------------------------------------------------------------------------------------------------------ log: c:\Imbook\bwebpage\Section3\mma13p1bayesthm.txt log type: text opened on: 24 May 2005, 11:04:08 . . ********** OVERVIEW OF MMA13P1BAYESTHM.DO ********** . . * STATA Program . * copyright C 2005 by A. Colin Cameron and Pravin K. Trivedi . * used for "Microeconometrics: Methods and Applications" . * by A. Colin Cameron and Pravin K. Trivedi (2005) . * Cambridge University Press . . * Chapter 13.2.2 page 424 . * Create Figure 13.1 . * (1) Bayes Analysis illustrated using normal distribution and prior . . * No data are needed. . . ********** SETUP . . set more off . version version 8.2 . set scheme s1mono /* Graphics scheme */ . . ********** DATA DESCRIPTION ********** . . * Model is y ~ normal(theta, sigmesq) where sigmasq is known. . * and the prior is theta ~ normal(mu, tau) . * which gives a normal posterior . * n is set below in set obs . . ********** CREATE DATA ********** . . * The likleihood and prior are normal so the posterior is also normal . . * Will evaluate the densities at points between 0 and 15 . set obs 150 obs was 0, now 150 . gen xeval = 0.1*_n . . * Likelihood with sigmasq known . scalar nobs = 50 . scalar ybar = 10 . scalar sigmasq = 100 . gen likelihood = normden(xeval,ybar,sqrt(sigmasq/nobs)) . . * Prior . scalar mu = 5 . scalar tausq = 3 . gen prior = normden(xeval,mu,sqrt(tausq)) . . * Posterior given sample mean of using . scalar tau1sq=1/((nobs/sigmasq)+(1/tausq)) . scalar mu1 = tau1sq*((ybar*nobs/sigmasq)+(mu/tausq)) . gen posterior = normden(xeval,mu1,sqrt(tau1sq)) . . scalar list mu1 = 8 tau1sq = 1.2 tausq = 3 mu = 5 sigmasq = 100 ybar = 10 nobs = 50 . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- xeval | 150 7.55 4.344537 .1 15 likelihood | 150 .0666548 .0944174 6.44e-12 .2820948 prior | 150 .0665247 .0804685 1.33e-08 .2303294 posterior | 150 .0666667 .1131755 1.85e-12 .3641828 . . graph twoway (line likelihood xeval, clstyle(p2)) /* > */ (line prior xeval, clstyle(p3)) /* > */ (line posterior xeval, clstyle(p1)), /* > */ scale (1.2) plotregion(style(none)) /* > */ title("Bayes: Likelihood, Prior and Posterior") /* > */ xtitle("Evaluation point", size(medlarge)) xscale(titlegap(*5)) /* > */ ytitle("Density", size(medlarge)) yscale(titlegap(*5)) /* > */ legend(pos(10) ring(0) col(1)) legend(size(small)) /* > */ legend( label(1 "Likelihood N[10,2]") label(2 "Prior N[5,3]") /* > */ label(3 "Posterior N[8,1.2]") ) . graph save Ch13_Bayes1, replace (file Ch13_Bayes1.gph saved) . graph export Ch13_Bayes1.wmf, replace (file c:\Imbook\bwebpage\Section3\Ch13_Bayes1.wmf written in Windows Metafile format) . . ********** CLOSE OUTPUT ********** . log close log: c:\Imbook\bwebpage\Section3\mma13p1bayesthm.txt log type: text closed on: 24 May 2005, 11:04:12 ----------------------------------------------------------------------------------------------------