Fall 2009/10
Computational Statistics - Course (52609) and Seminar (52804)
Benjamin Yakir
Mondays 14:30-16:15, Soc. 2305
Contact Info:
Announcements
Requirements
- You are required to read the relevant bibliography before class. Instructions regarding the required reading for each class are given below.
- Homework assignments will be handed during class. It is recommended that you try to address the assignments before class. Solutions to the assignments will be discussed in class and/or given on the web. It is required that you go over the solutions and understand them.
- Two take-home assignments will be given during the first semester. At the end of the course there will be a final exam. Each one of the midterm assignments will determine 20% of the final score. The final exam will determine 60% of the score.
- The second semester will be constructed as a seminar. Reading material will be assigned to the participants. The material will be present in class and related statistical issues will be investigate. The outcome of the investigation will be summarized in writting.
Bibliography
- R for Beginners by Emmanuel Paradis.
- Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy by B. Efron and R. Tibshirani (Statistical Science, 1986, Vol. 1, No. 1, 54-77). Here is an alternative link to the paper.
- Maximum Likelihood from Incomplete Data via the EM Algorithm by A. P. Dempster, N.M. Laired and D.B. Rubin (JRSS B, 1977, Vol. 39, No. 1, 1-38). Here is an alternative link to the paper.
- Explaining the Gibbs Sampler by G. Casella and E.I. George (The American Statistician, 1992, Vol. 46, No. 3, 167-174).
Here is an alternative link to the paper.
Reading
- For the class of 19-10-09: Read the the first chapter of the class notes:
on Background in Statistics and R and do Homework 1.
(A solution to the homework can be found here.)
- For the class of 26-10-09: Read the the Section 1 and 2 of the paper on the bootstrap.
For homework: Program the parametric and non-parametric bootstrap of the bi-normal distribution. It is recommended
to investigate the statistical properties of the procedures. For that, you can generate samples under known conditions and
apply the procedure to them. Iterate several times and base the assessment on the sampling distribution.
- For the class of 2-11-09:
Read Sections 3, 4 and 5. For homework: program the bootstrap for at least one of the procedures.
You may use existing R functions for application of the statistical procedure in the example that you are analyzing.
In class we considered the example of Cox Regression using this code. For homework
you may investigate the statistical properties of the bootstrap procedure and compare them to the asymptotic estimator
which is produced by the coxph procedure. Alternatively, you may consider the other examples.
- For the class of 9-11-09: We discussed the EM algorithm and demonstrated it for the
normal mixture problem. We ran this code as a dmonstration. For next week read Sections 1-3
of the EM paper by
Dempster et al..
- For the class of 21-12-09: We will finish the discussion of the EM analysis in the context
of factor analysis. We will go over this code for the implementation of the algorithm. We will
start dealing with the Gibbs sampler.
- For the class of 28-12-09: We will fix the error in the code for the implementation of the EM in Factor Analysis. A paper that gives the details of the algorithm can be found here. We will discuss the Gibbs sampler. We used this code in class.
- For the class of 04-01-10: We will continue the discussion on the Gibbs samples for MCMC computation. You may read some old class notes on Markov chains and the MCMC algorithms in general and discuss
the Gibbs sampler in particular. Hopefully, we will start running the code that deals with the problem
of cluster analysis based on genetic information and the application of the Gibbs sampler.
- For the class of 18-01-10: We will read this paper and discuss the more general Metropolis-Hastings algorithm.
Assignments
Seminar
Useful Links