Statistics 246: Statistical Theory and Methods III
Course Announcement
Policies and Class Orientation
News
- (5/17) Class this Thursday will be given by Baoguan. Marc will be travelling for the rest of the week and will miss his OH this Friday. I, Marc, wrote very brief comments on your proposals and left them in the box outside my office. There are 6 students attempting something with GARCH. To you I request that you look at how well your estimates perform in some simulation experiment. There are a number of quite ambitious proposals. For these I hope you will budget your time. To everyone, I remind you that what is important is to try something out, to learn something, and to communicate what you learn. The papers are guides to suggest feasible projects and to help when you are stuck, but you are free to depart from them in whatever way serves the primary objectives just explained. I wish you all good luck and will be happy to try to help, but I'm not going to be available (except by infrequent email) until Sun/Mon. In the interests of time, I accept that there are not going to be any more homeworks; what I plan to do is to post solutions to an unassigned homework.
- (5/15) Still looking for a project/paper? Interested in MCMC? Try this equal-energy sampler paper or papers by Neal
- (5/11) Final project requirements posted in handouts.
- (5/2) Baoguan will hold an OH from 5-6 tomorrow (5/3). Marc will hold OH from 2-4. Homework 2 will be returned into the box outside Eck 134 (Marc's office) by 1pm.
- (4/27) Homework 3 was extended to Tuesday (5/2). You have an in-class exam on Thursday (5/4). Final projects are due Wednesday the 31st of May (5/31).
- (4/19) I am expecting Homework 2 tomorrow including problem 3. Clarification for problem 1: The problem asks you about the sampling
distribution of the simple Monte Carlo estimate. What do I mean? Well,
each time we perform a simple Monte Carlo with n samples, we get a
particular value as the estimate for the integral. I mean for you to make
a histogram representing the sampling distribution of this value. I.e.
repeat the Monte Carlo estimation procedure many times and make a
histogram of the results. Also compute the SD of the results. This
represents the actual variability of the procedure. I then ask you to
compare this with "typical Monte Carlo standard error values". That is,
with the standard error (of the sample mean) based on a single Monte Carlo
sample and the usual normal approximation. Of course, the standard error
itself is a random variable: sometimes it is too high or low. I'm asking
if it is typically a decent estimate for this problem. (To be precise, you could make a histogram of its sampling distribution as well, but that isn't required.) Remark: my
expectation is that it will be a decent estimate for the second function,
sin(x)^2, and would not be for the first (but I don't ask you to verify
this). (Why? Because the integrand has lower variance)
- (4/13) There is a general extension on Homework 2 until the 20th. The midterm is also delayed. Details will follow. Also, we'll have recitations on Weds at 5 in Eck 117 while demand lasts.
- (4/12) Homework 2 Clarification: On problem 1 you do not need to find an analytical expression for the "sin^2" case.
- (3/29) The recitation will be delayed until 5pm because of room scheduling conflicts.
- (3/28) Welcome to the new course. Page updated. Orientation edited slightly. If you need an introduction to programming in R, please attend the recitation tomorrow.
Homeworks
- HW1 (two die source) (due Thurs April 6) (solution)
- HW2 (due Thursday April 20th) (solution)
- HW3 (due Tuesday May 2nd) [P.S. problem 3 is complete.] (solution)
Lectures
Other Handouts
Recitations
(As announced below)
- R programming lecture notes here.
- Computing in R for beginners: Wed. March 29 at 5pm in Eckhart 117
- Computing in R 2: Wed. April 19th at 5pm in Eckhart 117
- And so on for subsequent Wednesdays while demand lasts.
Contact Information
- Marc Coram: Eckhart 134. OH Fri 3-4. (773) 702-9095
[Visiting me at other times is preferable to having to write long emails]
- Baoguan Ke: OH Mon 3-4 in Eck 131
Course Text:
Computational Statistics, Givens and Hoeting. Wiley 2005
Midterm/Quiz:
Midterm in class on Thursday April 20th. You may bring 1 page of notes (two-sided). Tentative Topics: calculation of Gibbs updates, of conditional densities, of transformed densities, of Metropolis-Hastings ratios, random walk on graphs, Bayes rule.
References for Course Material
Rice : Mathematical Statistics and Data Analysis
G&H : Givens & Hoeting, Computational Statistics
* Joint Distribution & Conditional Distribution : Rice, p.69-86
* Maximum Likelihood Method : Rice, p.253-258 ; G&H, p.9-10
* Sufficient Statistics : Rice, p.280-284
* Exponential Family : Rice, p.283
* Markov Chain : G&H, p.14-17
and Introduction to Probability Model, Academic Press, 7th Ed. 2000
* Chapter 7 of G&H (some of ch 8)
Links: