Related papers: Concatenation of Markov processes
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves…
For a continuous-time Markov process, we characterize the law of the first jump location when started from an arbitrary initial distribution, in terms of the invariant distribution of an auxiliary Markov process. This could be of interest…
I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…
We consider Markov chain Monte Carlo methods for calculating conditional p values of statistical models for count data arising in Box-Behnken designs. The statistical model we consider is a discrete version of the first-order model in the…
Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical…
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions.…
We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
Radiative processes such as synchrotron radiation and Compton scattering play an important role in astrophysics. Radiative processes are fundamentally stochastic in nature, and the best tools currently used for resolving these processes…
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…
These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…
Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding.…
The Monte Carlo event generators (MC) are used for the simulation of different processes in high energy physics. To achieve the best description of the data, the parameters of simulations are adjusted (tuned) with different methods. In this…