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We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools invo...
In this paper we develop Foster-type criteria guaranteeing tightness for Markov chains which are not necessarily irreducible. The results include criteria for both tightness of the marginal distributi...
We describe a new estimator of the stationary density of a Markov chain on general state space. The new estimator is easier to compute, converges faster, and empirically gives visually superior estima...
We introduce a new class of density estimators, termed look-ahead density estimators, for performance measures associated with a Markov chain. Look-ahead density estimators are given for both transien...
We provide a generalization of Hoeffding’s inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expec...
In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and ...
We determine an explicit Gr¨obner basis, consisting of linear forms and determi-nantal quadrics, for the prime ideal of Raftery’s mixture transition distribution model for Markov chains. When the stat...
Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions.
We study properties and parameter estimation of finite-state homogeneous continuous-time bivariate Markov chains.
We define a conjugate prior for the reversible Markov chain of order r. The prior arises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from ...
Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the ...
Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the ...
For a Markov transition kernel $P$ and a probability distribution $ \mu$ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\mu} = \sum_k \mu(k)P^k.$ I...
In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional ...
In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric e...

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