We live in an era dominated by global financial crises, climate change, floods, droughts, bushfires, global epidemics and many other stochastic phenomena. In addition, this is also an era where, thanks to computer, sensor and satellite technologies, data are collected on a scale unimaginable only a few years ago. These twin drivers of the need to understand and manage uncertainty on the one hand and to exploit valuable information stored in enormous data bases on the other hand, ensure that subjects of Stochastic Modelling and Statistics are more relevant than ever. Consequently, the work of Flinders' Statistics and Stochastic Modelling research group focusses on problems related to risk management, probability modeling, classification theory and analysis of survival data. Specific projects, currently being investigated are listed below.
Professional and community engagement
Alan Branford is President of the South Australian Branch of the Statistical Society of Australia Inc.
Local grade inflation and local proportion of withdrawals
Alan Branford and his collaborators Jonathan Kuhn and Aaron Warren from Purdue University North Central and Diane Maletta from University of Notre Dame have been investigating relationships between grade inflation and proportion of withdrawals, at a small public university in the US. The findings of these investigations will appear in the Research of Higher Education Journal, published by Academic and Business Research Institute (AABRI).
The study was based on the assumption that educational institutions must be accountable to communities in general and students in particular, and fair and consistent assessment is an important component of this. If assigned grades for one group of students are higher than grades for a similar group of students, then grade inflation is said to be localised to the first group relative to the second. Local grade inflation is essentially a form of favouritism; one group of students is favored over another group of students. Identifying the behavior of local grade inflation involves comparing local grade point averages (LGPAs) of the grade distributions of different groups of students. Local grade point averages were calculated from the grades of individual students. Grade distributions for 7,500 class sections from a small public Midwestern University, from fall 1998 to fall 2007, were collected and analysed. Statistically significant (p-value < 0.01) categorical explanatory variables for LGPAs were compared and contrasted with statistically significant categorical explanatory variables for local proportions of withdrawals (LPWs). Statistical analysis found clear evidence (p-value < 0.01) that both LGPA and LPW are significantly different for different explanatory variables such as courses and instructors, as well as subjects, departments and academic course levels, but not for instructor academic qualifications, gender, and job category, nor for academic year, academic semester and class time period. Moreover, the R^2 measures of fit of model to data for one-variable, two-variable and multi-variable LGPA-dependent analysis of variance models were mostly larger than for equivalent LPW-dependent one-variable, two-variable and multi-variable models.
Unlocking the grid: the future of the electricity distribution network
This project consists of work carried out under Australian Research Council Linkage Grant (Dr. J.Boland, Mr D. Bruce, Prof J. A. Filar, Dr T. Wigley). Project titled “Unlocking the grid: the future of the electricity distribution network”. Duration: 2009-2011.
Increases in electricity demand lack uniformity in time and space. Power networks across Australia need considerable reinvestment over the next decade or so. This research models optimum placement of nodes within existing networks to best fit future spatial structure of demand. Significant benefits can be gained through a scientific design of the planned grid architecture, enabling timely and efficient incorporation of new wind or solar farms, and a carbon emission efficient and cost effective electricity grid management strategy.
Strategic integration of renewable energy systems into the electricity grid
This project consists of work carried out under Australian Research Council (Discovery Grant) ( Dr J. Boland and Prof. J.A. Filar). Project titled “Strategic integration of renewable energy systems into the electricity grid”. Duration: 2009-2011.
Electricity generation companies are using renewable energy systems to lower greenhouse gas emissions (GHG), but without determining which mixture of technologies is most beneficial. We exploit advanced stochastic modelling and dynamic optimisation techniques to structure the integration of renewable energy systems into the electricity supply system, to provide the greatest reduction in GHGs, at least cost, while maintaining supply strictures set by the National Electricity Market Management Company. Our methods aim to determine the mix of resources needed to schedule this integration to cater for the stochastic nature of both electricity demand and renewable energy resources while meeting mandatory targets.
Regime-switching volatility models: Classical and Bayesian approaches
Regime switching models or volatility models have become very popular in financial modelling especially in such studies of financial markets during the recent Global Financial Crisis in 2007–2008. The regime switching models such as Threshold Autoregressive (TAR), Smoothing TAR (STAR) or the volatility models such as GARCH models and its variants have revolutionised the way that many statistical problems can be approached in modelling of complex systems. Classical inference of parametric TAR or STAR or GARCH models has been considered in the literature since 1986s to very recently in contrast to the limited study in the combination of TAR-GARCH and STAR-GARCH and in Bayesian inference of TAR/STAR or STAR-GARCH models. This project is significant because we will include a modified EM algorithm (Classical) or an RJMCMC algorithm (Bayesian) or its variant that fully accounts for model order uncertainty in univariate or bivariate TAR or STAR(p)-GARCH(s,q) models, that is, we assume that (p,s,q) are the parameters of the models. The project aims and concepts are innovative because thorough prior sensitivity analysis will be presented and modified EM, RJMCMC or other novel MCMC algorithms will be developed, both theoretically and computationally, for TAR or STAR(p)-GARCH(s,q) models.
Bayesian hidden Markov model of DNA sequence sehmentation: short sequence modelling and identification of change points
Short biological motifs in DNA sequences, such as transcription factor (TF) binding sites and splicesites, are of considerable interest to biologists. The binding of TFs to specific DNAsequences near the transcription start site is one of the first steps to determine whether a gene is turned on or off. Splice sites are the boundaries between exons and introns, consisting of 5 inch donor sites at the exon/intron junctions, and 3 inch acceptor sites at the intron/exon junctions. The variability in these motifs makes it difficult to identify all the potential sites precisely, but well-characterized features of these signals make it possible to model the signals statistically and do better than using non statistical rules.This project focuses on the simulation, estimation, specificity and sensitivity of a hidden Markov model describing short biological motifs inDNA sequences and identifying its change point.