AUSTRALIAN RESEARCH COUNCIL
Centre of Excellence for Mathematics
and Statistics of Complex Systems

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List below are research staff, research students, honours students, vacation scholars and visitors attached to the Queensland site.

Staff [Some projects are listed below]

  • Prof. Phil Pollett, Chief Investigator and Director (Qld)
  • Dr Ross McVinish, Research Fellow

PhD students (current) [Projects are listed below]

  • Robert Cope, Animal Movement Between Populations Deduced from Family Trees - a Test Case on Dugongs in Southern Queensland
  • Dejan Jovanović, Fault Detection in Complex and Distributed Systems
  • Aminath Shausan, Stochastic Models for Epidemics in Population Networks
  • Andrew Smith, Spatially structured metapopulation models within static and dynamic environments

PhD students (graduated) [Theses descriptions below]

  • Fionnuala Buckley, Analytical Methods for Stochastic Discrete-time Metapopulation Models (PhD awarded April 2011)
  • Ben Cairns, Hitting Times for Markov Population Processes Subject to Catastrophes (PhD awarded December 2005)
  • Ben Gladwin, Long Time Scale Simulations of Biological Molecular Systems (PhD awarded December 2007)
  • Dharma Lesmono, Stochastic Models of Election Timing (PhD awarded September 2007)
  • Daniel Pagendam, Experimental Design and Inference for Population Models (PhD awarded November 2010)
  • Joshua Ross, Density Dependent Markov Population Processes: Models and Methodology (PhD awarded March 2007)
  • David Sirl, On the Analysis of Absorbing Markov Processes (PhD awarded May 2008)
  • Antony Stace, Volume Weighted Average Price Options (PhD awarded June 2007)
  • Thomas Taimre, Advances in Cross-Entropy Methods (PhD awarded May 2009)

Other research students (graduated) [Theses descriptions below]

  • Nicholas Denman, Topics in Quasi Stationarity of Markov Chains (MPhil awarded April 2008)
  • Olena Kravchuk, Trigonometric Scores Rank Procedure with Application to Long-Tailed Distributions (PhD awarded May 2006)

Coursework Masters students

  • Chung Kai Chan, Quasi-stationary Distributions of Continuous-Time Markov Chains and their Application to Metapopulation Models, 2009
  • Daniel Pagendam, Experimental Design and Inference for Population Models, 2006

Honours students

  • Trent Spears, Extreme Value Theory with Applications, 2011-2012
  • Yui Sze (Jessica) Chan, A Stochastic Metapopulation Model that Accounts for Habitat Dynamics and Landscapes with Ample Resources, 2011
  • Alex Ridley, A Network-Based Approach to Modelling Epidemics, 2009
  • Robert Cope, Quasi-Birth-and-Death Process, 2008
  • Jeanette Palmer, Markovian Models for Stress Release and Transfer, 2006
  • Leesa Wockner, Genetic Modelling and Random Walks, 2006-07
  • Zdravko Botev, Stochastic Methods of Optimization, Simulation and Learning, 2005
  • Andrew Garton, The Fibonacci Sequence and the Golden Section in Western Art Music of the Twentieth Century, 2005
  • Caitlin James, Measuring Persistence of Populations using Importance Sampling with Cross-Entropy, 2003-2004 [Honours talk]
  • Thomas Taimre, Noisy Optimisation via Randomized Algorithms, 2004
  • David Sirl, Uniqueness Conditions for Continuous-Time Markov Chains, 2003

Advanced Study Program in Science students

  • Robert Cope, Importance Sampling Strategies for Assigning Hybrid Alleles to Parental Populations, 2006

Vacation scholars

  • Ryan Heneghan, Exploring Vaccination Methods for an SIR Epidemic on a Random Population Network with Household Structure and Varying Rates of Infectivity and Severity, 2013-14
  • Patrick Laub, Fixed Point Methods for Loss Networks, 2012-13
  • Trent Spears, Probability with Martingales for Economics and Finance, 2010-11
  • Trent Spears, The Development and Contemporary Applications of Stochastic Processes, 2009-10
  • Chung Kai Chan, Quasi-stationary Distributions in Markovian Models, 2007-08
  • Robert Cope, Importance Sampling Strategies for Assigning Hybrid Alleles to Parental Populations, 2006-07
  • Connie McDonagh, Traffic Flow in Telecommunications Networks, 2005-06
  • Ian Nester, Metapolulation Models, 2005-06 [report]
  • Jeanette Palmer (ICE-EM Scholar), Network Models for Seismicity, 2005-2006 [report]
  • Leesa Wockner, Models for Spatially Structured Metapopulations, 2005-06
  • Laurel Yu, Modelling Bistability in Telecommunications Systems, 2005-06 [report]
  • Nathan Jackson, The CE Toolbox, 2004-05 [report]
  • Caitlin James, The Cross-Entropy Method for Rare Event Simulation, 2003-04
  • Thomas Taimre, The Cross-Entropy Method for Rare Event Simulation and Randomized Optimization, 2003-04 [report|programs]

Visiting fellows

  • Andrew Barbour (University of Zurich and University of Melbourne), January 2013
  • Malwina Luczak (Queen Mary, University of London), January 2013
  • Andrew Barbour (University of Zurich and University of Melbourne), April 2012
  • Malwina Luczak (University of Sheffield), November 2011
  • Gideon Weiss (University of Haifa), February 2011
  • Andrey Lange (Bauman Moscow State Technical University, Moscow) November 2009
  • Jean Bernard Lasserre (Laboratoire d'Architecture et d'Analyse des Systèmes, Centre National de la Recherche Scientifique, Toulouse), November 2009
  • Mary Myerscough (University of Sydney), June 2009
  • Erik van Doorn (University of Twente), May 2009
  • Philip O'Neill (University of Nottingham), March 2009
  • Sophie Hautphenne (Université Libre de Bruxelles), February 2009
  • Jean Bernard Lasserre (Laboratoire d'Architecture et d'Analyse des Systèmes, Centre National de la Recherche Scientifique, Toulouse), October 2008
  • Olena Kravchuk (UQ School of Land, Crop and Food Sciences), July-October 2008
  • Dharma Lesmono (Parahyangan Catholic University), September 2007-January 2008
  • Jean Hu (Northwestern University), February-May 2007
  • Paul Slade (University of Adelaide), March-April 2006
  • Jiri Tuma (Charles University), October-November 2005
  • Peter Smith (University of Canterbury), July 2005
  • Flora Spieksma (University of Leiden), July 2005
  • Tony Pakes (University of Western Australia), April 2005
  • Anyue Chen (University of Greenwich), April 2005
  • Gideon Weiss (University of Haifa), February 2005
  • Peter Taylor (MASCOS CI, University of Melbourne), February 2005
  • Tony Pakes (University of Western Australia), February 2005
  • Nigel Bean (University of Adelaide), February 2005
  • Andrew Barbour (University of Zurich), September 2004
  • Anyue Chen (University of Greenwich), July-August 2004
  • Ruyun Ma (Northwest Normal University, China), February 2004-February 2005
  • Kin Ping Hui (DSTO, Australia), January 2004
  • Soren Asmussen (University of Aarhus), January 2004
  • Erik van Doorn (University of Twente), March-May 2003

Former staff

  • Dr Iadine Chadès, Research Fellow (August 2008-August 2009). Now at CSIRO (Ecosystems Science Division)
  • Dr Martin O'Hely, Research Fellow (September 2004-November 2007). Now at the Walter and Eliza Hall Institute of Medical Research (Bioinformatics Division)
  • Dr Hanjun Zhang, ARC Centre Fellow (January 2003-December 2007). Now at Xiangtan University (School of Mathematics and Computational Science)

Staff and student projects

Prof. Phil Pollett, Chief Investigator and Director (Qld)

Phil's research is in the field of mathematical modelling, and is chiefly concerned with the theory of stochastic processes and applications in ecology, epidemiology, parasitology, telecommunications and chemical kinetics.

A current project: General stochastic models for branching

This is joint work with Hanjun Zhang, Anyue Chen (University of Liverpool and Junping Li (Central South University, Changsha). A common feature of branching models is that particles or individuals behave independently producing descendants according to the same rule. However, since particles may interact, through collision or some other mechanism, this branching property may be lost. For this reason, more general branching models have been proposed. We are studying a particularly interesting class, which we call the weighted (or non-linear) Markov branching processes. We are examining questions concerning the existence and uniqueness of such processes, and criteria for extinction.

Dr Ross McVinish, Research Fellow

Ross has research experience in a number of areas of probability and statistics, from Lévy processes and stochastic processes displaying long memory, to Bayesian nonparametrics, and computation for Bayesian statistics and time series analysis.

A current project: Statistical inference for partially observed metapopulations

A common type of metapopulation model is a presence-absence model in discrete time with a Markov dependence structure. This type of model only tracks whether or not each patch within the metapopulation is occupied and the future state of the metapopulation depends only on the present state. When all patches within the metapopulation are observed, the likelihood function can be written explicitly which makes estimation relatively straightforward. However, it is not always possible to perform a complete census of a metapopulation. This may be due to costs associated with a census or due to accessibility or perhaps the locations of some patches are unknown. In these situations we may attempt to make inference about the metapopulation based only on the observations from a small number of patches.

In theory one can still perform likelihood based inference given only partially observation of the metapopulation. To form the likelihood function based on partial observation, one takes the likelihood function based on complete observation and integrates out those unobserved patches. Typically, the necessary integration is performed using simulation based methods. However, when the number of patches is large, the situation where partial observation would be most common, accurate integration can be very challenging.

An alternative to using an exact likelihood is to use an approximate likelihood based letting the number of patches increase to infinity. We provide certain conditions under which the model for the observed patches converges to a time-inhomogeneous Markov chain. This provides an explicit approximate likelihood function which can then be used in either maximum likelihood estimation (MLE) or Bayesian estimation. Under rather mild conditions, we show that the exact MLE converges to the proposed approximate MLE as the number of patches increases. Similarly for the Bayesian estimate, we prove convergence of the exact posterior distribution to the proposed approximate posterior distribution.

Unfortunately, when the exact likelihood function is replaced by the asymptotic approximation, a loss of efficiency is incurred. To investigate the degree of the efficiency loss, we carry out a simulation study using two metapopulation models. The exact MLE and Bayesian estimates will be evaluated using a sequential Monte Carlo algorithm.

Dr Iadine Chadès, Research Fellow (August 2008-August 2009)

Iadine has research intersests in mathematical modelling and decision making in ecology and conservation biology. She is presently a Research Scientist at CSIRO Ecosystems Science.

Dr Martin O'Hely, Research Fellow (September 2004-November 2007)

Martin is interested in applications of probability to the biological sciences. The bulk of his research to date has addressed problems in population genetics. Martin is presently Research Officer in the Bioinformatics Division at the Walter and Eliza Hall Institute (Melbourne).

Dr Hanjun Zhang, ARC Centre Fellow (January 2003-December 2007)

Hanjun is known internationally for contributions to Markov process theory. Hanjun presently holds a position in the School of Mathematics and Computational Science at Xiangtan University.

Fionnuala Buckley, AMSI-MASCOS PhD Scholar (2007-09)

Thesis title: Analytical Methods for Stochastic Discrete-time Metapopulation Models

(PhD awarded April 2011)

The term 'metapopulation' is used to describe a population confined to a network of geographically separated habitat patches that may suffer extinction locally and be recolonized through dispersal of individuals from other patches. Fionnuala has studied discrete-time Markov chain models that account for seasonal variation in metapopulations, assuming that colonisation and extinction occur in distinct successive phases (one might envisage an annual cycle, with local populations being susceptible to extinction during winter, while new populations establish in empty patches during the spring); a census takes place either at the end of successive colonisation phases (EC model) or at the end of successive extinction phases (CE model) and the state of the Markov chain is the state of the population at a census time. Whilst this approach has become predominant in the applied metapopulation literature, because it provides a vehicle for parameter estimation and permits control mechanisms to be investigated using simple optimisation tools such as dynamic programming, generally only numerical and simulation methods have been used to analyse discrete time metapopulation models (and, then, typically only the EC case).

Fionnuala's work provides the first detailed mathematical analysis of these models. She has derived a law of large numbers, which is used to identify an approximating (discrete-time) deterministic trajectory, and a central limit theorem, which establishes that the scaled fluctuations about this trajectory have an approximating autoregressive structure. This was done for a class of time-inhomogeneous Markov chains that share the salient features of her metapopulation models, and then applied to those models in order to draw conclusions about real ecological systems.

Ben Cairns, MASCOS PhD Scholar (2003-05)

Thesis title: Hitting Times for Markov Population Processes Subject to Catastrophes

(PhD awarded December 2005)

Ben worked on a range of problems in stochastic modelling of complex biological systems. He determined the extinction probabilities and expected extinction times for the Markovian catastrophe process in continuous time, with a general transition rate function, and gave necessary and sufficient conditions for explosivity. Ben developed truncation procedures for estimating persistence in populations which may be affected by catastrophic events, and which are either unbounded or have very large ceilings. He developed theory for first-exit time problems in the context of general piecewise-deterministic processes, providing a general, robust numerical procedure for estimating first-exit times and implemented this using techniques from interval analysis.

Ben is a research scientist in the Cancer Epidemiology Unit at the University of Oxford having previously held a postdoctoral position in the School of Biological Sciences at the University of Bristol.

Yui Sze (Jessica) Chan, PhD student (2012-2013)

(withdrawn)

Robert Cope, PhD student (2009-2014)

Thesis title (provisional): Animal Movement Between Populations Deduced from Family Trees - a Test Case on Dugongs in Southern Queensland

The aim is to develop a new method for estimating animal movements using information contained in family trees. Movement estimates are essential to population models that assist natural resource managers to plan species recovery and to predict the effect of future challenges, such as human-mediated activities and climate change. I will evaluate ways of constructing family trees from genetic data and develop a statistic that describes animal movement between populations that is based on the families whose members were sampled in more than one population; empirical data has been sourced from a long-term mark-recapture study of dugongs in Moreton Bay, and new samples from two adjacent populations.

Nicholas Denman, Part-time MPhil Student

Thesis title: Topics in Quasi Stationarity of Markov Chains

(MPhil awarded July 2007)

Quasi-stationary distributions are tools that allow one model the long-term behaviour of processes that "die out". Convergence of standard truncation methods for evaluating quasi-stationary distributions is not always guaranteed, and it is desirable to have algorithms that avoid truncation. An algorithm which avoids truncation in computing stationary distributions is the GTH Algorithm. It completely avoids subtraction, and it was shown that the algorithm computes stationary distributions with low relative error, and even extremely small stationary probabilities with high accuracy. A simple principle has been proposed: that many algorithms in non-negative arithmetic produce results with low relative error. Nick explored how this principle applies to the evaluation of quasi-stationary distributions. He examined an algorithm for computing the dominant eigenvectors which uses non-negative arithmetic and which gives demonstrably low relative error.

Nicholas is a risk consultant with Energy Edge (Brisbane) Ltd.

Benjamin Gladwin, MASCOS PhD Scholar (2003-04)

Thesis title: Long Time Scale Simulations of Biological Molecular Systems

(PhD awarded December 2007)

Ben works primarily on long time-scale molecular dynamics. Traditionally, molecular processes are seen from a classical physics perspective and use various forward integration algorithms to provide thermodynamic information from trajectories. These techniques are primarily limited by computational resource constraints. A series of new algorithms were proposed which achieves low resolution trajectories of any time scale. One of the difficulties of these approaches is estimation of the overall time in which a molecular process takes place. Ben used mean first passage times to provide an initial trajectory through the molecules' conformation space. This approach reduces errors introduced by poor time-scale estimation. The practitioner is also provided with a starting point for a trajectory search using more traditional deterministic algorithms.

Ben is currently a medical student at Flinders University School of Medicine.

Dejan Jovanović, AMSI-MASCOS PhD Scholar (2009-11)

Thesis title (provisional): Fault Detection in Complex and Distributed Systems

The primary goal is to develop a theoretical framework based on Markov processes in order to detect, identify and isolate faults in complex and distributed systems. The aim is to improve overall safety and reduce any negative impact on the environment due to a fault. There are three main tasks. The first is development of local stochastic models, which need to be capable of interpreting the local environment's state. At the core is estimation of transition probabilities. The second is extracting the features of local models in the case of non-faulty and faulty operating conditions. In order to assist local models to achieve satisfactory results, design and implementation of a multi-agent system is proposed. The next task is planning an optimal action to protect the environment. Finally, the framework has to allow for the possibility of incorporating local expert knowledge about the system.

Dejan Jovanovic
Olena Kravchuk, Part-time PhD Student

Thesis title: Trigonometric Scores Rank Procedures with Applications to Long-tailed Distributions

(PhD awarded May 2006)

Long-tailed distributions have become extremely popular for modelling stochastic noise in many applications including image analysis, finance and environmental data analysis. However, often the tail behaviour of such distributions is not precisely known and nonparametric statistical procedures are evoked to perform inference about the location and scale characteristics. Olena's work proposes several new rank procedures that are efficient for a wide range of unimodal, symmetric, long-tailed distributions.

Olena is a Lecturer in Biometrics in the School of Land, Crop and Food Sciences, The University of Queensland.

Dharma Lesmono, MASCOS PhD Scholar (2004-05)

Thesis title: Stochastic Models of Election Timing

(PhD awarded July 2006)

Dharma made several major contributions to the study of election forecasting. He derived a model for the early election call problem that accounts for the possibility of a government using control tools, termed "boosts", to induce shocks in the opinion polls by making timely policy announcements or economic actions. These actions improve the government's popularity and have some impact on the early-election exercise boundary. He is presently working on some theoretical extensions the basic framework. He is studying a bounded mean-reverting process, used in the pricing of energy options and in election forecasting. He aims to provide conditions for existence and uniqueness of a bounded mean-reverting stochastic differential equation whose drift coefficient does not satisfy either of the usual Lipschitz or linear growth conditions.

Dharma is a Lecturer in the Department of Mathematics, Parahyangan Catholic University, Indonesia.

Daniel Pagendam, AMSI-MASCOS PhD Scholar (2007-09)

Thesis title: Experimental Design and Inference for Population Models

(PhD awarded November 2010)

Statistical Inference for discretely observed stochastic models is an active and challenging area of research. However, whilst much attention has been given to methodologies for parameter estimation, little work has been done to find optimal schedules for observing these processes. Daniel addresses the topic of optimal experimental design for density dependent Markovian models, which routinely encountered in ecology and epidemiology, with a view to improving the manner in which data is collected for both controlled and natural experiments.

He frames the search for optimal designs using the classical D-optimality criterion, so that the series of observations of the process maximizes the determinant of the Fisher information matrix. The resulting designs maximize the precision of the maximum likelihood estimator. In the case of some simple one parameter models, the optimal observation times can be obtained analytically and he has derive one such design for the simple death process. He showed that this design is closely related to the optimal design for the simple birth process.

When models are more complicated, such as when more than one parameter is involved, the Fisher information matrix, which lies at the heart of many classical optimality criteria, can rarely be arrived at analytically. Daniel shows how Gaussian diffusion approximations can be used to obtain an approximation to the Fisher information matrix for density dependent Markovian models. When this method is coupled with the cross-entropy method of stochastic optimization, he is able to obtain optimal observation times rapidly.

Daniel has also shown how diffusion approximations can be used for parameter estimation in multi-dimensional, multi-parameter epidemic models with data collected during an outbreak of Russian influenza in a boarding school serving as an example application of his methodology. He has examined optimal design for some commonly used epidemiological models, including the SI, SIS and SIR epidemics, and has made recommendations for the design of experimental epidemics or transmission studies.

Dan is currently OCE Postdoctoral Research Fellow within the CSIRO Mathematics, Informatics and Statistics Division.

Joshua Ross, MASCOS PhD Scholar (2004-06)

Thesis title: Density Dependent Markov Population Processes: Models and Methodology

(PhD awarded February 2007)

Joshua developed continuous-time Markov chain models for metapopulations that inhabit a dynamic landscape. He established deterministic and diffusion approximations for these processes, and derived normal approximations to their (quasi-)stationary distributions. He also investigated the costs and decisions of controlling populations that have a negative impact on their habitat. For two commonly used control regimes, suppression and reduction, he gave population managers direction on how best to choose the control parameters. Joshua compared the predicted extinction time estimates derived from continuous-time Markov chain models with the estimates from their appropriate Ornstein-Uhlenbeck approximating diffusion and a simple Brownian motion approximation. In joint work with Thomas Taimre he developed a method for estimating the parameters of a wide class of continuous-time Markov chains called density-dependent Markov chains. The only other known approach to estimating parameters for such processes is computationally infeasible when the state space, or uncertainty in the parameter values, is too large. This new procedure makes use of the above-mentioned diffusion approximations, and in the situations where the approach is most commonly applied, the estimates improve as the state space increases in size. Several applications of this procedure are currently under investigation.

Joshua is currently Lecturer in Applied Mathematics within the School of Mathematical Sciences, The University of Adelaide, having previously held a Research Fellowship at King's College Cambridge UK and a post-doctoral research assistantship at the University of Warwick.

Aminath Shausan, MASCOS PhD Scholar (2010-13)

Thesis title (provisional): Stochastic Models for Epidemics in Population Networks

I will study the spread of infection in "small world" population networks, where the network is made up of many local links and fewer long range "shortcuts". When an infection is introduced, it may spread locally and eventually die out (imagine an infection spreading in a small town). I will consider the effect of infection via long range links (think of an infection introduced by an airline passenger) and provide a stochastic model to describe the spread of the infection throughout the network, addressing several questions concerning stability and the duration of the epidemic.

My starting point will be a model where the network is made up of many local links and fewer long range "shortcuts". Previous researchers investigated the distribution of the inter-point network distances, their results being framed in terms of approximations whose accuracy increases with the size of the network. I propose to study the spread of epidemics on these networks, using approximation methods (which become more accurate as the network grows in size) to determine whether or not there is a critical level, in terms of the limiting proportion of long-range links, that causes the infection to take hold, and, below which the epidemic dies out. It is hoped that results of the project will be of use to epidemiologists and ecologists, and indeed of use practitioners in fields where "network" is an appropriate paradigm.

David Sirl, AMSI-MASCOS PhD Scholar (2005-06)

Thesis title: On the Analysis of Absorbing Markov Processes

(PhD awarded May 2008)

David's PhD thesis is concerned with the analysis of absorbing discrete-state Markov processes. He looked at the problem of establishing the existence of quasi-stationary distributions (QSDs). He proved results on exponential convergence rates and established the existence of a QSD for a particular chemical reaction model.

David studied a well-known and important exponential convergence rate: Kingman's decay parameter. He adapted results of Mu-Fa Chen to give explicit bounds for the decay parameter of a birth-death process in terms of the transition rates, an immediate corollary of which is a necessary and sufficient condition for the decay parameter to be positive, and analysed these bounds analytically and numerically.

David also investigated an application of the analysis of absorbing Markov chains in ecology. He considered a threatened species occupying a habitat which consists of a number of discrete patches. He extended existing models to allow for the possibility that one can protect certain patches from disturbances. He discussed deterministic approximations, which become both computationally necessary, and mathematically more accurate, as the system size becomes large. He used both the full stochastic model and the deterministic approximation to investigate the effect on the viability of the population of two management options: creating more patches, or protecting existing patches from disturbance events. The optimal management plan was determined under a given a total budget and per-patch costs for these two possible actions.

David is currently Lecturer in Statistics, Mathematics Education Centre, Loughborough University UK, having previously held a research fellowship in the School of Mathematical Sciences, University of Nottingham UK.

Andrew Smith, AMSI-MASCOS PhD Scholar (2009-12)

Thesis title (provisional): Spatially structured metapopulation models within static and dynamic environments

A metapopulation is a population that occupies several geographically separated habitat patches. Although the individual patches may become empty through local extinction, they may be recolonized through migration from other patches. There is considerable empirical evidence which suggests that a balance between migration and extinction is reached that enables metapopulations to persist for long periods, and there has been considerable interest in developing methods that account for the persistence of these populations and which provide an effective means of studying their long-term behaviour before extinction occurs.

I will begin by looking at basic patch-occupancy models that merely record which patches are occupied. The main aim is to exploit recent developments in stochastic network theory by adapting models that were developed originally for the study of telecommunications systems. By recording the numbers of individuals in the various patches we can incorporate local patch dynamics, spatial structure and migration patterns. I will adopt the powerful diffusion approximation technique that has been used so effectively in the analysis of patch-occupancy models.

Antony Stace, MASCOS PhD Scholar (2004-05)

Thesis title: Volume Weighted Average Price Options

(PhD awarded July 2007)

Antony developed methods for the valuation of a Volume Weighted Average Price option (VWAP). This is an option which has a strike which is a VWAP. He obtained a number of results about these options including an approximation to the price by moment matching and also a series solution. Antony also investigated a numerical solution to the partial differential equation that describes the price of the option by finite differences. This procedure presents a number of challenges; simple finite difference methods are impractical due to the curse of dimensionality, so alternating direction implicit and splitting methods were investigated.

Antony is a risk consultant with Energy Edge (Brisbane) Ltd, having previously held a position on the financial risk management team of Pricewaterhouse Coopers (Auckland, New Zealand).

Thomas Taimre, AMSI-MASCOS PhD Scholar (2005-07)

Thesis title: Advances in Cross-Entropy Methods

(PhD awarded May 2009)

The Cross-Entropy Method is a technique used for solving estimation, simulation and optimisation problems. Thomas Taimre's work has helped consolidate our understanding of the Cross-Entropy Method and several of its generalisations, as well as its connection with importance sampling and other Monte Carlo methods. Thomas has elucidated several new major applications of cross-entropy methodology to optimisation problems. He has developed new methods within the generalised cross-entropy framework which enable one to construct state- and time-dependent importance sampling algorithms, and he has developed a new algorithm for counting solutions to difficult binary-encoded problems.

Thomas is presently a Lecturer in the UQ School of Mathematics and Physics


The Centre of Excellence for Mathematics and Statistics
of Complex Systems is funded by the Australian Research
Council, with additional support from the Queensland
State Government and the University of Queensland