Unformatted text preview: it’s a good choice a lot of the time. What is the distinction between the inverse transform method and saying Q ( v ) = P ( u ) | du dv | , then computing the derivative and plugging in, where P ( u ) is uniform? Is this the same thing? No, this expression can’t be used directly for the problem we’re trying to solve. We know Q ( v ): it’s the function we are trying to pick values from. If u is a uniform variable, P ( u ) is just a constant, 1 / ( b-a ), where [ a,b ] is the interval we are selecting over, and it’s just 1 for [0 , 1]. Selecting u and plugging in to Q ( v ) = | du dv | is just going to give values of Q ( v ), not variables v distributed according to Q ( v ). But if you integrate Q ( v ) = | dF dv | (writing u ( v ) = F ( v )), you get the expression relating the value of uniformly-selected u to Q ( v ): this is the inverse transform expression u = R v F ( v ) dv . Then v = F-1 ( u ) will have the distribution you want....
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- Fall '11
- Derivative, Inverse transform sampling, inverse transform method