When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution into domains of attraction of local modes. Domain-based representations are defined to summarize the probability masses of and conditiona...

We present Monte-Carlo generalized EM equations for learning in nonlinear state space models. The difficulties lie in the Monte-Carlo E-step which consists of sampling from the posterior distribution of the hidden variables given the observations. The new idea presented in this paper is to generate samples from a Gaussian approximation to the true posterior from which it is easy to obtain indep...

Consider an aged-ordered population Zl, Z2, ... , where Z; is the frequency of the ith oldest allele and .EZi = 1. From this population consider an aged-ordered sample of size n with 1 alleles and the frequencies in age-order denoted by M = (/; ml, m2"" ml). vVe calculate the posterior distribution and posterior moments from the population frequency of the oldest allele, Zl, given the sample M,...

The purpose of this study was to document the neural distribution patterns within the human soleus muscle using 3D computer modelling. Through serial dissection, pinning, and digitization, nerve distribution and muscle volume of a human cadaveric soleus muscle were documented and a detailed 3D computer model of neural distribution within the muscle volume was generated. Branching patterns demon...

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter which can be readily elicited. The main technical contribution ...

Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting approximation. Recently, there has a trend of using neural networks to approximate the variational posterior distribution due to the flexibility of neural netw...

When the Gibbs sampler is used to estimate posterior distributions (Gelfand and Smith, 1990), the question of how many iterations are required is central to its implementation. When interest focuses on quantiles of functionals of the posterior distribution , we describe an easily-implemented method for determining the total number of iterations required, and also the number of initial iteration...

In filtering problems the (posterior) state distribution p(x) is recursively estimated given observations y and state dynamics. For nonlinear observation functions, the state distribution can becomemultimodal. Common Solutions are 1.Unimodal Gaussian filter using linearization of obs. function. 2. “Bank of filters” using multiple independent unimodal filters. We present a variational approach f...