In this paper we develop an original and general framework for automatically optimizing the statistical properties of Markov chain Monte Carlo (MCMC) samples, which are typically used to evaluate complex integrals. The Metropolis-Hastings algorithm is the basic building block of classical MCMC methods and requires the choice of a proposal distribution, which usually belongs to a parametric fami...

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges sampling from parameter posterior of a network via MCMC. Such culminate to lack convergence posterior. Nevertheless, this shows that nonconverged chain, generated MCMC space network, can yield marginalization valuable predictive distribution ...

Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the deve...

Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implic...

Many formal models of cognition implicitly use subjective probability distributions to capture the assumptions of human learners. Most applications of these models determine these distributions indirectly. We propose a method for directly determining the assumptions of human learners by sampling from subjective probability distributions. Using a correspondence between a model of human choice an...

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--part...

Markov chain Monte Carlo, or MCMC, is a way to sample probability distributions that cannot be sampled practically using direct samplers. This includes a majority of probability distributions of practical interest. MCMC runs a Markov chain X1, X2, . . ., where Xk+1 is computed from Xk and some other i.i.d. random input. From a coding point of view, a direct solver is X = fSamp();, while the MCM...

One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called the target density) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scient...

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tauequivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills1. For parallel and congeneric test form...