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       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
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