in a finite stationary markov chain, transition probabilities may depend on some explanatoryvariables. a similar problem has been considered here. the corresponding posteriors are derived andinferences are done using these posteriors. finally, the procedure is illustrated with a real example.

We consider the stability problem of discrete Markov chains when their transition matrices are perturbed. For finite irreducible Markov chains many perturbation bounds for the stationary vector are available. In this paper, we identify a condition under which these bounds are carried over to discrete irreducible Markov chains which are not finite.

In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurrence and intensity model we obtain Markov Chain Analogue Year gamma model (MCAYGM), Markov Chain Analogue Year exponentia...

We show that an automorphism of a unital AF C∗-algebra with a certain approximate Rohlin property has the Rohlin property. This generalizes a result of Kishimoto. Using this we show that the shift automorphism on the bilateral C∗-algebra associated with an aperiodic irreducible shift of finite type has the Rohlin property.

ing from the example, suppose that there are n subpopulations that have reached equilibrium sizes N1, . . . Nn and let mij be the probability that an individual in subpopulation i is a descendant of an individual in subpopulation j. That is, to build up subpopulation i in generation t + 1, we sample Ni times with replacement from generation t, picking at random from subpopulation j with probabi...

Graphical models are popular statistical tools which are used to represent dependentor causal complex systems. Statistically equivalent causal or directed graphical modelsare said to belong to a Markov equivalent class. It is of great interest to describeand understand the space of such classes. However, with currently known algorithms,sampling over such classes is only feas...

We extend the notion of Evolutionarily Stable Strategies introduced by Maynard Smith & Price [6] in 1973 for models ruled by a single fitness matrix A, to the framework of stochastic games developed by Lloyd Shapley [13] in 1953 where, at discrete stages in time, players play one of finitely many matrix games, while the transitions from one matrix game to the next follow a jointly controlled Ma...

In this paper we propose an iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor. This method is an extension of a method of Collatz (1942) for calculating the spectral radius of an irreducible nonnegative matrix. Numerical results show that our proposed method is promising. We also apply the method to studying higher-order Markov chains.

These notes accompany a lecture at the summer school on mathematics for bioinformatics, Centre de Recherches Mathematiques, Montreal, August 2003. I develop basic Markov models for sequence evolution and show how these may be used to estimate evolutionary divergences between sequences. I then discuss extensions of the basic model to situations where the evolutionary rate varies over time and fo...

In this paper, we derive the bounds formulas for the asymptotic tail distribution in a queue whose arrival process is a superposition of general periodic Markov sources. Note that we make no assumption for the structure of the general periodic Markov sources except that the underlying Markov chains are irreducible. The periodic source model in this paper is thus rather general. Taking initial s...