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STT 461: Computations in Probability and Statistics

MWF, 11:30 am- 12:20 pm, 314 Ernst Bessey Hall

In this course we will cover computational methods commonly used in statistics, including algorithms used for fitting and non-linear regressions, maximum likelihood estimation, simulation of random variables, bootstrap, cross-validation and algorithms for implementing high dimensional regressions.

Instructor: Hyokyoung G. Hong. (hhong@msu.edu)

Office hours: Mon and Wed: 2:00 pm- 3:00 pm Wells Hall C435

TA: Jialin Qu (qujialin@stt.msu.edu)

Software: The course will be mostly based on R.

Approach: Although the focus of the course is on computational methods, for each topic we will first describe the problem from a statistical perspective. If they exist, exact analytical solutions will be discussed and implemented. Otherwise numerical methods will be presented. Derivations will be presented in class and students are expected to take their own notes. Scripts for computations will be developed in class and a summary will be posted in this repository. Students are expected to bring their own laptops. If you do not have access to a laptop, please check with the instructor to get access to one.

Evaluation: The evaluation will be based on biweekly HW and two in-class exams.

Textbook: There is no required textbook. However, the following are good textbooks that will guide you learning about statistical analyses in R.

Statistical computing with R. Maria L. Rizzo, Chapman & Hall

An Introduction to Statistical Learning. This book covers many of the topics we will discuss.

Course Content

Note: this is a tentative list of topics, if time permits we will try to cover all of them; however, the list of topics is ambitious and we may not cover all the topics listed.

  • Quick Introduction to R

  • Matrix Algebra in R

  • Inverse CDF method pdf

  • Acceptance-rejection method pdf

  • Monte Carlo integration method pdf

  • Importance sampling pdf

  • Ordinary Least Squares: Estimation & Inference pdf * Derivation of closed-form solution * Computation using lm, lsfit * Computing estimates, SEs and p-values using matrix operations * Transformation

  • Logistic regression: Estimation & Inference pdf * Odds and odds ratio * Likelihood * Computation using glm

  • Bootstrap pdf * Inclass assignment pdf patch csv

  • Example 2 pdf

  • Permutation pdf

  • Inclass assignment pdf

Homework

  • HW1

  • HW2

  • HW3 (pdf) (rmd)

  • HW4 (pdf) (rmd)

  • HW5 (pdf) (rmd) Note: (1) the correction of 1) in Problem 1. Richness>3 -> Richness>40
    (2) The value of phat=mean(c(t0,reps)>=t0) is the porportion of replicates Tstar that are at least as large as the observed test statistic (an approximate p-value). For a two-tail test the empirical p-value is 2*phat if phat<=0.5 (it is 2(1-phat) if phat>0.5).

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