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Stochastic modelling is based on the idea of substituting random processes, with known properties, for unknown elements of the system. If these finer features of the substitute processes mimic closely those of the true underlying processes, then the model, at a coarser level, can provide useful insights concerning the system under investigation. Determining a sufficiently good match between the processes is the difficulty, requiring mathematical and statistical tools, and usually some knowledge of the application subject. A particularly useful product of stochastic models is the inbuilt treatment of variability. With advances in computing, the field is gaining in power and utility, simulation techniques in particular making feasible models too intractable for analytic techniques. This does, however, create new problems with estimating parameters in such complex systems, particularly sensitivity issues with model formulation and observations of high leverage.
My major interest is in hazard estimation, particularly from earthquakes and volcanos. Such models can be structural, designed to aid understanding of the phenomenon or, by fitting to historical data and extrapolating forward, be used for forecasting. I have also worked on the statistical properties of stochastic processes useful in hazard forecasting, and on computational methods for their solution.
The second major theme of my research is management OR; the quantitative techniques used in the management, monitoring and control of production processes and services. Most of my activity centres on statistical inference for hazard models in reliability and survival analysis, and statistical quality control, including quality assurance, the effect of correlation on production processes, continuous inspection procedures, and design of sampling plans. I also use simulation and statistical analysis, usually in a consulting context.
Links between the two themes are formed by work on approximations for performance measures in telecommunications networks, and the effects of network externality in market behaviour using stochastic models. Recent work includes applications to biostatistics and fluvial dating/climatology.
I'm Professor in Geostatistics, in the Statistics Group and in Volcanic Risk Solutions at Massey University in Palmerston North, New Zealand. My research is focussed on estimation of hazard from volcanoes and earthquakes, with interests in related problems from survival analysis and process control.
I moonlight as an Associate Editor for the Australian & New Zealand Journal of Statistics and for Statistics in Volcanology (https://scholarcommons.usf.edu/siv/), and am a member of the New Zealand Volcano Science Advisory Panel
Estimation of volcanic hazard using stochastic models. Statistical models for earthquake interaction.
Inference and computational methods for stochastic processes.
Reliability and survival analysis, particularly in complex systems.
Statistical quality control and acceptance sampling methods.
Stochastic operations research, including simulation and statistical analysis.
Field of research codes
Applied Mathematics (010200): Applied Statistics (010401): Biostatistics (010402):
Earth Sciences (040000): Geology (040300): Geophysics (040400):
Mathematical Sciences (010000): Operations Research (010206):
Seismology and Seismic Exploration (040407):
Statistics (010400): Stochastic Analysis and Modelling (010406):
Volcanic hazard analysis.
Project Title: NSC - Hazard: Resillience to NZ's hazard spectrum
Date Range: 2015 - 2019
Funding Body: Institute of Geological & Nuclear Sciences Ltd
Project Title: Living with Volcanic Risk
Date Range: 2004 - 2015
Funding Bodies: Foundation for Research, Science & Technology; Institute of Geological & Nuclear Sciences Ltd