The Weibull distribution has been widely used in survival and engineering reliability analysis. In life testing experiments is fairly common practice to terminate the experiment before all the items have failed, that means the data are censored. Thus, the main objective of this paper is to estimate the reliability function of the Weibull distribution with uncensored and censored data by using B...

Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large number of likelihood terms that need to be calculated at each iteration. In order to perform Bayesian inference for a large set of time series, we consider an al...

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an independent N -sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interactin...

In many situations it is important to be able to propose N independent realizations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an independent N -sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interactin...

Adaptive Markov Chain Monte Carlo (MCMC) algorithms attempt to ‘learn’ from the results of past iterations so the Markov chain can converge quicker. Unfortunately, adaptive MCMC algorithms are no longer Markovian, so their convergence is difficult to guarantee. In this paper, we develop new diagnostics to determine whether the adaption is still improving the convergence. We present an algorithm...

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...

This paper presents Markov-Chain-Monte-Carlo (MCMC) procedures to sample uniformly from the collection of datasets that satisfy some revealed preference test. The MCMC for GARP test combines a Gibbs-sampler with simple hit and run step. It is shown has uniform distribution as its unique invariant it converges this at an exponential rate.