Wmu s6880 11b s6880 class notes 11b 37 an example

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Unformatted text preview: exact form of the former is nontrivial. (WMU) S6880 #11b S6880, Class Notes #11b 3/7 An Example Hatching Insect Eggs, Conditioned on M For simplicity, consider only two variable case by conditioning on M = m. That is, consider (for a > 0, b > 0, λ > 0 and m ≥ 1) f (x , y ) ∝ m x +a −1 y (1 − y )m−x +b−1 . x Then fY (y ) ∼ beta(a, b), fX |Y (x |y ) ∼ binomial(m, y ), and fY |X (y |x ) ∼ beta(x + a, m − x + b), and f (x ) = m B (x + a, m − x + b) , x B (a, b) a beta-binomial distribution. To generate X in this two-variable form, Gibbs samplers is called for. (WMU) S6880 #11b S6880, Class Notes #11b 4/7 An Example Hatching Insect Eggs, Conditioned on M , continued Suppose a random sample of size n from X is wanted. For each target random variate x , starts from an initial sample value y0 . Generate n Gibbs sequences of length k (pre-set) based on these initial y values. Use the final value of (xk , yk ) for each sequence. (WMU) S6880 #11b S6880, Class Notes #11b 5/7 An Example Hatching Insect Eg...
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