Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Intelligent decision support for family financial planning

In today’s financial markets characterized by constantly changing tax laws and increasingly complex transactions, the demand for family financial planning (FFP) services is rising dramatically. However, the current trend to develop advisory systems that focus mainly on the financial or investment side fails to consider the whole picture of FFP. Separating financial or investment advice from legal and accounting advice may result in conflicting advice or important omissions that could lead to users suffering financial loss. In this paper, we propose a conceptual model for FFP decision-making process, followed by a novel architecture to support an aggregated FFP decision process by utilizing intelligentagents and Web-services technology. A prototype system for supporting FFP decision is presented to demonstrate the advances of the proposed Web-service multi-agentsbased system architecture and business value.

On the inverse parabolicity of pdf equations in turbulent flows

The focus of the present work is the well-known feature of the probability density function (PDF) transport equations in turbulent flows-the inverse parabolicity of the equations. While it is quite common in fluid mechanics to interpret equations with direct (forward-time) parabolicity as diffusive (or as a combination of diffusion, convection and reaction), the possibility of a similar interpretation for equations with inverse parabolicity is not clear. According to Einstein's point of view, a diffusion process is associated with the random walk of some physical or imaginary particles, which can be modelled by a Markov diffusion process. In the present paper it is shown that the Markov diffusion process directly associated with the PDF equation represents a reasonable model for dealing with the PDFs of scalars but it significantly underestimates the diffusion rate required to simulate turbulent dispersion when the velocity components are considered.

The influence of memory for prior instances on performance in a conflict detection task

In 3 experiments, the authors examined the role of memory for prior instances for making relative judgments in conflict detection. Participants saw pairs of aircraft either repeatedly conflict with each other or pass safely before being tested on new aircraft pairs, which varied in similarity to the training pairs. Performance was influenced by the similarity between aircraft pairs. Detection time was faster when a conflict pair resembled a pair that had repeatedly conflicted. Detection time was slower, and participants missed conflicts, when a conflict pair resembled a pair that had repeatedly passed safely. The findings identify aircraft features that are used as inputs into the memory decision process and provide an indication of the processes involved in the use of memory for prior instances to make relative judgments.

Referral to rehabilitation following traumatic brain injury: practitioners and the process of decision-making

The study aimed to examine the factors influencing referral to rehabilitation following traumatic brain injury (TBI) by using social problems theory as a conceptual model to focus on practitioners and the process of decision-making in two Australian hospitals. The research design involved semi-structured interviews with 18 practitioners and observations of 10 team meetings, and was part of a larger study on factors influencing referral to rehabilitation in the same settings. Analysis revealed that referral decisions were influenced primarily by practitioners' selection and their interpretation of clinical and non-clinical patient factors. Further, practitioners generally considered patient factors concurrently during an ongoing process of decision-making, with the combinations and interactions of these factors forming the basis for interpretations of problems and referral justifications. Key patient factors considered in referral decisions included functional and tracheostomy status, time since injury, age, family, place of residence and Indigenous status. However, rate and extent of progress, recovery potential, safety and burden of care, potential for independence and capacity to cope were five interpretative themes, which emerged as the justifications for referral decisions. The subsequent negotiation of referral based on patient factors was in turn shaped by the involvement of practitioners. While multi-disciplinary processes of decision-making were the norm, allied health professionals occupied a central role in referral to rehabilitation, and involvement of medical, nursing and allied health practitioners varied. Finally, the organizational pressures and resource constraints, combined with practitioners' assimilation of the broader efficiency agenda were central factors shaping referral. (C) 2004 Elsevier Ltd. All rights reserved.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape: to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913-958,2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that. under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing that mainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopper Bryodema tuberculata.

Stochastic modelling of the invasion process of nematodes in fly larvae

Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larval after a fixed period of time. Non-linear birthrates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Collaborative decision-making processes for maintaining biodiversity: Two Australian case studies

There have been many models developed by scientists to assist decision-makers in making socio-economic and environmental decisions. It is now recognised that there is a shift in the dominant paradigm to making decisions with stakeholders, rather than making decisions for stakeholders. Our paper investigates two case studies where group model building has been undertaken for maintaining biodiversity in Australia. The first case study focuses on preservation and management of green spaces and biodiversity in metropolitan Melbourne under the umbrella of the Melbourne 2030 planning strategy. A geographical information system is used to collate a number of spatial datasets encompassing a range of cultural and natural assets data layers including: existing open spaces, waterways, threatened fauna and flora, ecological vegetation covers, registered cultural heritage sites, and existing land parcel zoning. Group model building is incorporated into the study through eliciting weightings and ratings of importance for each datasets from urban planners to formulate different urban green system scenarios. The second case study focuses on modelling ecoregions from spatial datasets for the state of Queensland. The modelling combines collaborative expert knowledge and a vast amount of environmental data to build biogeographical classifications of regions. An information elicitation process is used to capture expert knowledge of ecoregions as geographical descriptions, and to transform this into prior probability distributions that characterise regions in terms of environmental variables. This prior information is combined with measured data on the environmental variables within a Bayesian modelling technique to produce the final classified regions. We describe how linked views between descriptive information, mapping and statistical plots are used to decide upon representative regions that satisfy a number of criteria for biodiversity and conservation. This paper discusses the advantages and problems encountered when undertaking group model building. Future research will extend the group model building approach to include interested individuals and community groups.