1. the oesophageal plexus is in the structure and arrangement of its larger branches constant. ·2 . two trunks arise from the oesophageal plexus, the . anterior vagal trunk and the posterior vagal trunk; each trunk contains fibers of both left and right vagi nerves. 3. these vagal trunks in the majority of instances pass through the oesophageal opening of the diaphragm each in the form of the o...

The posterior distribution of a small-scale illustrative econometric model is used to compare symmetric simple importance sampling with asymmetric simple importance sampling. The numerical results include posterior first and second order moments, numerical error estimates of the first order moments, posterior modes, univariate marginal posterior densities and bivariate marginal posterior densit...

VEM approximates the posterior distribution by a variational distribution that is as close as possible to the posterior. It minimizes the Kullback-Leibler divergence The approximation is done by restricting the solutions to the ones that satisfy The E-step approximates the distribution and the M-step optimizes the hyperparameters with respect to this distribution. They can be decomposed in stag...

1.1 The Tractability-Fit Tradeoff in Variational Approximations The goal of a variational approximation is to approximate a posterior, p(β|Y ) by making an approximating distribution, q(β), as close as possible to the true posterior (Bishop, 2006). We search over the space of approximating distributions in order to find the particular distribution with the minimum KL-divergence with the actual ...

A review of Bayesian restoration of digital images based on Monte Carlo techniques is presented. The topics covered include Likelihood, Prior and Posterior distributions, Poisson, Binary symmetric channel and Gaussian channel models of Likelihood distribution, Ising and Potts spin models of Prior distribution, restoration of an image through Posterior maximization, statistical estimation of a t...

In this paper, we use the Markov property introduced in Balan and Ivanoff (2002) for set-indexed processes and we prove that a Markov prior distribution leads to a Markov posterior distribution. In particular, by proving that a neutral to the right prior distribution leads to a neutral to the right posterior distribution, we extend a fundamental result of Doksum (1974) to arbitrary sample spaces.

The local variational method is a technique to approximate an intractable posterior distribution in Bayesian learning. This article formulates a general framework for local variational approximation and shows that its objective function is decomposable into the sum of the Kullback information and the expected Bregman divergence from the approximating posterior distribution to the Bayesian poste...

Markov chain Monte Carlo (MCMC) methods use computer simulation of Markov chains in the parameter space. The Markov chains are defined in such a way that the posterior distribution in the given statistical inference problem is the asymptotic distribution. This allows to use ergodic averages to approximate the desired posterior expectations. Several standard approaches to define such Markov chai...

We propose a non-rigid surface registration method that registers a statistical point distribution model (PDM) to given images and that estimates the posterior marginal distribution of each of the points. We construct a statistical model of the locations of the points based on a set of corresponding points on training surfaces, which is generated by an entropy-based particle system. Given a new...

Bayesian methods are experiencing increased use for probabilistic ecological modelling. Most Bayesian inference requires the numerical approximation of analytically intractable integrals. Two methods based on Monte Carlo simulation have appeared in the ecological/environmental modelling literature. Though they sound similar, the Bayesian Monte Carlo (BMC) and Markov Chain Monte Carlo (MCMC) met...