Use the data augmentation algorithm to estimate the posterior density of the parameter n in the linkage

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Use the data augmentation algorithm to estimate the posterior density of the parameter n in the linkage model in question 3.


Question 3.

Smith (1969, Section 21.10) quotes an example on genetic linkage in which we have observations x = (x1, x2 , x3 , x4) with cell probabilities

( +n, n ;(  n), (1 n)+k).The values quoted are x1 = 461, x2 = 130, x= 161 and X4 = 515. Divide x1 into Y0 and Y1 and X4 into y4 and Y5 to produce augmented data y = (y0, Y1, Y2, y3, Y4, Y5) and use the EM algorithm to estimate n. 

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