Research Priorities 2007

• Population models - how do we best estimate the risk of extinction?
• Mathemtical models for populations of native fauna - what is the best management strategy: reduction or suppression?
• Parameter estimation in continuous-time Markovian models - can we estimate the parameters efficiently when the process is observed at discrete time points?
• Option pricing - can we price options whose payoff depends on the volume weighted average price?

Researchers

• Chief Investigator: Phil Pollett
• ARC Centre Fellow: Hanjun Zhang
• PhD student : Daniel Pagendam
• PhD student : Thomas Taimre

Sub-themes

• Population models
• Branching processes
• Diffusion approximations
• Option pricing

Research Outcomes

• The risk of extinction was estimated using diffusion and other approximations for a variety of population models based on discrete-state Markov processes.
• A branching model with nonlinear weights was introduced, and criteria were established for the existence and uniqueness of processes whose transition functions satisfy both the forward and backward equations.
• Optimal sampling procedures were developed for some simple population models. These were compared with the simpler equidistant design, where the population is sampled at regular intervals.
• A birth-death process allowing catastrophes was studied where the transition rates were allowed to depend on the population size. An explicit expression for the expected time to extinction was obtained, which is valid in all cases where extinction is certain to occur.
• Population models were created that allow management programmes to be assessed. Two common control regimes were considered: reduction and suppression. Direction was given on how to best choose the control parameters, thus allowing population managers to select reduction levels and control rates.
• A general approach to estimating parameters of continuous-time Markov chains from discretely sampled data was combined with a new stochastic model for transmission of hospital-acquired infections that accounts for dynamic bed occupancy. This provided a means of assessing the efficacy of management strategies designed to decrease the prevalence of such infections.
• Bounds were derived for the decay parameter of absorbing birth-death processes. The accuracy of these bounds was assessed for several models, including the stochastic logistic model.
• A method was developed to find the price of several options whose payoff depends on a volume weighted average price (VWAP). Fixed and floating strike VWAP together with digital VWAP contracts were considered.

Awards and Achievements

• Nicholas Denman completed his MPhil degree (awarded July 2007) at the University of Queensland on "Topics in Quasi Stationarity of Markov Chains". He is currently reading for his PhD at the University of Queensland.
• AMSI-MASCOS PhD Scholar Daniel Pagendam was awarded the International Biometrics Society (IBS) Australasian Regional Travel Award to attend the International Biometric Conference (Dublin, Ireland, July 2008).
• AMSI-MASCOS PhD Scholar Daniel Pagendam received a Student Commendation for his paper titled "Optimal sampling and problematic likelihood functions in a simple population model" presented at the 17th Biennial Congress on Modelling and Simulation (University of Canterbury, Christchurch, New Zealand, December 2007).
• Phil Pollett (with Janet Lanyon, School of Integrative Biology, University of Queensland, and Jennifer Ovenden and Damien Broderick, Queensland Department of Primary Industries and Fisheries) was awarded $225,000 for a project titled "Animal movement between populations deduced from family trees: a test case on dugongs in southern Queensland" under the ARC Linkage Grant Scheme (2008-2010). Collaborating organizations: Queensland Department of Primary Industries and Fisheries, Consolidated Rutile Ltd and Sea World.
• MASCOS PhD Scholar Joshua Ross completed his PhD degree (awarded February 2007) at the University of Queensland on "Density Dependent Markov Population Processes: Models and Methodology". Joshua currently holds a Research Fellowship at King's College Cambridge UK, having previously held a post-doctoral research assistantship at the University of Warwick.

Industry Collaborators

• CS Energy Ltd, Brisbane
• Energy Edge Ltd, Brisbane

Collaborating Researchers

• Ben J. Cairns (University of Bristol)
• Anyue Chen (University of Hong Kong)
• Junping Li (Central South University, Changsha)
• Joshua V. Ross (University of Cambridge)

Highlight Publications

• Pollett, P.K., Zhang, H. and B.J. Cairns (2007) A note on extinction times for the general birth, death and catastrophe process. Journal of Applied Probability 44, 565-568.
• Ross, J.V. and P.K. Pollett (2007) On costs and decisions in population management. Ecological Modelling 201, 60-66.