Efficient computation of updated lower expectations for imprecise continuous-time hidden Markov chains

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix `imprecise' refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables; in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables

Hitting Times and Probabilities for Imprecise 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 the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains

Hitting times and probabilities for imprecise 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 the same lower and upper expected hitting times, and similarly the hitting probabilities are the same for these three types. Moreover, we provide a characterisation of these quantities that directly generalises a similar characterisation for precise, homogeneous Markov chains

Imprecise Continuous-Time Markov Chains

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models computationally tractable, they rely on a number of assumptions that may not be realistic for the domain of application; in particular, the ability to provide exact numerical parameter assessments, and the applicability of time-homogeneity and the eponymous Markov property. In this work, we extend these models to imprecise continuous-time Markov chains (ICTMC's), which are a robust generalisation that relaxes these assumptions while remaining computationally tractable. More technically, an ICTMC is a set of "precise" continuous-time finite-state stochastic processes, and rather than computing expected values of functions, we seek to compute lower expectations, which are tight lower bounds on the expectations that correspond to such a set of "precise" models. Note that, in contrast to e.g. Bayesian methods, all the elements of such a set are treated on equal grounds; we do not consider a distribution over this set. The first part of this paper develops a formalism for describing continuous-time finite-state stochastic processes that does not require the aforementioned simplifying assumptions. Next, this formalism is used to characterise ICTMC's and to investigate their properties. The concept of lower expectation is then given an alternative operator-theoretic characterisation, by means of a lower transition operator, and the properties of this operator are investigated as well. Finally, we use this lower transition operator to derive tractable algorithms (with polynomial runtime complexity w.r.t. the maximum numerical error) for computing the lower expectation of functions that depend on the state at any finite number of time points

An Investigation of Business Transformation Disruptors at the Military Strategic Command Level

This dissertation contributes an empirical research on business transformation disruption in the military. Specifically, this exploratory research seeks a better understanding of disruption of business transformation and some of the factors that are likely to impact the transformation process at the military strategic command level. A lack of empirical studies existing in the literature, coupled with the continuous transformation challenges faced by military organizations, make it necessary to conduct this empirical study of business transformation disruption in the military. This research was carried out utilizing a two-phase mixed-methods approach. The first phase included qualitative data gathering through a series of discussions and focus groups that provided an initial understanding of the phenomena and the basis needed to formulate the research conducted in the second phase. From this initial phase, three main research categories were established which focused on Leadership Turbulence, Resistance to Business Transformation, and Lack of Agility in Military Culture. A quantitative data collection and analysis was conducted in the second phase to test a set of seven hypotheses. A total of 1,095 data points were collected from senior level military and civil servants of a U.S. Army strategic command organization (Training and Doctrine Command) using a self-administered online survey. The results of this investigation suggest that a) frequent turnover of a commander or commanding general, b) perceived inconsistencies of leadership guidance, and c) perceived disincentives for achieving organizational process efficiencies are associated to disrupting business transformation goals and initiatives. Conversely, this initial investigation failed to support that d) collaboration with colleagues, e) reluctance to adopting different business processes, f) perceived negative assessments of process improvement initiatives, and g) dissent tolerance are associated to the disruption of business transformation efforts at the military strategic command level. The findings of this study highlight the importance of considering a wide range of critical success factors in the transformation of military strategic commands. The results of this research can be used by engineering managers, practitioners, and academics as a complement to their research and teaching efforts with respect to organizational change and transformation