Research Priorities

• Calibrating population models - how do we efficiently calibrate Markovian models from discrete-sampled abundance data?
• Quantitative risk stratification - how do we characterize patient risk in clinical trials and predict outcomes for other populations of risk?
• Quasi stationarity in Markovian models - can we model quasi stationarity and the risk of extinction in populations that can be modelling using reducible Markov chains?

Researchers

• Chief Investigator: Phil Pollett
• Research Fellow: Iadine Chadès
• Research Fellow: Ross McVinish
• PhD student: Robert Cope
• PhD student: Daniel Pagendam
• PhD student: Nimmy Thaliath
• Coursework Masters student: Chung Kai Chan

Collaborating Researchers

• Prof Erik van Doorn, University of Twente
• Dr Banti Fentie, Queensland Department of Environment and Resource Management
• Dr D. Roberts, Queensland Department of Environment and Resource Management
• Dr Joshua Ross, University of Cambridge

Research Projects

• Calibrating population models [images]

  Project leader: Phil Pollett (UQ)
  Researchers: Daniel Pagendam (UQ) and Joshua Ross (University of Cambridge)

  We have derived a computationally efficient method for calibrating a wide class of Markovian models from discrete-sampled abundance data, thus extending our earlier work [Ross, J.V., Taimre, T. and P.K. Pollett (2006) On parameter estimation in population models. Theoretical Population Biology 70, 498-510] to multi-dimensional and non-stationary processes. They are illustrated with reference to disease and population models, including application to infectious count data from an outbreak of Russian influenza (A/USSR/1977 H1N1) in an educational institution. The methodology is also shown to provide an efficient, simple and yet rigorous approach to calibrating disease processes with a gamma-distributed infectious period.

  Research outputs

  • Fentie, B., Pagendam, D. and D. Roberts (2009) Visual comparison of spatial patterns of annual suspended sediment loads estimated by two water quality modelling approaches. In (Eds. Anderssen, R.S., Braddock, R.D. and Newham, L.T.H.) Proceedings of the 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation, July 2009, pp. 3315-3321.
  • Pagendam, D.E. and P.K. Pollett (2009) Optimal sampling and problematic likelihood functions in a simple population model. Environmental Modeling & Assessment 14, 759-767.
  • Ross, J.V., Pagendam, D.E. and P.K. Pollett (2009) On parameter estimation in population models II: multi-dimensional processes and transient dynamics. Theoretical Population Biology 75, 123-132.
• Quantitative patient risk stratification

  Project leader: Phil Pollett (UQ)
  Researchers: David Chan (Massachusetts Institute of Technology), Milton Weinstein (Harvard University)

  Many clinical decisions require patient risk stratification. We introduce the concept of limiting conditional distributions to describe the proportion of surviving patients occupying each disease state. Such distributions can quantitatively describe risk stratification. Using recently established conditions for the existence of a positive limiting conditional distribution in a general Markov chain, we describe a framework for risk stratification using the limiting conditional distribution. We apply this framework to a clinical example of a treatment indicated for high-risk patients, first to infer the risk of patients selected for treatment in clinical trials and then to predict the outcomes of expanding treatment to other populations of risk. A positive limiting conditional distribution exists only if patients in the earliest state have the lowest combined risk of progression or death. We show that outcomes and population risk are interchangeable. For the clinical example, we suggest that previous clinical trials have selected the upper quintile of patient risk for this treatment, but also show that expanded treatment would weakly dominate this degree of targeted treatment, and universal treatment may be cost effective. We have shown that limiting conditional distributions exist for most Markovian models of progressive diseases and are well suited to represent risk stratification quantitatively. This framework can characterize patient risk in clinical trials and predict outcomes for other populations of risk.

  Research outputs

  • Chan, D.C., Pollett, P.K. and M.C. Weinstein (2009) Quantitative risk stratification in Markov chains with limiting conditional distributions. Medical Decision Making 29, 532-540.
• Quasi-stationarity in discrete-time Markovian models

  Project leader: Phil Pollett (UQ)
  Researchers: Erik van Doorn (University of Twente)

  We have studied Markov chains in discrete time with a single absorbing state and a finite set S of transient states. We determined the limiting behaviour of such a chain as time n tends to infinity, conditional on survival up to n. It is known that, when S is irreducible, the limiting conditional distribution of the chain equals the (unique) quasi-stationary distribution of the chain, while the latter is the (unique) r-invariant distribution for the one-step transition probability matrix of the (sub)Markov chain on S, r being the Perron-Frobenius eigenvalue of this matrix. Addressing similar issues in a setting in which S may be reducible, we have identified all quasi-stationary distributions and obtain a necessary and sufficient condition for one of them to be the unique r-invariant distribution. We also revealed conditions under which the limiting conditional distribution equals the r-invariant distribution if it is unique.

  Research outputs

  • Van Doorn, E.A and P.K. Pollett (2009) Quasi-stationary distributions for reducible absorbing Markov chains in discrete time. Markov Processes and Related Fields 12, 191-204.

Awards and Achievements

• Research Fellow Iadine Chadès (with Tara Martin, CSIRO Sustainable Ecosystems) was awarded a grant of CAD$13,000 from the World Wildlife Fund Canada Endangered Species Recovery Fund for a project titled "Can sea otter and abalone co-exist at not at risk levels?" (2008-2009)
• Research Fellow Iadine Chadès was awarded a grant of €4,000 from Réseau National des Systèmes Complexes to build collaborations on the theme of spatial POMDP (2008-2010)
• Research Fellow Ross McVinish was awarded a grant of $11,910 under the UQ New Staff Research Start-up Fund Scheme for a project titled "Bayesian nonparametric methods for system identification"
• AMSI-MASCOS PhD Scholar Thomas Taimre completed his PhD degree (awarded May 2009) at the University of Queensland: thesis title "Advances in Cross-Entropy Methods"