Statistics

The group is interested in a number of areas of probability and theoretical and applied statistics and in the application of these methods in a number of areas of science.

• Research areas
• Specialities of individual researchers

Contact person: Dr Qiying Wang (email: Q.Wang@maths.usyd.edu.au)

Research areas

• Applied probability, modelling and inference concerns the application of probability theory to systems that involve random phenomena. In particular, it applies probability theory and stochastic systems to solve applied problems in various fields such as finance, insurance, biology and medical science. Specific research areas of interest include: Trend diagnostics, model estimation, characterisations of probability distributions, Markov chain Monte Carlo methods, mixture models, geometric processes, generalized linear models, exchangeability and population genetics models, risk and survival analysis and modelling and inference in phylogenetics.

  Researchers: J. Chan, D. Marchev, S. Müller, J. Ormerod, J. Robinson, M. Stewart, N. Weber.

• Asymptotic Methods are used in all areas of statistics to provide approximations and are the basis of much of classical probability. We have interests in limit theorems, Edgeworth expansions, Berry-Essen bounds, large deviations, saddle-point approximations, nonparametric estimation and change-point models.

  Researchers: S. Müller, J. Robinson, M. Stewart, Q Wang, N. Weber.

• Bioinformatics refers to the developing field of applying quantitative reasoning including mathematical modeling, statistical analysis and computer science methodology to study large biological datasets. Such datasets are generated through high throughput biotechnological assays such as modern sequencing technologies and in analyzing these we gain insight into fundamental biological processes. Specific problems that we work on include the analysis of proteomics data, of gene regulation and DNA replication initiation.

  Researchers: U. Keich, S. Müller, J. Ormerod, J. Yang.

• Computational statistics aims to design algorithms for implementing statistical methods on computers, including the ones unthinkable before the computer age (e.g. bootstrap, wavelets, multiscale image processing), as well as to cope with analytically intractable problems it includes computationally-intensive statistical methods such as inverse problems, Markov chain Monte Carlo methods, density estimation and generalized additive models.

  Researchers: U. Keich, D. Marchev, S. Müller, J. Ormerod, J. Yang.

• Extreme value theory. The statistical analysis of extreme values is important for many disciplines, including finance, insurance and environmental sciences. The main goals of extreme value theory are to understand the behavior of maxima and of values that exceed a certain threshold. Multivariate extreme value theory investigates among others the analysis of spatial extremes, the estimation of support curves and risk assessment of financial assets

  Researchers: J. Chan, S. Müller, J. Robinson, M. Stewart.

• Time Series and Stochastic Processes covers the theory of random processes with dependence, in particular: stochastic volatility models for financial applications, biological modeling, finite and infinite non-negative matrices and their ergodicity and fractional processes.

  Researchers: J. Chan, S. Peiris, Q Wang, N. Weber.

Specialities of individual researchers

Academic and research staff

• Dr Jennifer Chan
  Generalised Linear Mixed Models, Bayesian Robustness, Heavy Tail Distributions, Scale Mixture Distributions, Geometric Process for Time Series Data, Applications for Insurance Data.
• Dr Uri Keich
  Bioinformatics: creating tools for the discovery and analysis of sequence motifs, study of DNA replication origins. Computational statistics: designing fast and numerically stable algorithms for evaluating the significance of exact tests.
• Dr Dobrin Marchev
  Markov chain Monte Carlo methods, Hidden Markov models, Order restricted inference.
• Dr Samuel Müller
  Extreme Value Theory, Model Selection, Robust Methods, Applied Statistics.
• Dr. John Ormerod
  Variational Approximations, Generalised Linear Mixed Models, Splines, Data Mining, Semiparametric Regression and Missing Data.
• Assoc. Prof. Shelton Peiris
  Time Series Analysis, Estimating Functions and Applications, Statistics in Finance, Financial Econometrics, Time Dependent Categorical Data.
• Dr Michael Stewart
  Mixture Models, Extremes of Stochastic Processes, Statistics in Biological Sciences
• Dr Qiying Wang
  Nonstationary time series econometrics, Nonparametric statistics, Econometric Theory, Local Time Theory, Self-normalized limit theory.
• Professor Neville Weber
  U-statistics, Exchangeability, Probability Limit, Generalized Linear Models, Asymptotic Approximations.
• Dr Jean Yang
  Applied Statistics, Statistical Bioinformatics, Integrative Analysis of Microarray, Sequence and Protein Data, Statistical Computing.

Retired members active in research

• Dr H.J. D’Abrera
  Non-parametric Estimation, Robustness, Statistics Teaching/Education.
• Mrs M. Phipps
  Power Functions and P-values.
• Assoc. Prof. M.P. Quine
  Stochastic processes, Occupancy problems, Applied probability, Geometric Probability.
• Emeritus Professor J. Robinson
  Resampling Methods, Asymptotic Methods in Statistics Modelling and Inference in Biology.
• Emeritus Professor E. Seneta
  Finite and infinite non-negative Matrices and their Ergodicity, Probability Inequalities, History of Probability and Statistics.