Related papers: The Engel algorithm for absorbing Markov chains
Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed…
Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…
We propose a method to efficiently integrate truncated probability densities. The method uses Markov chain Monte Carlo method to sample from a probability density matching the function being integrated. The required normalisation or…
We discuss a non-reversible, lifted Markov-chain Monte Carlo (MCMC) algorithm for particle systems in which the direction of proposed displacements is changed deterministically. This algorithm sweeps through directions analogously to the…
Mahlmann and Schindelhauer (2005) defined a Markov chain which they called $k$-Flipper, and showed that it is irreducible on the set of all connected regular graphs of a given degree (at least 3). We study the 1-Flipper chain, which we call…
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov…
The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…
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…
D. Hensley showed in 1994 that the number of steps taken by the Euclidean algorithm to find the greatest common divisor of two natural numbers less than or equal to n follows a normal distribution in the limit as n tends to infinity. V.…
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…
This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To…
We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…
A lumping of a Markov chain is a coordinate-wise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the…
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,…
Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent…
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons,…
Let g : $\Omega$ = [0, 1] d $\rightarrow$ R denote a Lipschitz function that can be evaluated at each point, but at the price of a heavy computational time. Let X stand for a random variable with values in $\Omega$ such that one is able to…
We consider homogeneous multidimensional continued fraction algorithms, in particular a family of maps which was introduced by F. Schweiger. We prove his conjecture regarding the existence of an absorbing set for those maps. We also…
We study an elementary Markov process on graphs based on electric flow sampling (elfs). The elfs process repeatedly samples from an electric flow on a graph. While the sinks of the flow are fixed, the source is updated using the electric…
In this paper, we study consistent and partially exchangeable sequences of Markov chains on a finite state space. We provide a characterisation of the admissible transition rates via a decomposition into individual and coordinated motion of…