|
|
A-Z Index | Campus Map | Phonebook | Calendars |
STAT 675 − Statistical Computing
Prerequisite(s): STAT 566/MATH 566, or equivalent, and knowledge of a computer programming language such as R, FORTRAN, Python, or C/C++.
Description: Techniques of advanced computational statistics. Numerical optimization and integration pertinent for statistical calculations; simulation and Monte Carlo methods including Markov chain Monte Carlo (MCMC); bootstrapping; smoothing/density estimation; and other modern topics.
This course in Statistical Computing provides graduate students in statistics, biostatistics, mathematics, and related disciplines with with the modern methodologies and issues associated with computational statistics. The course strikes a balance between theoretical foundations and computational implementation.
Spring 2022
The textbook is Statistical Computing with R, 2nd edition (2019) by Maria L. Rizzo. Additional online resources are available at the book's Github Site. The course syllabus gives complete information.
Attendance
This course is presented online, via your D2L access site.
Homework Assignments - Spring 2022
Homeworks are based on exercises from the textbook.Homeworks are due as assigned. No exceptions.
These assignments are subject to revision with prior notice.Textbook Date due Chapters Exercises --------------------------------------------------------------- Feb. 17 (10 points) 13 1,4,6 14 External exercises A,B Mar. 1 (15 points) 3 1,4,8,9*,11,12,14,18* Mar. 18 3,13,14 Midterm Exam May 4 (25 points) 6 1,3,6,7,14 8 4, 5(basic, perc., BCa only), 8, 9*, 10(find the data here) 11 2, 8(use θ~U(0,1) for prior), 9, 11 12 1, 7, 8, 9 May 6 Comprehensive Final Exam * problem optional
Specialized Downloads - Spring 2022
Textbook Errata List.
Sample R code for gamma distn. MLE via 1-d uniroot() solution as in Example 14.2 and via 2-d optim() solution as in Example 14.3, applied to Cordeiro-Simas (2009) data.
Sample R code for missing-data exponential distn. MLE via EM algorithm as in Example 14.A.
Sample R code for RNG for X~Beta(2,2) in Example 3.7, including Q-Q plot and Kolmogorov-Smirnov test.
Sample R code for RNG for X~Beta(3,2) in Example 3.8, including Q-Q plot and Kolmogorov-Smirnov test.
Sample R code for exploration of Monte Carlo integration in Example 6.2.
A short commentary on Antithetic variables for Monte Carlo integration.
Sample R code for stratified sampling in Example 6.13.
Sample R code for empirical c.d.f. in Example 8.1.
Sample R code for bootrapping a correlation coefficient for the Law School data in Example 8.3.
Sample R code for jackkinfing a correlation coefficient for the Law School data in Exercise 8.1.
Sample R code for BCa intervals with jackkinfe-based acceleration for the Law School data in Example 8.A.
Sample R code for quadratic regression analysis with the ironslag data in Example 8.17.
Sample R code for MCMC Beta-Binomial Bayesian analysis with an Exponential prior and an Exponential proposal in Example 11.A.
Illustrating the vagaries of Metropolis-Hastings Markov chain generation: different trace plots and histograms for the same model (Maxwell target with Exponential proposal).
Sample R code for Average Shifted Histogram (ASH) density estimator in Example 12.6.
Sample R code for kernel density estimator (KDE) in Example 12.7.
Sample R code for 2-D kernel density estimator (KDE) in Example 12.15.
Selected online encyclopedia entries on statistical computing (access requires the University Library's online subscription):
Background on pseudo-random number generation and generation of pseudo-random variables. Aspects of Monte Carlo simulation and numerical integration. Features of bootstrap and jackknife resampling methods. Markov chain Monte Carlo (MCMC) methodology and algorithms. Background on density estimation and kernel methods. Various methods of numerical analysis, including root finding, optimization, and the EM Algorithm.
Slides by C. Robert and G. Casella on Monte Carlo methods with R.
Slides by Q. Fang on Diagnostics for MCMC burn-in.
Some comments by C. Geyer on the difficulties with MCMC diagnostics.
General R Language Downloads/Links
Suggested reading: The R Guide, ver. 2.5
R language comprehensive archive
R language FAQ page
R language online introduction
The views and opinions expressed in this page are strictly those of the page author. The contents of the page have not been reviewed by the University of Arizona.