MidtermMa - MIDTERM EXAM(ISYE8843 FALL 2004 Chengyuan Ma...

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MIDTERM EXAM (ISYE8843 FALL 2004) Chengyuan Ma School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA 30332, USA [email protected] 1. SOLUTION TO PROBLEM 1 the matlab code for this problem. clear all ; close all ; y1 = [25.8 19.8 28.6 29.4 22.3 33.8 33.8 27.8 29.6] ; y2 = [16.5 23.5 13.5 34.6 16.9 18.8 26.1 18.4 17.2 11.6 20.2] ; y3 = [24.0 29.1 16.0 24.8 27.0 10.9 11.8 23.2 17.7 23.9 24.6 24.0 27.2 23.7] ; % set random generator seed randn(’seed’,1) y1_mean = mean(y1) ; n1 = 9 ; s1_2 = var(y1) ; y2_mean = mean(y2) ; n2 = 11 ; s2_2 = var(y2) ; y3_mean = mean(y3) ; n3 = 14 ; s3_2 = var(y3) ; % set the parameters to be simulated Mu_1 = [] ; Mu_2 = [] ; Mu_3 = [] ; Psi = [] ; Tau2 = [] ; Sigma2 = [] ; Sigma1_2 = [] ; Sigma2_2 = [] ; Sigma3_2 = [] ; % set the parameters k = 3 ;
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a0 = 1 ; c0 = 1 ; d0 = 1 ; f0 = 1 ; g0 = 0.1 ; psi0 = 10 ; zeta0 = 0.1 ; M = 5000 ; burn = 1000 ; % generate initial values tau2 = 1 / rand_gamma(c0/2, d0/2) ; sigma2 = rand_gamma(f0/2, g0/2) ; sigma1_2 = 1 / rand_gamma(a0/2, a0 * sigma2 / 2) ; sigma2_2 = 1 / rand_gamma(a0/2, a0 * sigma2 / 2) ; sigma3_2 = 1 / rand_gamma(a0/2, a0 * sigma2 / 2) ; psi = randn(1,1) * sqrt(tau2/zeta0) + psi0 ; % Starting simulation for ii = 1 : M mu1 = randn(1,1) * sqrt(1/(n1/sigma1_2 + 1/tau2)) + . .. (n1 * y1_mean/sigma1_2 + psi/tau2)/(n1/sigma1_2 + 1/tau2) ; mu2 = randn(1,1) * sqrt(1/(n2/sigma2_2 + 1/tau2)) + . .. (n2 * y2_mean/sigma2_2 + psi/tau2)/(n2/sigma2_2 + 1/tau2) ; mu3 = randn(1,1) * sqrt(1/(n3/sigma3_2 + 1/tau2)) + . .. (n3 * y3_mean/sigma3_2 + psi/tau2)/(n3/sigma3_2 + 1/tau2) ; psi = randn(1,1) * sqrt(tau2/(k + zeta0)) + . .. (mu1 + mu2 + mu3 + zeta0 * psi0)/(k + zeta0); tau2 = 1 / rand_gamma((c0 + k + 1)/2, . .. (d0 + (mu1 - psi)ˆ2 + (mu2 - psi)ˆ2 + .
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This note was uploaded on 10/23/2011 for the course ISYE 8843 taught by Professor Vidakovic during the Spring '11 term at Georgia Tech.

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MidtermMa - MIDTERM EXAM(ISYE8843 FALL 2004 Chengyuan Ma...

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