Modelling: Markov Chains and Markov Processes

Abstract

Under uncertainty, the construction of models requires that we distinguish known from unknown realities and find some mechanisms (such as constraints, theories, common sense and more often intuition) to reconcile our knowledge with our lack of it. For this reason, modelling is not merely a collection of techniques but an art in blending the relevant aspects of a problem and its unforeseen consequences with a descriptive, yet tractable, mathematical methodology. To model under uncertainty, we typically use probability distributions (explicitly or implicitly in constructing mathematical models of processes) to describe quantitatively the set of possible events that may unfold over time. Specification of these distributions (for example, whether these are binomial, Poisson, Normal etc.) are important and based on an understanding of the process. Moments of such processes tend to reflect the trend and the degrees to which we are more or less certain about the events as they occur.