chapter3new - Sampling Importance Resampling (SIR) Another...

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Sampling Importance Resampling (SIR) Another method to simulate (almost) from f based on g Assumption: f g known up to a constant, i.e. f = c 1 ˜ f and g = c 2 ˜ g c 1 , c 2 > 0 unknown. 1. Generate y 1 , y 2 ,..., y m iid g 2. Compute w j = ˜ f ( y j ) ˜ g ( y j ) for j = 1 ,..., m 3. Make x = y j with prob w j , i.e., 1/14
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Notes: I The almost means: x | y 1 ,..., y , d f , i.e., P [ x A | y 1 ,..., y m ] m →∞ Z A f ( x 0 ) dx 0 I The sample y 1 ,..., y m and the weights can be reused to generate x 1 ,..., x n 00 g 2/14
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Leave-one-out: How does the inference change when removing a datum. I Let y n = ( y 1 ,..., y n ) be the vector observations and I y - i = ( y 1 ,..., y i - 1 , y i + 1 ,..., y n ) the observations after removing the i -th one I Assume p ( y n | θ ) = Q i p ( y i | θ ) I Assume we have a posterior sample θ 1 ,...,θ m p ( θ | y n ) We can generate θ - i p ( θ | y - i ) by setting θ - i = θ j w.p. w
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chapter3new - Sampling Importance Resampling (SIR) Another...

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