Related papers: Robust estimation of a Markov chain transition mat…

We establish Bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies and encompass the classical Bernstein inequality for…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…

A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…

Epidemic dynamics in a stochastic network of interacting epidemic centers is considered. The epidemic and migration processes are modelled by Markov's chains. Explicit formulas for probability distribution of the migration process are…

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be…

We compute the stationary distribution of a continuous-time Markov chain which is constructed by gluing together two finite, irreducible Markov chains by identifying a pair of states of one chain with a pair of states of the other and…

Markov chain Monte Carlo algorithms play a key role in the Bayesian approach to phylogenetic inference. In this paper, we present the first theoretical work analyzing the rate of convergence of several Markov chains widely used in…

Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…

Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…

State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a…

We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…

We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. Although mixing can be arbitrarily slow, we show that if the Markov chain has a $k$th order…

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by…

Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…