Re: Bernoulli variables again
- To: mathgroup at smc.vnet.net
- Subject: [mg46551] Re: Bernoulli variables again
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Mon, 23 Feb 2004 02:15:42 -0500 (EST)
- References: <c1amhq$3qt$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Because of the peculiar structure of the expression below, you may profit from the transformation x[i_]->1-y[i]. A lot of extra complexity is due to all those 1 - xi. If your problems can be cast in terms of the y[i], this will help a lot. If you HAVE to go back to x[i] at some point, I think I'd do it as late in the game as possible. But I doubt it's necessary. After all, the y[i] are Bernoulli too, with an easy transformation between the probabilities associated. Bobby jmyers6761 at aol.com (JMyers6761) wrote in message news:<c1amhq$3qt$1 at smc.vnet.net>... > Consider the following expresion where each of the xn are Bernoulli variables: > > 1 - (1 - (1 - (1 - x1) (1 - x2)) x4) (1 - (1 - (1 - x2) (1 - x3)) x5) > > when this expression is Expanded we get: > > x1 x4+x2 x4 - x1 x2 x4 + x2 x5 + x3 x5 - x2 x3 x5 - x1 x2 x4 x5 - x2^2 x4 x5 + > x1 x2^2 x4 x5 - x1 x3 x4 x5 - x2 x3 x4 x5 + 2 x1 x2 x3 x4 x5 + x2^2 x3 x4 x5 - > x1 x2^2 x3 x4 x5 > > but since a Bernoulli variable, x, can take on only values of 0 or 1 and x^n = > x this expression is subject to the transformation x^n-> x with the following > result: > > x1 x4 + x2 x4 - x1 x2 x4 + x2 x5 + x3 x5 - x2 x3 x5 - x2 x4 x5 - x1 x3 x4 x5 + > x1 x2 x3 x4 x5 > > My question is does anyone know how to transform such an unexpanded expression > without having to first do an Expand? The actual expressions I am dealing with > have a very large number of fully expanded terms ( > 10^6) and as a result > Mathematica runs out of memory attemting to Expand the expressions. I know that > the resulting expressions, after the Bernoulli transformation, if they could be > expanded, would still be large but the number of terms would be much smaller, > on the order of 10^3 terms. Does anyone know of a technique that could used to > transform the unexpanded expression? > > Thank you for your thoughts. > > Al Myers