Question: 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,

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, x₃= 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.

( +n, n ;( n), (1 n)+k).

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