Related papers: Constrained Monte Carlo Markov Chains on Graphs
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…
A main question in graphical models and causal inference is whether, given a probability distribution $P$ (which is usually an underlying distribution of data), there is a graph (or graphs) to which $P$ is faithful. The main goal of this…
With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By…
A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to…
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance…
Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated…
In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and…
The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Markov chain Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty.…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We…
We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master…
Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the…
Motivated by applications in Markov chain Monte Carlo, we discuss what it means for one Markov chain to be an approximation to another. Specifically included in that discussion are situations in which a Markov chain with continuous state…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…