Related papers: Quenched phantom distribution functions for Markov…
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
The Metropolis-Hastings method is often used to construct a Markov chain with a given $\pi$ as its stationary distribution. The method works even if $\pi$ is known only up to an intractable constant of proportionality. Polynomial time…
We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…
We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…
We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
We consider weighted graphs satisfying sub-Gaussian estimate for the natural random walk. On such graphs, we study symmetric Markov chains with heavy tailed jumps. We establish a threshold behavior of such Markov chains when the index…
Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g.…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…