Computing the stationary distribution of a large finite or countably infinite state space Markov Chain has become central to many problems such as statistical inference and network analysis. Standard methods involve large matrix multiplications as in power iteration, or simulations of long random walks, as in Markov Chain Monte Carlo (MCMC). For both methods, the convergence rate is is difficul...

This paper analyzes a (1, λ)-Evolution Strategy, a randomized comparison-based adaptive search algorithm optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are investigated: first, the case where the step-size is constant, and second, the case where the step-size is adapted using cumulative step-size adaptation. We exhibit fo...

Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by applications to Markov chain Monte Carlo algorithms. For Markov chains on finite state spaces, previous authors have obtained a number of very useful bounds, including those which involve choices of paths. Unfortunately, many Markov chains which arise in practice are not finite. In this paper, we...

This paper presents a novel and generic distributed swarm guidance algorithm using inhomogeneous Markov chains that guarantees superior performance over existing homogeneous Markov chain based algorithms, when the feedback of the current swarm distribution is available. The probabilistic swarm guidance using inhomogeneous Markov chain (PSG–IMC) algorithm guarantees sharper and faster convergenc...

0. Introductory Remarks. This collection which I refer to as “Barebones Background for Markov Chains" is really a set of notes for lectures I gave during the spring quarters of 2001 and 2003 on Markov chains, leading up to Markov Chain Monte Carlo. The prerequisite needed for this is a knowledge of some basic probability theory and some basic analysis. This is really not a basic course in Marko...

This paper presents the statistical inference on the parameters of the Burr type III distribution, when the data are Type-II hybrid censored. The maximum likelihood estimators are developed for the unknown parameters using the EM algorithm method. We provided the observed Fisher information matrix using the missing information principle which is useful for constructing the asymptotic confidence...

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT...

This paper presents a fine-grained parallel genetic algorithm with mutation rate as a control parameter. The function of the mutation rate is similar to the function of temperature parameter in the simulated annealing [Lundy’86, Otten’89, and Romeo’85]. The parallel genetic algorithm presented here is based on a Markov chain [Kemeny’60] model. It has been proved that fine-grained parallel genet...