Statistics 601: Advanced Statistical Methods
Fall 2012
Instructor: Mark S. Kaiser
Office: 3411 Snedecor
Email: mskaiser@iastate.edu
TA: Wei Zhang
Office:
Email:
Lectures: MWF 11:00-11:50 Molecular Biology 1428
Labs: W 1:10-3:00 Snedecor 1105
Lecture and Lab Notes: Available for purchase at Copy Works on Welch Ave.
Grading: There will be assignments, at least one in-class exam, and either a final or class project
Topic Outline
1. Introduction
1.1. Concepts of Probability
1.2. Approaches to Statistical Analysis
2. Randomization
2.1. Populations and Population Units, Attributes and Responses
2.2. The Experimental Approach
3. Modeling Concepts
3.1. Abstraction, Random Variables, Distributions
3.2. Classes of Distributions; Exponential Families, Exponential Dispersion Families,
Location-Scale Families
3.3. Objectives of Analysis
4. Additive Error Models
4.1. Constant Variance Models
4.2. Known Variance Parameters
4.3. Unknown Variance Parameters
5. Models Based on Response Distributions
5.1. Random and Systematic Model Components
5.2. Generalized Linear Models
6. Models with Multiple Random Components
6.1. Mixed Models
6.2. Hierarchical Models
6.3. Latent Variable Models
7. Models Based on Stochastic Processes
7.1. Random Fields and Stationarity
7.2. Time Series Models
7.3. Markov Random Field Models
8. Basic Frequentist Estimation
8.1. Moment-Based Estimators
8.2. Least Squares
8.3. Basic Likelihood
9. Modified and False Likelihoods
9.1. Profile Likelihoods
9.2. Marginal/Conditional Likelihoods
9.3. Quasi-Likelihood and Estimating Equations
9.4. Pseudo-Likelihoods
9.5. Composite Likelihoods
10. Parametric Bootstrap
10.1.
Comparison Functions and Bootstrap Basics
10.2.
Basic and Percentile Intervals
11. Model Assessment
11.1.
Residuals
11.2.
Cross Validation
11.3.
Simulation-Based Model Assessment
11.4.
Issues in Model Assessment
12. Basic Bayes
12.1.
Bayesian Paradigms
12.2.
Sequential Bayes
12.3.
Prior Distributions
12.4.
Bayes Factors
12.5.
Posterior Predictive Model Assessment
13. Simulation of Posterior Distributions
13.1.
Fundamental Principles of Simulation
13.2.
Basic Simulation Methods
13.3.
Markov Chain Samplers – Metropolis and Gibbs
13.4.
Monitoring Convergence
Iowa State University complies with the American with Disabilities Act and Section 504 of the
Rehabilitation Act. Any student who may require an accommodation under such provisions
should contact the instructor as soon as possible and no later than the end of the first week of
class or as soon as you become aware. No retroactive accommodations will be provided in this
class. Please make sure that Disability Resources staff members send a SAAR form verifying the
disability and specifying the accommodation needed. The Disability Resources office is located
on the main floor of the Student Services Building, Room 1076, 515 294-7220.