**
POLI 272 BAYESIAN METHODS
Eighth Assignment
Due 8 December 2009 (Extra Credit!)**

- Use the Examples that I have posted of Ernesto Calvo's Interface with WINBUGS to analyze some 2000
U.S. Census data by Congressional District (including D.C.) contained in this
**STATA**file:

Here are the variables:

Run the regression (with the appropriate priors for the betas and tau) of the Percentage of Owner Occupied Housing -- owner00 -- on white00, black00, asian00, and hispanic00. Compare the results to**. d Contains data from C:\Inetpub\ftproot\wf1\census2000.dta obs: 436 vars: 9 1 Nov 2001 16:39 size: 26,160 (97.5% of memory free) ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- statenmlong str20 %20s name of state district byte %8.0g congressional district number total_pop double %10.0g total population of CD white00 float %9.0g White% CD black00 float %9.0g Black% CD asian00 float %9.0g Asian% CD hispanic00 float %9.0g Hispanic% CD owner00 float %9.0g % Owner-Occupied housing units CD statenm str7 %9s name of state ------------------------------------------------------------------------------- Sorted by: statenm district . summ Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- statenmlong | 0 district | 436 9.958716 10.20201 1 52 total_pop | 436 655617 252357.5 6.7359 5633875 white00 | 436 74.72752 19.26287 16.8 97.7 black00 | 436 13.56628 19.08027 .3 188 -------------+-------------------------------------------------------- asian00 | 436 3.640826 5.391247 .1 53.5 hispanic00 | 436 12.23096 16.20432 .6 86 owner00 | 436 65.83693 11.93698 8 84.3 statenm | 0****STATA**.

- Write your own rejection sampler for a substantive problem. For example, here are four
**R**programs illustrating rejection sampling -- two using the Cauchy distribution as the proposal distribution, and two using the Normal distribution as the proposal distribution -- with the posterior distribution a simple beta -- 6X(1-X):

rejection_sampling_cauchy.r

rejection_sampling_normal.r

rejection_sampling_cauchy_scalefactor.r -- this version finds the "c" value by optimizing over the difference in logs

rejection_sampling_normal_scalefactor.r this version finds the "c" value by optimizing over the difference in logs

- "Roll your own"
**WINBUGS**application to a substantive problem of interest to you. Be sure to fully document the problem and the code as well as presenting the appropriate output.