A direct projection method for Markov chains
نویسنده
چکیده
A direct method based on oblique projections is adapted to compute the stationary distribution vector of a finite Markov chain. The algorithm can also be used to compute the group inverse of the corresponding generator matrix. It is shown how to update the stationary vector and other quantities of interest when one row of the transition probability matrix is modified. A GTH-like variant that appears to compute the stationary probabilities to high relative accuracy is developed. © 2004 Elsevier Inc. All rights reserved.
منابع مشابه
Empirical Bayes Estimation in Nonstationary Markov chains
Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical Bayes estimators for the transition probability matrix of a finite nonstationary Markov chain. The data are assumed to be of a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...
متن کاملThe Rate of Rényi Entropy for Irreducible Markov Chains
In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.
متن کاملEstimation of the Entropy Rate of ErgodicMarkov Chains
In this paper an approximation for entropy rate of an ergodic Markov chain via sample path simulation is calculated. Although there is an explicit form of the entropy rate here, the exact computational method is laborious to apply. It is demonstrated that the estimated entropy rate of Markov chain via sample path not only converges to the correct entropy rate but also does it exponential...
متن کاملEvaluation of First and Second Markov Chains Sensitivity and Specificity as Statistical Approach for Prediction of Sequences of Genes in Virus Double Strand DNA Genomes
Growing amount of information on biological sequences has made application of statistical approaches necessary for modeling and estimation of their functions. In this paper, sensitivity and specificity of the first and second Markov chains for prediction of genes was evaluated using the complete double stranded DNA virus. There were two approaches for prediction of each Markov Model parameter,...
متن کاملTaylor Expansion for the Entropy Rate of Hidden Markov Chains
We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004