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Unformatted text preview: MC convergence MH. Ch 8. Not to turn in. Hw Ch 8. Convergence Explain clearly what you do and why you are making the (convergence) decision. Ex 1. According to exercise 1 in MH. Hw 6 p ( μ  α ) = 1 B ( a μ , a μ /α ) α a μ μ a μ 1 (1 + αμ ) a μ + a μ /α , and the integrated likelihood function is given by p ( k  α ) = integraldisplay ∞ p ( k  α, μ ) p ( μ  α ) dμ (1) = bracketleftBigg productdisplay j 1 B ( k j + 1 , α 1 )( k j + α 1 ) bracketrightBigg B ( a μ + ∑ j k j , ( J + a μ ) /α ) B ( a μ , a μ /α ) , where k denotes the sample k = ( k 1 , . . . , k J ) ∼ NegBin( μ, α ), and p ( k  α, μ ) = producttext j p ( k j  α, μ ) is the likelihood function. Assume that α ∼ exponential( mean = 0 . 5) and that you observed k = c (16 , 24 , 4 , , 13 , 2 , 6 , 5 , 2 , 1 , 34 , 1 , 4 , 12 , 2 , 18 , 8 , 15 , 12 , 18) Considering q ( y  x ) = exponential( y  mean = 0 . 838). 1. We ran three chains with corresponding starting values α (1) 1 = 0 . 1 , α (1) 2 = 1 , α (1) 3 = 2 of length T = 10 4 . Figure 1 shows the output of indices=100:T acf(alphas[indices,1],main="") acf(alphas[indices,2],main="") acf(alphas[indices,3],main="") What does this figure tell you?, If you wanted a quasiindependent chain, what would be the batch size that you would use?, why? 2. Using alphas[indices=100:T,], I compute the KS statistic comparing the first half of the chain vs its second half and the KS comparing chains 1 and 2. Figure 2 1 of 8 MC convergence MH. Ch 8. Not to turn in....
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This note was uploaded on 01/29/2012 for the course STAT 6866 taught by Professor Womack during the Fall '11 term at University of Florida.
 Fall '11
 Womack

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