Publications

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailedU+2014smallerU+2014state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences ...

This paper proposes a method for fitting a two-state imprecise Markov chain to time series data from a two-state non-Markovian process. Such non-Markovian processes are common in practical applications. We focus on how to fit modelling parameters based on data from a process where time to transition is not exponentially distributed, thereby violating the Markov assumption. We do so by first fitting a many-state (i.e. having more than two states) ...

When a discrete-time homogenous Markov chain is observed at time intervals that correspond to its time unit, then the transition probabilities of the chain can be estimated using known maximum likelihood estimators. In this paper we consider a situation when a Markov chain is observed on time intervals with length equal to twice the time unit of the Markov chain. The question then arises of characterizing probability matrices whose square ...

The present paper investigates the embedding problem for time-homogeneous Markov chains. A discrete-time Markov chain with time unit 1 is embeddable in case there exists a compatible Markov chain regarding time unit 1/m (with m > 1 integer number). An embeddable Markov chain has a transition matrix for which there exists an m-th root that is a probability matrix. The present paper examines the embedding problem for discrete-time Markov chains ...

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as sets of homogeneous Markov chains, as sets of more general stochastic processes, and as game-theoretic probability models. Our first contribution is that all these different types of imprecise Markov chains have ...

Within the set of discrete-time Markov chains, a Markov chain is embeddable in case its transition matrix has at least one root that is a stochastic matrix. The present paper examines the embedding problem for discrete-time Markov chains with three states and with real eigenvalues. Sufficient embedding conditions are proved for diagonalizable transition matrices as well as for non-diagonalizable
transition matrices and for all possible ...

Drought is a slow and creeping phenomenon that occurs more frequently in arid and semi-arid regions. In recent decades, among natural disasters influencing human societies the number or frequency of drought event has increased more than others. In this context, the prediction of drought intensity, duration and frequency can help to take the necessary precautions and reduce drought risk. This study employs Markov chains of different orders (0, 1, ...

In general, the transition matrix of a Markov chain is a stochastic matrix. For a system that is modeled by a Markov chain, the transition matrix must reflect the characteristics of that system. The present paper introduces a particular class of transition matrices in order to model Markov systems for which, as the length of the time interval becomes greater, a transition from one state to another is more likely. We call these transition ...

We study the average behaviour of imprecise Markov chains; a generalised type of Markov chain where local probabilities are partially specified, and where structural assumptions such as Markovianity are weakened. In particular, we prove a pointwise ergodic theorem that provides (strictly) almost sure bounds on the long term average of any real function of the state of such an imprecise Markov chain. Compared to an earlier ergodic theorem by De ...