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1. deconvolution (score: 1): Author: Xao Ping <xao_ping@yahoo.com>; Date: Mon, 16 Jun 2003 14:15:14 -0700 (PDT); Dear All: Suppose that I have a sample Y. Suppose also that it is known that Y=X+E where X is considered as a signal and E as noise. The PDFs of X and E are known: F(y, theta) and G(e, xi). Parameter; /archives/html/s-news/2003-06/msg00100.html (7,504 bytes)
2. Re: deconvolution (score: 1): Author: Spencer Graves <spencer.graves@PDF.COM>; Date: Mon, 16 Jun 2003 14:33:36 -0700; If you can provide more structure, then we might be able to do something. For example, are all the x[i]'s and e[i]'s independent of each other? If you assume some correlation structure among either t; /archives/html/s-news/2003-06/msg00101.html (8,929 bytes)
3. Re: deconvolution (score: 1): Author: Spencer Graves <spencer.graves@PDF.COM>; Date: Tue, 17 Jun 2003 06:15:15 -0700; I'm not certain I understand your terminology. "Finite Mixture distributions" are distributions that are, for example, 20% N(0, sigma^2) and 80% beta(shape1, shape2). Your use of the term "mixture" d; /archives/html/s-news/2003-06/msg00109.html (13,034 bytes)
4. Re: deconvolution (score: 1): Author: Spencer Graves <spencer.graves@PDF.COM>; Date: Tue, 17 Jun 2003 09:03:54 -0700; Now I think I can answer your question: Treat "x" as a parameter to be estimated in maximizing the following likelihood: c*exp(-0.5*((y-x)/sigma)^2)*(x^(shape1-1))*((1-x)^(shape2-1)) Take the logarit; /archives/html/s-news/2003-06/msg00116.html (16,596 bytes)
5. Re: deconvolution (score: 1): Author: Prof Brian Ripley <ripley@stats.ox.ac.uk>; Date: Tue, 17 Jun 2003 17:20:55 +0100 (BST); Here `x' is not a parameter, so it is not a `likelihood': rather some sort of MAP estimator. You have a prior for X, and observe Y=X+E. It is easy to get the posterior p(X | Y), but it is not at all; /archives/html/s-news/2003-06/msg00117.html (19,296 bytes)
6. Re: deconvolution (score: 1): Author: Spencer Graves <spencer.graves@PDF.COM>; Date: Tue, 17 Jun 2003 09:34:01 -0700; Great: So use function "integrate" to get the mean for x given y, sigma, shape1, and shape2? More generally, if Xao Ping has an objective function to be maximized or minimized, one could choose x to; /archives/html/s-news/2003-06/msg00118.html (18,269 bytes)
7. deconvolution (score: 1): Author: Xao Ping <xao_ping@yahoo.com>; Date: Wed, 18 Jun 2003 10:08:12 -0700 (PDT); Dear All: Many thanks to Spencer Graves, Brian Ripley and Manoel Pacheco for a great help with my request about deconvolution. After the discussion, I've realized that basically an appropriate framew; /archives/html/s-news/2003-06/msg00130.html (7,619 bytes)
8. Re: deconvolution (score: 1): Author: Spencer Graves <spencer.graves@PDF.COM>; Date: Wed, 18 Jun 2003 10:28:00 -0700; Have you tried Google? I got lots of hits for "introduction to Bayesian statisics" and even "Bayesian biostatistics". hth. spencer graves Xao Ping wrote: Dear All: Many thanks to Spencer Graves, Bria; /archives/html/s-news/2003-06/msg00131.html (8,867 bytes)

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