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## People matching "Optimally Chosen Quadratic Forms for Partitioning "

 Associate Professor Gary Glonek Associate Professor in StatisticsMore about Gary Glonek...
 Associate Professor Inge Koch Associate Professor in StatisticsMore about Inge Koch...
 Professor Matthew Roughan Professor of Applied MathematicsMore about Matthew Roughan...
 Professor Patty Solomon Professor of Statistical BioinformaticsMore about Patty Solomon...
 Dr Simon Tuke Lecturer in StatisticsMore about Simon Tuke...

## Courses matching "Optimally Chosen Quadratic Forms for Partitioning "

 Analysis of multivariable and high dimensional data Multivariate analysis of data is performed with the aims to 1. understand the structure in data and summarise the data in simpler ways; 2. understand the relationship of one part of the data to another part; and 3. make decisions or draw inferences based on data. The statistical analyses of multivariate data extend those of univariate data, and in doing so require more advanced mathematical theory and computational techniques. The course begins with a discussion of the three classical methods Principal Component Analysis, Canonical Correlation Analysis and Discriminant Analysis which correspond to the aims above. We also learn about Cluster Analysis, Factor Analysis and newer methods including Independent Component Analysis. For most real data the underlying distribution is not known, but if the assumptions of multivariate normality of the data hold, extra properties can be derived. Our treatment combines ideas, theoretical properties and a strong computational component for each of the different methods we discuss. For the computational part -- with Matlab -- we make use of real data and learn the use of simulations in order to assess the performance of different methods in practice. Topics covered: 1. Introduction to multivariate data, the multivariate normal distribution 2. Principal Component Analysis, theory and practice 3. Canonical Correlation Analysis, theory and practice 4. Discriminant Analysis, Fisher's LDA, linear and quadratic DA 5. Cluster Analysis: hierarchical and k-means methods 6. Factor Analysis and latent variables 7. Independent Component Analysis including an Introduction to Information Theory The course will be based on my forthcoming monograph Analysis of Multivariate and High-Dimensional Data - Theory and Practice, to be published by Cambridge University Press. More about this course...

## Events matching "Optimally Chosen Quadratic Forms for Partitioning "

 Watching evolution in real time; problems and potential research areas. 15:10 Fri 26 May, 2006 :: G08. Mathematics Building University of Adelaide :: Prof Alan Cooper (Federation Fellow)Abstract...Recent studies (1) have indicated problems with our ability to use the genetic distances between species to estimate the time since their divergence (so called molecular clocks). An exponential decay curve has been detected in comparisons of closely related taxa in mammal and bird groups, and rough approximations suggest that molecular clock calculations may be problematic for the recent past (eg <1 million years). Unfortunately, this period encompasses a number of key evolutionary events where estimates of timing are critical such as modern human evolutionary history, the domestication of animals and plants, and most issues involved in conservation biology. A solution (formulated at UA) will be briefly outlined. A second area of active interest is the recent suggestion (2) that mitochondrial DNA diversity does not track population size in several groups, in contrast to standard thinking. This finding has been interpreted as showing that mtDNA may not be evolving neutrally, as has long been assumed. Large ancient DNA datasets provide a means to examine these issues, by revealing evolutionary processes in real time (3). The data also provide a rich area for mathematical investigation as temporal information provides information about several parameters that are unknown in serial coalescent calculations (4).References: Ho SYW et al. Time dependency of molecular rate estimates and systematic overestimation of recent divergence times. Mol. Biol. Evol. 22, 1561-1568 (2005); Penny D, Nature 436, 183-184 (2005). Bazin E., et al. Population size does not influence mitochondrial genetic diversity in animals. Science 312, 570 (2006); Eyre-Walker A. Size does not matter for mitochondrial DNA, Science 312, 537 (2006). Shapiro B, et al. Rise and fall of the Beringian steppe bison. Science 306: 1561-1565 (2004); Chan et al. Bayesian estimation of the timing and severity of a population bottleneck from ancient DNA. PLoS Genetics, 2 e59 (2006). Drummond et al. Measurably evolving populations, Trends in Ecol. Evol. 18, 481-488 (2003); Drummond et al. Bayesian coalescent inference of past population dynamics from molecular sequences. Molecular Biology Evolution 22, 1185-92 (2005).
 A Bivariate Zero-inflated Poisson Regression Model and application to some Dental Epidemiological data 14:10 Fri 27 Oct, 2006 :: G08 Mathematics Building University of Adelaide :: University Prof Sudhir PaulAbstract...Data in the form of paired (pre-treatment, post-treatment) counts arise in the study of the effects of several treatments after accounting for possible covariate effects. An example of such a data set comes from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Also, these data may show extra pairs of zeros than can be accounted for by a simpler model, such as, a bivariate Poisson regression model. In such situations we propose to use a zero-inflated bivariate Poisson regression (ZIBPR) model for the paired (pre-treatment, posttreatment) count data. We develop EM algorithm to obtain maximum likelihood estimates of the parameters of the ZIBPR model. Further, we obtain exact Fisher information matrix of the maximum likelihood estimates of the parameters of the ZIBPR model and develop a procedure for testing treatment effects. The procedure to detect treatment effects based on the ZIBPR model is compared, in terms of size, by simulations, with an earlier procedure using a zero-inflated Poisson regression (ZIPR) model of the post-treatment count with the pre-treatment count treated as a covariate. The procedure based on the ZIBPR model holds level most effectively. A further simulation study indicates good power property of the procedure based on the ZIBPR model. We then compare our analysis, of the decayed, missing and filled teeth (DMFT) index data from the caries prevention study, based on the ZIBPR model with the analysis using a zero-inflated Poisson regression model in which the pre-treatment DMFT index is taken to be a covariate
 A mathematical look at dripping honey 15:10 Fri 4 May, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Yvonne Stokes :: University of AdelaideAbstract...Honey dripping from an upturned spoon is an everyday example of a flow that extends and breaks up into drops. Such flows have been of interest for over 300 years, attracting the attention of Plateau and Rayleigh among others. Theoretical understanding has, however, lagged behind experimental investigation, with major progress being made only in the last two decades, driven by industrial applications including ink-jet printing, spinning of polymer and glass fibres, blow-moulding of containers, light bulbs and glass tubing, and rheological measurement by fibre extension. Albeit, the exact details of the final stages of breakup are yet to be fully resolved. An aspect that is relatively unexplored is the evolution of drop and filament from some initial configuration, and the influence of initial conditions on the final breakup. We will consider a drop of very viscous fluid hanging beneath a solid boundary, similar to honey dripping from an upturned spoon, using methods that allow examination of development and behaviour from early time, when a drop and filament begin to form, out to large times when the bulk of the fluid forms a drop at the bottom of a long thin filament which connects it with the upper boundary. The roles of gravity, inertia and surface tension will be examined.
 An Introduction to invariant differential pairings 14:10 Tue 24 Jul, 2007 :: Mathematics G08 :: Jens KroeskeAbstract...On homogeneous spaces G/P, where G is a semi-simple Lie group and P is a parabolic subgroup (the ordinary sphere or projective spaces being examples), invariant operators, that is operators between certain homogeneous bundles (functions, vector fields or forms being amongst the typical examples) that are invariant under the action of the group G, have been studied extensively. Especially on so called hermitian symmetric spaces which arise through a 1-grading of the Lie algebra of G there exists a complete classification of first order invariant linear differential operators even on more general manifolds (that allow a so called almost hermitian structure). This talk will introduce the notion of an invariant bilinear differential pairing between sections of the aforementioned homogeneous bundles. Moreover we will discuss a classification (excluding certain totally degenerate cases) of all first order invariant bilinear differential pairings on manifolds with an almost hermitian symmetric structure. The similarities and connections with the linear operator classification will be highlighted and discussed.
 Likelihood inference for a problem in particle physics 15:10 Fri 27 Jul, 2007 :: G04 Napier Building University of Adelaide :: Prof. Anthony DavisonAbstract...The Large Hadron Collider (LHC), a particle accelerator located at CERN, near Geneva, is (currently!) expected to start operation in early 2008. It is located in an underground tunnel 27km in circumference, and when fully operational, will be the world's largest and highest energy particle accelerator. It is hoped that it will provide evidence for the existence of the Higgs boson, the last remaining particle of the so-called Standard Model of particle physics. The quantity of data that will be generated by the LHC is roughly equivalent to that of the European telecommunications network, but this will be boiled down to just a few numbers. After a brief introduction, this talk will outline elements of the statistical problem of detecting the presence of a particle, and then sketch how higher order likelihood asymptotics may be used for signal detection in this context. The work is joint with Nicola Sartori, of the Università Ca' Foscari, in Venice.
 Fermat's Last Theorem and modular elliptic curves 15:10 Wed 5 Sep, 2007 :: G08 Mathematics Building University of Adelaide :: Dr Mark KisinMedia...Abstract...I will give a historical talk, explaining the steps by which one can deduce Fermat's Last Theorem from a statement about modular forms and elliptic curves.
 Regression: a backwards step? 13:10 Fri 7 Sep, 2007 :: Maths G08 :: Dr Gary GlonekMedia...Abstract...Most students of high school mathematics will have encountered the technique of fitting a line to data by least squares. Those who have taken a university statistics course will also have heard this method referred to as regression. However, it is not obvious from common dictionary definitions why this should be the case. For example, "reversion to an earlier or less advanced state or form". In this talk, the mathematical phenomenon that gave regression its name will be explained and will be shown to have implications in some unexpected contexts.
 The Linear Algebra of Internet Search Engines 15:10 Fri 5 Oct, 2007 :: G04 Napier Building University of Adelaide :: Dr Lesley Ward :: School of Mathematics and Statistics, University of South AustraliaAbstract...We often want to search the web for information on a given topic. Early web-search algorithms worked by counting up the number of times the words in a query topic appeared on each webpage. If the topic words appeared often on a given page, that page was ranked highly as a source of information on that topic. More recent algorithms rely on Link Analysis. People make judgments about how useful a given page is for a given topic, and they express these judgments through the hyperlinks they choose to put on their own webpages. Link-analysis algorithms aim to mine the collective wisdom encoded in the resulting network of links. I will discuss the linear algebra that forms the common underpinning of three link-analysis algorithms for web search. I will also present some work on refining one such algorithm, Kleinberg's HITS algorithm. This is joint work with Joel Miller, Greg Rae, Fred Schaefer, Ayman Farahat, Tom LoFaro, Tracy Powell, Estelle Basor, and Kent Morrison. It originated in a Mathematics Clinic project at Harvey Mudd College.
 Statistical Critique of the International Panel on Climate Change's work on Climate Change. 18:00 Wed 17 Oct, 2007 :: Union Hall University of Adelaide :: Mr Dennis TrewinAbstract...Climate change is one of the most important issues facing us today. Many governments have introduced or are developing appropriate policy interventions to (a) reduce the growth of greenhouse gas emissions in order to mitigate future climate change, or (b) adapt to future climate change. This important work deserves a high quality statistical data base but there are statistical shortcomings in the work of the International Panel on Climate Change (IPCC). There has been very little involvement of qualified statisticians in the very important work of the IPCC which appears to be scientifically meritorious in most other ways. Mr Trewin will explain these shortcomings and outline his views on likely future climate change, taking into account the statistical deficiencies. His conclusions suggest climate change is still an important issue that needs to be addressed but the range of likely outcomes is a lot lower than has been suggested by the IPCC. This presentation will be based on an invited paper presented at the OECD World Forum.
 Moderated Statistical Tests for Digital Gene Expression Technologies 15:10 Fri 19 Oct, 2007 :: G04 Napier Building University of Adelaide :: Dr Gordon Smyth :: Walter and Eliza Hall Institute of Medical Research in Melbourne, AustraliaAbstract...Digital gene expression (DGE) technologies measure gene expression by counting sequence tags. They are sensitive technologies for measuring gene expression on a genomic scale, without the need for prior knowledge of the genome sequence. As the cost of DNA sequencing decreases, the number of DGE datasets is expected to grow dramatically. Various tests of differential expression have been proposed for replicated DGE data using over-dispersed binomial or Poisson models for the counts, but none of the these are usable when the number of replicates is very small. We develop tests using the negative binomial distribution to model overdispersion relative to the Poisson, and use conditional weighted likelihood to moderate the level of overdispersion across genes. A heuristic empirical Bayes algorithm is developed which is applicable to very general likelihood estimation contexts. Not only is our strategy applicable even with the smallest number of replicates, but it also proves to be more powerful than previous strategies when more replicates are available. The methodology is applicable to other counting technologies, such as proteomic spectral counts.
 Global and Local stationary modelling in finance: Theory and empirical evidence 14:10 Thu 10 Apr, 2008 :: G04 Napier Building University of Adelaide :: Prof. Dominique Guégan :: Universite Paris 1 Pantheon-SorbonneAbstract...To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guégan, 1994), the EXPAR model (Haggan and Ozaki, 1980), the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guégan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under specific conditions on the parameters, then the forecast points and the forecast intervals are available. Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense. Now non-stationarity modelling has also a long tradition in econometrics. This one is based on the conditional moments of the data generating process. It appears mainly in the heteroscedastic and volatility models, like the GARCH and related models, and stochastic volatility processes (Ghysels, Harvey and Renault 1997). This non-stationarity appears also in a different way with structural changes models like the switching models (Hamilton, 1988), the stopbreak model (Diebold and Inoue, 2001, Breidt and Hsu, 2002, Granger and Hyung, 2004) and the SETAR models, for instance. It can also be observed from linear models with time varying coefficients (Nicholls and Quinn, 1982, Tsay, 1987). Thus, using stationary unconditional moments suggest a global stationarity for the model, but using non-stationary unconditional moments or non-stationary conditional moments or assuming existence of states suggest that this global stationarity fails and that we only observe a local stationary behavior. The growing evidence of instability in the stochastic behavior of stocks, of exchange rates, of some economic data sets like growth rates for instance, characterized by existence of volatility or existence of jumps in the variance or on the levels of the prices imposes to discuss the assumption of global stationarity and its consequence in modelling, particularly in forecasting. Thus we can address several questions with respect to these remarks. 1. What kinds of non-stationarity affect the major financial and economic data sets? How to detect them? 2. Local and global stationarities: How are they defined? 3. What is the impact of evidence of non-stationarity on the statistics computed from the global non stationary data sets? 4. How can we analyze data sets in the non-stationary global framework? Does the asymptotic theory work in non-stationary framework? 5. What kind of models create local stationarity instead of global stationarity? How can we use them to develop a modelling and a forecasting strategy? These questions began to be discussed in some papers in the economic literature. For some of these questions, the answers are known, for others, very few works exist. In this talk I will discuss all these problems and will propose 2 new stategies and modelling to solve them. Several interesting topics in empirical finance awaiting future research will also be discussed.
 Elliptic equation for diffusion-advection flows 15:10 Fri 15 Aug, 2008 :: G03 Napier Building University of Adelaide :: Prof. Pavel Bedrikovsetsky :: Australian School of Petroleum Science, University of Adelaide.Abstract... The standard diffusion equation is obtained by Einstein's method and its generalisation, Fokker-Plank-Kolmogorov-Feller theory. The time between jumps in Einstein derivation is constant. We discuss random walks with residence time distribution, which occurs for flows of solutes and suspensions/colloids in porous media, CO2 sequestration in coal mines, several processes in chemical, petroleum and environmental engineering. The rigorous application of the Einstein's method results in new equation, containing the time and the mixed dispersion terms expressing the dispersion of the particle time steps. Usually, adding the second time derivative results in additional initial data. For the equation derived, the condition of limited solution when time tends to infinity provides with uniqueness of the Caushy problem solution. The solution of the pulse injection problem describing a common tracer injection experiment is studied in greater detail. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions of the direct simulation.

## Publications matching "Optimally Chosen Quadratic Forms for Partitioning "

Publications
CleanBGP: Verifying the consistency of BGP data
Flavel, Ashley; Maennel, Olaf; Chiera, Belinda; Roughan, Matthew; Bean, Nigel, International Network Management Workshop, Orlando, Florida 19/10/08
Energy balanced data gathering in WSNs with grid topologies
Chen, J; Shen, Hong; Tian, Hui, 7th International Conference on Grid and Cooperative Computing, China 24/10/08
Data fusion without data fusion: localization and tracking without sharing sensitive information
Roughan, Matthew; Arnold, Jonathan, Information, Decision and Control 2007, Adelaide, Australia 12/02/07
Strengthened forms of an integral inequality arising in connection with the large sieve
Pearce, Charles; Pecaric, Josip, 8th International Conference on Nonlinear Functional Analysis and Applications, Seoul, South Korea 09/08/04
Optimal multilinear estimation of a random vector under constraints of casualty and limited memory
Howlett, P; Torokhti, Anatoli; Pearce, Charles, Computational Statistics & Data Analysis 52 (869–878) 2007
Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras
Eastwood, Michael; Somberg, P; Soucek, V, Journal of Geometry and Physics 57 (2539–2546) 2007
Statistics in review; Part 1: graphics, data summary and linear models
Moran, John; Solomon, Patricia, Critical care and Resuscitation 9 (81–90) 2007
The multivariate Faa di Bruno formula and multivariate Taylor expansions with explicit integral remainder term
Leipnik, R; Pearce, Charles, The ANZIAM Journal 48 (327–341) 2007
Computer algebra derives normal forms of stochastic differential equations
Roberts, Anthony John,
Experimental Design and Analysis of Microarray Data
Wilson, C; Tsykin, Anna; Wilkinson, Christopher; Abbott, C, chapter in Bioinformatics (Elsevier Ltd) 1–36, 2006
Is BGP update storm a sign of trouble: Observing the internet control and data planes during internet worms
Roughan, Matthew; Li, J; Bush, R; Mao, Z; Griffin, T, SPECTS 2006, Calgary, Canada 31/07/06
Modelling multivariate extreme flood events
Wong, Hui; Need, Steven; Adamson, Peter; Lambert, Martin; Metcalfe, Andrew, 30th Hydrology and Water Resources Symposium, Launceston, Tasmania 04/12/06
Watching data streams toward a multi-homed sink under routing changes introduced by a BGP beacon
Li, J; Bush, R; Mao, Z; Griffin, T; Roughan, Matthew; Stutzbach, D; Purpus, E, PAM2006, Adelaide, Australia 30/03/06
Data-recursive smoother formulae for partially observed discrete-time Markov chains
Elliott, Robert; Malcolm, William, Stochastic Analysis and Applications 24 (579–597) 2006
Optimal linear estimation and data fusion
Elliott, Robert; Van Der Hoek, John, IEEE Transactions on Automatic Control 51 (686–689) 2006
Secure distributed data-mining and its application to large-scale network measurements
Roughan, Matthew; Zhang, Y, Computer Communication Review 36 (7–14) 2006
Optimal estimation of a random signal from partially missed data
Torokhti, Anatoli; Howlett, P; Pearce, Charles, EUSIPCO 2006, Florence, Italy 04/09/06
Optimal recursive estimation of raw data
Torokhti, Anatoli; Howlett, P; Pearce, Charles, Annals of Operations Research 133 (285–302) 2005
Combining routing and traffic data for detection of IP forwarding anomalies
Roughan, Matthew; Griffin, T; Mao, M; Greenberg, A; Freeman, B, Sigmetrics - Performance 2004, New York, USA 12/06/04
IP forwarding anomalies and improving their detection using multiple data sources
Roughan, Matthew; Griffin, T; Mao, M; Greenberg, A; Freeman, B, SIGCOMM 2004, Oregon, USA 30/08/04
The data processing inequality and stochastic resonance
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Noise in Complex Systems and Stochastic Dynamics, Santa Fe, New Mexico, USA 01/06/03
Stochastic resonance and data processing inequality
McDonnell, Mark; Stocks, N; Pearce, Charles; Abbott, Derek, Electronics Letters 39 (1287–1288) 2003
Resampling-based multiple testing for microarray data analysis (Invited discussion of paper by Ge, Dudoit and Speed)
Glonek, Garique; Solomon, Patricia, Test 12 (50–53) 2003
Direct computation of the performance index for an optimally controlled active suspension with preview applied to a half-car model
Thompson, A; Pearce, Charles, Vehicle System Dynamics 35 (121–137) 2001
On the best quadratic approximation of nonlinear systems
Torokhti, Anatoli; Howlett, P, IEEE Transactions on Circuits and Systems I - regular papers 48 (595–602) 2001
Best estimators of second degree for data analysis
Howlett, P; Pearce, Charles; Torokhti, Anatoli, ASMDA 2001, Compiegne, France 12/06/01
Optimal successive estimation of observed data
Torokhti, Anatoli; Howlett, P; Pearce, Charles, International Conference on Optimization: Techniques and Applications (5th: 2001), Hong Kong, China 15/12/01
Statistical analysis of medical data: New developments - Book review
Solomon, Patricia, Biometrics 57 (327–328) 2001
Disease surveillance and data collection issues in epidemic modelling
Solomon, Patricia; Isham, V, Statistical Methods in Medical Research 9 (259–277) 2000
Multivariate Hardy-type inequalities
Hanjs, Z; Pearce, Charles; Pecaric, Josip, Tamkang Journal of Mathematics 31 (149–158) 2000