The restoration of a hidden process X from an observed process Y is often performed in the framework of hidden Markov chains (HMC). HMC have been recently generalized to triplet Markov chains (TMC). In the TMC model one introduces a third random chain U and assumes that the triplet T = (X,U, Y ) is a Markov chain (MC). TMC generalize HMC but still enable the development of efficient Bayesian al...

Software architecture is considered one of the most important indices of software engineering today. Software Architecture is a technical description of a system indicating its component structures and their relationships, and is the principles and rules governing designing. The success of the software depends on whether the system can satisfy the quality attributes. One of the most critical as...

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [6] and the continuous time setting [1, 3]. In this note, we describe the prototype model checker E T MC for discrete and continuous-time Markov chains...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [8] and the continuous time setting [1], [3]. In this short paper, we describe the prototype model checker E T MC for discrete and continuous-time Mark...

We propose a new model for multivariate Markov chains of order one or higher based on the mixture transition distribution (MTD) model. We call it the MTD-Probit. The proposed model presents two attractive features: it is completely free of constraints, thereby facilitating the estimation procedure, and it is more precise at estimating the transition probabilities of a multivariate or higher-ord...

This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on Jeffreys’ prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC) techniques. The performance of the Bayesian estimates is illustrated...

Interval Markov chains (IMCs) generalize ordinary Markov chains by having interval-valued transition probabilities. They are useful for modeling systems in which some transition probabilities depend on an unknown environment, are only approximately known, or are parameters that can be controlled. We consider the problem of computing values for the unknown probabilities in an IMC that maximize t...

Creating formal models for systems manually is time consuming and difficult. Automating the generation and verification of these formal models can reduce the overhead of developing the models. In this paper we propose an approach (MC-MC) to verifying and generating portions of the formal model using Markov chains. Learning Formal Models of Systems Formal models are used to explain the required ...