Fall, 2014 STA 705 - 001 Advanced
Computational Inference
Instructor: Dr. Mai Zhou
Office: MDS 343, Mailbox: MDS , Phone: 257-6912,
E-mail:
mai@ms.uky.edu, Web page (this page):
http://www.ms.uky.edu/~mai/sta705.html
Office Hours: TBA or by appointment.
Class: MWF 10:00 AM -- 10:50 AM at MDS 335. Final exam
time
Prereq: STA 605. STA 701
Course description:
The language of choice is R. Download a copy of R onto your own computer.
Making of R packages.
Numerical Optimization. EM Algorithm.
Resampling Methods including Bootstrap and Jackknife and more. Second order optimality of bootatrap.
Techniques in generating pseudo random numbers,
Markov Chain Monte Carlo Methods.
Simulations.
Generate random variable from a model.
High dimensional regression model: LASSO and PGA/OGA.
Reference books: (No one book
fits all our needs. I will draw materials from several books)
Numerical Optimization
by Nocedal and Wright. Springer 1999. (for Newton method etc)
An
Introduction to the Bootstrap by Efron and Tibshirani.
Chapman Hall/CRC 1993. (for bootstrap)
Bootstrap Methods and their
Applications
by Davison and Hinkley. Cambridge Univ. Press, 1997.
(more theoretical) The
bootstrap and Edgeworth Expansion by P. Hall. Springer
1992.
Monte Carlo Strategies in Scientific
Computing by J. Liu (2001) (for mcmc)
An Introduction
to R (this is included in the R download.)
A simple R package: MLEcauchy (under R-3.1.1 still have some warnings)
Useful Lecture Notes:
Rounding Error in R or other language, 2 3
EM 0 1 2 3 4 5 6 7
MLE 1 2 (spatial) 3 (spatial) 4(MLE of Cauchy)
MCMC: A simple example all in R; A longer example, using mcmc package here; Some notes. Some theoretical bases for MCMC 2.
R programming 1 2 (also example of Newton)
Newton method 1
Notes on S programming: 1
The bootstrap/re-sampling methods part is in another place: my sta662 notes
Old links (some may not work):
Simple example
el.test.3.R
el.test.simple
Notes from Iowa State U
A Chapter on Numerical Maximization
A book chapter on Matroplis Algorithm:
Free download
Example of EM
Computing: We not only going to
cover the practical side of the computing, but also the theoretical
side. Like the second order correctness
of bootstrap approximation. This is where you need Sta 701. The ability to
program software code and run them on computer is essential to this
course.
Some examples
of statistical/mathematical packages useful are: R/Splus, SAS, MatLab,
LimDep, Gauss, Ox etc. We mainly use R in this course.
Grading: Homework 35%; Two
Projects 25%; Midterm 20%; Final 20%.
Tentative
Topics/timeline
Homeworks.
References: Focus on equation (1), and ignor the w(r) and delta for the
time being.
Smoothed Rank
Regression.
Example of SQP
R function for one iteration of nonparametric EM regression
Example of bootstrap regression, 1
2
and 3
Some tips about
efficient R programming
Typesetting with Latex: including graph in the LaTeX and output PDF
University of Kentucky LaTeX Dissertation templatePh.D. Dissertation
Example of calling C from R: Example
Example of making an R package: Example
Toy Data ZhouM2 and some Note
High Dim Regression Example: 1, 2, 3
Q2
Central Limit Theorem ---> Edgeworth Expansion (Berry-Essen bound) ---> Bartlett Correction
---> Bootstrap Approximation. For mean, for censored data Hazard. for empirical likelihood ratio.