Mcintosh and Bruce
نویسنده
چکیده
We consider a discrete-time probabilistic inference system where the conclusions and inputs are probability measures on measurable spaces X,X and Y,Y respectively. We are given a kernel N from X to Y (N : X × Y → [0, 1]), which represents the way information about states of affairs (represented by X) is transmitted to a receptor (represented by Y ). Suppose that at time t = i the conclusion is given by a probability measure μi on X. Then given any input measure λi on Y we update μi, replacing it by μi+1 = λiPμi,N , where Pμi,N is the Bayes adjoint kernel for N and the ‘prior’ μi. In this way the conclusions evolve by conditional probability given a sequence of input measures. This is in contrast to classical Bayesian inference where the inputs are points of Y , and the conclusions are updated by conditioning a fixed Bayes posterior (defined with respect to a fixed prior) on the sequence of point inputs. In our case, as in classical Bayesian inference, the object is to obtain a (weakly) convergent sequence of conclusion measures μi. But in our case we have available a method called directed convergence strategy to facilitate convergence: metric criteria are employed to accept or reject input measures based on the degree of belief in the current conclusion. In this paper we develop sufficient conditions to execute this strategy using Lp metrics (after representing measures as their Radon-Nikodym derivatives). This work generalizes L∞ criteria for directed convergence presented in [4].
منابع مشابه
Author's response to reviews Common variation in EMSY and risk of breast and ovarian cancer: a case-control study using Title: HapMap tagging SNPs Authors:
Patrick R Benusiglio ([email protected]) Fabienne Lesueur ([email protected]) Craig Luccarini ([email protected]) Joan McIntosh ([email protected]) Robert N Luben ([email protected]) Paula Smith ([email protected]) Alison Dunning ([email protected]) Douglas F Easton ([email protected]) Bruce AJ Ponder ([email protected]) Paul D...
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