Related papers: Bayesian analysis for reversible Markov chains

Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…

We develop two models for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both are based on the mixture transition distribution, which constructs a transition probability tensor with additive mixing of…

Dirichlet distribution and Dirichlet process as its infinite dimensional generalization are primarily used conjugate prior of categorical and multinomial distributions in Bayesian statistics. Extensions have been proposed to broaden…

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its…

We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…

Let $P$ be the transition matrix of a finite, irreducible and reversible Markov chain. We say the continuous time Markov chain $X$ has transition matrix $P$ and speed $\lambda$ if it jumps at rate $\lambda$ according to the matrix $P$. Fix…

In this paper, we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity…

This pedagogical document explains three variational representations that are useful when comparing the efficiencies of reversible Markov chains: (i) the Dirichlet form and the associated variational representations of the spectral gaps;…

Consider a Markov process \omega_t at equilibrium and some event C (a subset of the state-space of the process). A natural measure of correlations in the process is the pairwise correlation \Pr[\omega_0,\omega_t \in C] - \Pr[\omega_0 \in…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

In this paper, we use the Markov property introduced in Balan and Ivanoff (J. Theor. Probab. 15, 2002, 553-588) for set-indexed processes and we prove that a Markov prior distribution leads to a Markov posterior distribution. In particular,…

We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…

We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…

The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant…

We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…

Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi-infinite matrices over $\mathbb{F}_q$. We present natural generalizations of both chains by placing generic…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…