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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
(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)
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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- Fall '14