Bayesian inference often requires integrating some function with respect to a posterior distribution. Monte Carlo methods are sampling algorithms that allow to compute these integrals numerically when they are not analytically tractable. We review here the basic principles and the most common Monte Carlo algorithms, among which rejection sampling, importance sampling and Monte Carlo Markov chai...

I propose a convergence diagnostic for Markov chain Monte Carlo (MCMC) algorithms based on couplings of a Markov chain with an auxiliary chain that is periodically restarted from a xed parameter value. The diagnostic provides a mechanism for estimating the spe-ciic constants governing the rate of convergence of geometrically and uniformly ergodic chains, and provides a lower bound on the eeecti...

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded t...

Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits non-canonical Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of the dynamics map onto the mechanics of a charged particle coupled to a magnetic field. W...

In this paper we propose a sequential Monte Carlo algorithm to estimate a stochastic volatility model with leverage effects and non constant conditional mean and jumps. We are interested in estimating the time invariant parameters and the non-observable dynamics involved in the model. Our idea relies on the auxiliary particle filter algorithm mixed together with Markov Chain Monte Carlo (MCMC) ...

Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods have emerged as the two main tools to sample from high-dimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly chosen and/or if highly corr...

Within the literature on non-cooperative game theory, there have been a number of algorithms which will compute Nash equilibria. This paper shows that the family of algorithms known as Markov chain Monte Carlo (MCMC) can be used to calculate Nash equilibria. MCMC is a type of Monte Carlo simulation that relies on Markov chains to ensure its regularity conditions. MCMC has been widely used throu...

distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract This paper develops Bayesian analysis for Constant Stress Accelerated Life Test (CSALT) under Type-II censoring scheme. Failure times are assumed to distribute as the three-parameter Generalized Logistic ...

Many statistical signal processing problems found in wireless communications involves making inference about the transmitted information data based on the received signals in the presence of various unknown channel distortions. The optimal solutions to these problems are often too computationally complex to implement by conventional signal processing methods. The recently emerged Bayesian Monte...

In hierarchical learning machines such as neural networks, Bayesian learning provides better generalization performance than maximum likelihood estimation. However, its accurate approximation using Markov chain Monte Carlo (MCMC) method requires huge computational cost. The exchange Monte Carlo (EMC) method was proposed as an improved algorithm of MCMC method. Although its effectiveness has bee...