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In a Hastings Algorithm fro Sampling from a proposed distribution, how fair or convenient is to use as a proposal distribution q(x1,x2) a uniform distribution. If using a uniform distribution, how is that distribution dependant on the X1 value to return an X2 value, that is, does the samples from the uniform distribution are done as usual or do I have to specify some input parameter dependant on X1. Note: I saw this in an introductory explanation of MCMC and hastings. Thank You |
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It's perfectly reasonable; what you end up getting is a special case of the independence sampler: any MH sampler where the proposal distribution is independent of the current state. It's not a very good choice for high-dimensional spaces, though, because you'll end up getting a ton of rejections once you reach a state with high probability. Two answer your second question, you don't need to do anything special to draw from the uniform distribution. It's independent of X1. Thanks, I was kinda puzzled by this, I usually saw q(x1,x2) where the input was directly related to the output.
(Nov 22 '10 at 01:16)
Leon Palafox
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