variables
  • Cummulative probability functions
  • Probability density and mass functions
  • PDFs: Lecture 2

• Common distributions functions (cont.)
  • Discrete distributions
  • Continuous distributions
  • PDFs: Lecture 3 (part 1: discrete), WinBUGS hand-out, Lecture 3 (part 2: continuous)
• Assignment #1 (pdf): due Thur, Sept 11

• Common distributions functions (cont.)
  • Continuous distributions (Lecture 3, part 2)
• Bayesian inference overview
  • Basics of statistical inference
  • Extension of Baye's rule to Bayesian inference
  • Readings: BDA Chpt 1
  • PDF: Lecture 4
• Single-parameter models and priors
  • Binomial example
  • Summarizing the posterior
  • Relationship to maximum likelihood
  • Conjugate priors
  • PDF: Lecture 5

• Single-parameter models and priors (cont.)
  • See Lecture 5 from Sept 11
• More single-parameter models
  • Poisson example
  • Exponential example
  • PDF: Lecture 6
• Assignment #2 (pdf): due Tues, Sept 23, SOLUTIONS

• LAB 1: Mond Sept 22, bring hand-out
• Intro to mulit-parameter models
  • Multinomial example
  • Normal example
  • PDF: Lecture 7
• More on choosing priors
  • Priors under different parameterizations
  • Transformation of variables
  • Non-informative/informative, Jeffery's, and proper/improper priors
  • PDF: Lecture 8
• Assignment #3 (pdf): due Thur, Oct 2, in class, CORRECTIONS: don't do problem 3 (i.e., exercise 7 in BDA, pg 97); in problem 2, parts a and b should be corrected such that phi = theta*(b-a) + a

• LAB 2: Mond Sept 29, bring hand-out and download data for lab: Biomass data v1 and Biomass data v2; New: Example code from in-class lab demo
• Introduction to computational approaches
  • Numerical methods for estimating the posterior
  • Overview of Markov chain Monte Carlo (MCMC)
  • PDF: Lecture 9

• Assignment #4 (pdf) and BeeData; due Mond Oct 13 by 5pm: SOLUTIONS: written parts and WinBUGS code
• No lab this week
• Introduction to hierarchical modeling
  • Hierarchical priors
  • Exchangeability
  • Graphical models
  • PDF: Lecture 10

• LAB 3: Mond Oct 13, bring hand-out and download data for lab, which is in a WinBUGS odc file: OrangeGrove data, and please bring any questions from Hmwk #4 regarding WinBUGs issues
• Introduction to hierarchical modeling (cont.)
  • See lecture 10 from last week
• Mid-term exam (Thur, Oct. 16)
  • Take-home portion: Exam problem (pdf) and data (pinusSLA)

• No lab this week
• Bayesian regression models
  • Overview
  • Simple linear regression example
  • PDF: Lecture 11 part I
  • Model checking
  • Transformations
  • Incorporating different types of covariates and interactions
  • PDF: Lecture 11 part II
• Assignment #5 (pdf) and microbe data (text or Excel formats); due in-class, Thur Oct 30. SOLUTIONS (mostly complete): part b and WinBUGS file with model and answers to remaining problems

• LAB 4: Mond Oct 27, bring hand-out and download data (in a WinBUGS odc file)
• Hierarchical linear models
  • Random & fixed effects
  • Sum-to-zero and sweeping for random effects
  • PDF: Lecture 12
  • Supplementary reading: See Gilks & Roberts chapter on strategies for modeling random effects in Bayesian models; sections 6.1 - 6.2.5 (i.e. thru page 97) are very useful.

• LAB 5: Mond Nov 3, view/print hand-out and download WinBUGS code
• Generalized linear models
• • Link functions
  • Poisson & binomial data examples
  • PDF: Lecture 13
• Nonlinear models
  • Modeling building and implementation
  • Model reparameterization
  • PDF: Lecture 14
• Assignment #6 (pdf) and salamander data (Amphibian WinBUGS file); due in-class, Thur Nov 13. Please read all directions carefully before starting the assignment. SOLUTIONS: problem 1 and WinBUGS file with model and answers to remaining problems.

• No lab this week
• Nonlinear models (cont.)
  • See Lecture 14
• Measurement error models
  • Measurement errors in covariates
  • Berkson model
  • PDF: Lecture 15
  • Supplementary reading: Dellaportes & Stephens (1995) Bayesian analysis of errors-in-variables regression models. Biometrics 51:1085-1095.

• LAB 6: Mond Nov 17, nonlinear model with reparameterization by sweeping; hand-out and WinBUGS code.
• Model comparison (2nd part of Lecture 15)
  • Deviance information criteria (DIC)
  • Posterior predictive loss
  • PDF: Lecture 15 addendum and WinBUGS example
  • Supplementary readings: Spiegelhalter et al. (2002) Bayesian measures of model complexity and fit. Journal Royal Statistical Society B 64:583-639; Carlin et al. (2006) Elements of hierarchical Bayesian inference. In: Clark & Gelfand (Eds.) Hierarchical Modeling for the Environmental Sciences: Statistical Methods and Applications. Oxford Univ. Press; sections 1.3.3.2 & 1.3.3.3 most relevant.
• Hierarchical Bayesian models (or, the "process sandwich")
• • The "process model" and "process error"
  • PDF: Lecture 16
• Parameter expansion & hierarchical variance models
• • Parameter expansion
  • PDF: Lecture 17
  • Supplementary readings: Gelman (2006) Bayesian Analysis, 1:515-533. Gelman (2004) Journal of the American Statistical Association, 99:537-545.
• Assignment #7 (pdf) and data (daphnia WinBUGS file); due in-class, Tues Nov 25. SOLUTIONS: WinBUGS file with model and answers to each problem.

• LAB 7: Mond Nov 24, Berkson model, posterior predictive loss, and parameter expansion; hand-out and WinBUGS code
• Parameter expansion & hierarchical variance models (cont. Lecture 17)
• • Alternative priors for hierarchical variance terms
  • Hierarchical modeling of variance terms
• Real examples of Bayesian and hierarchical Bayesian models
  • Vulnerability of plant stems & roots to drought stress: A nonlinear, hierarchical model with stochastic process errors (supp. reading: Ogle et al.); Powerpoint slides (pdf) and WinBUGS code (pdf)

• No lab this week
• Real examples of Bayesian and hierarchical Bayesian models
• • Vulnerability to caviation example, cont.
  • Bayesian meta-analysis of specific leaf area for 305 tree species; Powerpoint slides (pdf)
  • Implications of vulnerability to hurricane damage for long-term survival of tropical tree species (supp. reading: Ogle et al. 2006); Powerpoint slides (pdf)

• Final exam