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Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized rando...
We examine different ways of numerically computing the distribution function of conditional expectations where the conditioning element takes values in a finite or countably infinite outcome space. Bo...
We consider the problem of joint modelling of metabolic signals and gene expression in systems biology applications. We propose an approach based on input-output factorial hidden Markov models and pro...
Inferring phylogenetic trees from multiple sequence alignments often relies upon Markov chain Monte Carlo (MCMC) methods to generate tree samples from a posterior distribution. To give a rigorous appr...
We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation ...
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior...
Rich and complex time-series data, such as those generated from engineer-ing systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the p...
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is prov...
Two techniques have emerged from the recent literature as candidate solutions to the problem of missing data imputation, and these are the Expectation Maximisation (EM) Algorithm and the auto-associ...
Let f be a random variable with values in a metric space (X, d). For some class of metric spaces we define in terms of the metric d mathematical expectation of f as a closed bounded and non-empty s...
Linear conditional expectations and quadratic conditional variances determine a class of stochastic processes with independent increments. Characterizations of the Wiener, Poisson, gamma, negative ...
Let X and Y be R-valued random variables on a nonatomic probability space (8, 5, P). We give conditions under which Y can be approximated by a conditional expectation of X. In particular, we prove ...
Given an IID sample from a positive distribution, we provide a method for constructing rigorous finite sample lower confidence bounds for the expectation of the distribution. The method is based on co...
In [1], Z. Chen proved that, if for each terminal condition $xi$, the solution of the BSDE associated to the standard parameter $(xi, g_1)$ is equal at time $t=0$ to the solution of the BSDE associate...

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