Related papers: The Computational Complexity of Estimating Converg…
We survey recent results concerning the total-variation mixing time of the simple exclusion process on the segment (symmetric and asymmetric) and a continuum analog, the simple random walk on the simplex with an emphasis on cutoff results.…
Inter-channel mis-synchronisation can be a limiting factor to the time resolution of high performance timing detectors with multiple readout channels and independent electronics units. In these systems, time calibration methods employed…
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…
In this paper, selection of an active sensor subset for tracking a discrete time, finite state Markov chain having an unknown transition probability matrix (TPM) is considered. A total of N sensors are available for making observations of…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Bayesian inference using Markov Chain Monte Carlo (MCMC) on large datasets has developed rapidly in recent years. However, the underlying methods are generally limited to relatively simple settings where the data have specific forms of…
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
We discuss problems posed by the quantitative study of time inhomogeneous Markov chains. The two main notions for our purpose are merging and stability. Merging (also called weak ergodicity) occurs when the chain asymptotically forgets…
Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is…
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 consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…