In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node in a computer network) by monitoring the traffic in a small number of network nodes or edges. We formalize this task by defining the Markov Chain Monitoring ...

We investigate the importance sampling (IS) simulation for the sample average of an output sequence from an irreducible Markov chain. The optimal Markov chain used in simulation is known to be a twisted Markov chain, however, the proofs in [2], [3] are very complicated and do not give us a good perspective. We give a simple and natural proof for the optimality of the simulation Markov chain in ...

agricultural drought in iran is considered as a natural disaster especially for the farmers. although nobody can stop drought, but if its nature and its characteristics are studied, it can be predicted and the results can be reduced. this article studies drought in the province of sistaan and balouchestaan and the drought predictability in the province has been done base on a model that is made...

background: hepatitis b (hb) is a major global mortality. accurately predicting the trend of the disease can provide an appropriate view to make health policy disease prevention. this paper aimed to apply three different to predict monthly incidence rates of hb. methods: this historical cohort study was conducted on the hb incidence data of hamadan province, the west of iran, from 2004 to 2012....

One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called the target density) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scient...

Markov chain sampling has recently received considerable attention in particular in the context of Bayesian computation and maximum likelihood estimation. This paper discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods ...

This is an expository paper, focussing on the following scenario. We have two Markov chains, M and M. By some means, we have obtained a bound on the mixing time of M. We wish to compare M with M in order to derive a corresponding bound on the mixing time of M. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which...

Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity, convergence, and reversibility thereof before proceeding to a short overview of Markov chain Monte Carlo and the use of mixing time...