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...

1 Introduction Markov chain Monte Carlo (MCMC), which enables estimation in complex models via simulation, is now a widespread and accepted statistical tool, particularly in Bayesian analysis. Here, a distribution of interest, or target distribution, π, is approximated by a simulated chain {x

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 ...

Objetivo: Proponer un criterio para determinar el tamaño de muestra en simulaciones estocásticas MC (Monte Carlo) y MCMC (Markov chain Monte Carlo), garantizando una determinada precisión la estimación parámetros. Se busca que se garantice forma adimensional. Materiales métodos: El presente artículo propone buscando cumplir con objetivo planteado. Además, metodología aplicación del mismo. Resul...

Let P(E) be the space of probability measures on a measurable space (E, E). In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure π ∈ P(E). Non-linear Markov kernels (e.g. Del Moral (2004); Del Moral & Doucet (2003)) K : P(E) × E → P(E) can be constructed to admit π as an invariant distribution and have superior mixing...

We introduce a novel methodology for sampling from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. These problems are usually addressed using Sequential Monte Carlo (SMC) methods. The alternative Sequentially Interacting Markov Chain Monte Carlo (SIMCMC) scheme proposed here works by generating interacting non-Markovian sequences which...

We consider the combined use of visualization and sound for uncovering important structure in high-dimensional data. Our approach is based on Markov chain Monte Carlo (McMC) simulations. McMC is a popular computational tool for making analytical inferences from complex, high-dimensional probability densities. Given a particular target density p, we simulate a Markov chain that has p as its stat...

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theo...

Markov chain Monte Carlo (MCMC) is a simulation method commonly used for estimating expectations with respect to a given distribution. We consider estimating the covariance matrix of the asymptotic multivariate normal distribution of a vector of sample means. Geyer [9] developed a Monte Carlo error estimation method for estimating a univariate mean. We propose a novel multivariate version of Ge...

This paper presents a new approach for channel tracking and parameter estimation in cooperative wireless relay networks. We consider a system with multiple relay nodes operating under an amplify and forward relay function. We develop a novel algorithm to efficiently solve the challenging problem of joint channel tracking and parameters estimation of the Jakes’ system model within a mobile wirel...