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Statistics colloquia series

Engaging with universities and industry bodies around the world, the Department of Mathematics and Statistics presents a series of regular colloquiums and seminars during the year. The programs enhance the learning environment, linking students and staff with academic and industry experts.

For information on the statistics colloquium or seminar series at Melbourne, please contact Dr David Farchione on 03 9479 2091 or by sending an email to D.Farchione@latrobe.edu.au

Future programs

The minimum coverage probability of confidence intervals in regression after a preliminary F test

In the applied statistics literature on the one-way analysis of covariance, it is commonly recommended that a preliminary F test of the null hypothesis of "parallelism" be carried out. Preliminary F tests are also recommended in other linear regression model scenarios. Let s denote the number of parameters that are assumed to be zero in the description of the null hypothesis for this F test. Our aim is to find the coverage probability properties of a confidence interval for a specified linear combination of the regression parameters, constructed after a preliminary F test and based on the assumption that the selected model had been given to us a priori (as the true model). We describe a new elegant method for computing the minimum coverage probability of this confidence interval, that works well irrespective of how large s is.

Reference

Kabaila, P. & Farchione, D. (2012). The minimum coverage probability of confidence intervals in regression after a preliminary F test. Journal of Statistical Planning and Inference, 142, 956-964.

Speaker

Associate Professor Paul Kabaila, Department of Mathematics and Statistics, La Trobe University.

Time and Date

11am, Friday 24 February 2012.

Venue

Access Grid Room 310, Physical Sciences 2, La Trobe University, Melbourne Campus.

Past programs

Exploring Spatial Data in R

A non-mathematical talk on visualizing and analysing spatial data in R. I'll discuss the different types of spatial data, the main R packages needed for the analysis of those types, and present a selection of  examples from a wide range of application areas. I'll briefly illustrate how R can be used to visualize data in other software such as Google Earth and Quantum GIS. We'll look at geological data, rainforests, cancer cases, biological cells, and maps of our favourite Australian state.

Speaker

Dr Alec Stephenson, Swinburne University of Technology.

Time and Date

11am, Friday 4th November 2011.

Venue

Access Grid Room 310, Physical Sciences 2, La Trobe University, Melbourne Campus.

Thinking about sampling variability and replication: Confidence intervals beat p values

Understanding sampling variability is an important goal.  A useful approach is to consider replication.  What information do inferential techniques give about replication?  Confidence intervals (CIs) do well: A 95% CI is, approximately, an 83% prediction interval for the mean of a replication experiment.  A p value, however, gives almost no information about a replication result.  CIs beat p values, although for very small N a CI may be misleading.  I will present novel graphics and simulations, and emphasise cognition—how people read graphics and draw conclusions.  There is more in my book: Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis, Routledge, 2012. www.thenewstatistics.com

Speaker

Emeritus Professor Geoff Cumming, Statistical Cognition Laboratory, School of Psychological Science, La Trobe University.

Time & date

12pm Friday 21st October 2011.

Venue

Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.

Forecasting Model Validation

Forecasting models play a crucial role in many decision-making areas. Many tools have been developed for model selection and validation (on available data) but only a few exist for answering the question whether the model under the test is still valid for the new observations. This is especially true when one is looking for a quick answer after a small number of extra observations have become available or examines a nonparametric model. We present a method for analyzing the model, which has already been selected, and examining whether its predictive ability is still good enough or the model needs to be reworked. The proposed prediction capability procedure combines the ideas of nonparametric density estimation and principal function data analysis in order to clarify the question whether the new observed data comes from the same expected data generation process or not. If there is not enough evidence that the data generation process has been changed after the model has been selected, there is no reason to believe that the model lost its predictive abilities in the new reality.

Speaker

Julia Polak, Monash University.

Time & date

11am Friday 7th October 2011.

Venue

Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.

Title: Setting the Standard: Minimum examination competency

• Speaker: Monika Buljan, The Royal Australian College of General Practitioners.
• Time & date: 3pm Friday 1st July 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: When conducting examinations, especially on a large scale, one important issue that has always fascinated educators is how to determine a “good” pass mark, or cut score. For example, academically achieving 51% may be the minimum to pass a university unit to proceed to the next level, but that lies on the assumption that all exams are written at the same level in every department, year after year. We know that this is not the case, no matter how hard educators try to set the minimum competency level at particular value. Some units are naturally more challenging than others; achieving 51% (or any score for that matter) may or may not show a candidate’s competency in a unit. More importantly, if the cut score is meant to represent a standard, with high risks of Type 1 and Type 2 errors, how can the standard be transformed into a numerical value while reducing the associated risks? There is much debate about appropriate cut scores and the methods to determine them, especially for high risk national examinations. This presentation will aim to explore some Standard Setting methods, and if time permits, what happens to one of these methods as the reporting changes with technology.

Title: Estimating Burr XII Distribution Parameters Using Cross Entropy Method

• Speaker: Dr. Babak Abbasi, RMIT University.
• Time & date: 11am Friday 8th July 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The Burr XII distribution can closely approximate many other well known probability density functions such as the normal, gamma, lognormal, exponential distributions as well as Pearson type I, II, V, VII, IX, X, XII families of distributions. Considering a wide range of shape and scale parameters of the Burr XII distribution, it can have an important role in reliability modeling, risk analysis and statistical process control. However, estimating parameters of the Burr XII distribution can be a complicated task and the use of conventional methods such as Maximum Likelihood Estimation (MLE) and Moment Method (MM) is not straightforward. Some tables to estimate Burr XII parameters have been provided by Burr (1942) but they are not adequate for many purposes or data sets. In this presentation, We investigate the problems of estimating Burr XII parameters and develop a  Cross Entropy method in context of Maximum Likelihood Estimation (MLE) of Burr XII distribution for complete data or in presence of multiple censoring. A simulation study is conducted to assess the performance of the MLE via CE method for different parameter settings and sample sizes.

Title: Introduction to the research program: The effect of preliminary model selection on confidence intervals and the utilization of prior information in confidence set construction

• Speaker: A/Prof Paul Kabaila, La Trobe University.
• Time & date: 2pm Friday 24th June 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: I will describe the statistical techniques, such as invariance arguments, and the mathematical techniques, such as the truncation of integrals over infinite intervals, needed to compute these confidence intervals.

Title: A Simple Diffusion Limit for Flows in Stable Multi-Class Queueing Networks

• Speaker: Dr. Yoni Nazarathy, Swinburne University of Technology.
• Time & date: 11am Friday 17th June 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a relatively new area of Statistics, functional data analysis extends existing methodologies and theories from the areas of functional analysis, generalized linear models, multivariate data analysis, nonparametric smoothing, stochastic process and many others. In this talk, I aim to briefly present three papers on some visualization, modelling and forecasting techniques for functional data.

Title: Visualizing and forecasting functional time series

• Speaker: Dr. Han Shang, Department of Econometrics and Business Statistics, Monash University.
• Time & date: 2:00pm Friday 27th May 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Advances in data collection and storage have tremendously increased the presence of functional data, whose graphical representations are curves, images or shapes. As a relatively new area of Statistics, functional data analysis extends existing methodologies and theories from the areas of functional analysis, generalized linear models, multivariate data analysis, nonparametric smoothing, stochastic process and many others. In this talk, I aim to briefly present three papers on some visualization, modelling and forecasting techniques for functional data.

Title: The Five-fold Constellation and a Cryptographic Problem

Joint RMIT University and La Trobe University seminar

• Speaker: Professor Kathy Horadam (RMIT).
• Time & date: 3:30pm, Friday 13th May 2011.
• Venue: Szental Lecture Theatre, La Trobe University, Melbourne Campus
• Abstract: Over the past 20 years de Launey, Flannery, Galati, Hughes, Perera, Horadam, Rao and others have investigated correspondences between generalised Hadamard matrices, group cohomology, relative difference sets, divisible designs and uncorrelated sequences. These have revealed a deep network of corresponding objects in combinatorics, algebra and information transmission I call the Five-fold Constellation. Different ideas of equivalence of these objects, arising naturally in each area, can propagate around the Constellation. I will outline these correspondences and explain how equivalence for relative difference sets assists in the search for good cryptographic functions.

Title: Level-crossings of symmetric random walks

• Speaker: Dr. Vyacheslav Abramov.
• Time & date: 2:00pm Friday 6th May 2011.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Let X(1), X(2), ... be a sequence of independently and identically distributed random variables with EX(1)=0, and let S(0)=0 and S(t)=S(t-1)+X(t), t=1,2,..., be a random walk. Denote tau=inf{t>1: S(t)=< 0, if X(1)>0, and 1, otherwise. Let a denote a positive number, and let L(a) denote the number of level-crossings from the below (or above) across the level a during the interval [0,tau]. Under special assumptions, it is proved that there exists an infinitely increasing sequence a(n) such that the equality EL(a(n))=c P{X(1)>0} is satisfied, where c is a specified constant that does not depend on n. The result is illustrated for a number of special random walks. We also give non-trivial examples from queuing theory where the results of this theory are applied.

Title: Honours Thesis Presentations

• Time & date: 4:00pm Tuesday 23rd November 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Honours students will give presentations detailing work that they covered in their thesis topic:
  • Grant Campbell, Longitudinal Data Analysis with GEE, GLMM and GLLAMM.
  • Megh Shah, Levy Processes for Pricing Options.
  • Oguzhan Yilmaz, The coverage probability of confidence intervals in regression after two F-tests.

Title: Long-range dependence and non-semimartingale models in finance

• Speaker: Prof. Yu. Mishura, Kyiv National University, Ukraine.
  
• Time & date: 11:00am Friday 26th November 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: We consider the model of financial market that admits long-range dependence, or, in other words, has long memory. Long memory component is modelled with the help of fractional Brownian motion.  We establish non-arbitrage property of such model and the conditions of equilibrium of the  market. Fractional version of Girsanov theorem is used as a tool. The problem of quantile hedging is studied.

Title: Conditional predictive inference post model selection

• Speaker: Prof. Hannes Leeb, University of Vienna.
  
• Time & date: 11am Thursday 2nd December 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite, where no regularity conditions are imposed on unknown parameters, where the number of explanatory variables in a `good' model can be of the same order as sample size, and where the number of candidate models can be of larger order than sample size. The performance of inference procedures is evaluated conditional on the training sample.  Under weak conditions on only the number of candidate models and on their complexity, and uniformly over all data-generating processes under consideration, we show that a certain prediction interval is approximately valid and short with high probability in finite samples, in the sense that its actual coverage probability is close to the nominal one, and in the sense that its length is close to the length of an infeasible interval that is constructed by actually knowing the 'best' candidate model. Similar results are shown to hold for predictive inference procedures other than prediction intervals like, e.g., tests of whether a future response will lie above or below a given threshold.

Title: Currency Option Pricing: Mean Reversion and Multi-Scale Stochastic Volatility

• Speaker: Dr Jing Zhao.
  
• Time & date: 11:00am Friday 19th November 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: This work investigates the valuation of currency options when the underlying currency follows a mean-reverting lognormal process with multi-scale stochastic volatility. A closed-form solution is derived for the characteristic function of the log-asset price. European options are then valued by means of the Fourier inversion formula. The proposed model enables us to calibrate simultaneously to the observed currency futures and the implied volatility surface of the currency options within a unified framework. The fractional fast Fourier transform (FFT) is adopted to implement the Fourier inversion, thus ensuring that the grid spacing restriction of the standard FFT can be relaxed, which results in a more efficient computation. Using Monte Carlo simulation as a benchmark, our numerical examples show that the derived option pricing formula is accurate and efficient for practical use.

Title: Prediction in measurement error models

• Speaker: Dr Kathy Haskard, Australian Mathematical Sciences Institute.
  
• Time & date: 11:00am Friday 15th October 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: In geostatistical spatial modelling, data are typically assumed to have stationary covariance - because with only a single realisation of a random process it is difficult to estimate a covariance model that is different at different locations. However this assumption can be untenable in varied landscapes, and estimates of the variance of predictions can be badly affected. This is important, for example, in assessing climate change scenarios. Spectral tempering allows flexible spatial adaptation of spatial covariance; smoothness and variances can be adapted independently, with parameters that are simple and interpretable. This talk begins with an introduction to some geostatistical concepts, then describes spectral tempering in a graphical way, illustrating and validating with application to data on soil emissions of nitrous oxide, an important greenhouse gas. The method can be applied to many kinds of spatially-correlated data.

Title: Prediction in measurement error models

• Speaker: Dr Aurore Delaigle, University of Melbourne, Australia.
  
• Time & date: 11:00am Friday 24th September 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Predicting Y from a future X based on data (X_i,Y_i) is a fundamental inference problem. When X is observed accurately, the problem is that of standard regression estimation of E(Y|X). When the data X_i and future X are measured with error, prediction is sometimes less standard. With W denoting the future X measurement, prediction of Y requires estimation of E(Y|W). This is complicated when measurements are made under different conditions, so that errors in X_i and X are not identically distributed. We study this problem nonparametrically showing that convergence rates of estimators of E(Y|W) can vary from root-n to much slower nonparametric rates. We develop highly-adaptive, data-driven methods that perform well as illustrated by an interesting application in nutritional epidemiology.

Title: Functional Brain Mapping of Epilepsy

• Speaker: Dr David Abbott, Brain Research Institute, Melbourne, Australia.
  
• Time & date: 11:00am Friday 3rd September 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Advances in human neuroimaging technology, including functional magnetic resonance imaging (fMRI) with simultaneous electroencephalography (EEG), have made possible the non-invasive acquisition of whole-brain functional images at millimeter spatial resolution and millisecond temporal resolution. We are using this technology to unravel mysteries in epilepsy. A challenge is to process the large amount of data in an objective and meaningful way to determine where seizures arise in individual patients. More fundamentally we wish to determine the spatiotemporal pattern of brain activity that leads to a seizure in various types of epilepsy, as this knowledge may lead to new therapeutic targets. I will discuss the application of model-based and model-free data analysis methods to this problem.

Title: Honours and Postgraduate Diploma talks

• Speakers:
  • Grant Campbell, Application of multi-level models in longitudinal data analysis.
  • Helen Cuxson, Application of Bayesian Meta-Analysis in Evidence-Based Medicine.
  • Megh Shah, Continuous-time Pricing Models and their Applications.
  • Oguzhan Yilmaz, The coverage probability of confidence intervals in regression after two F-tests.
• Time & date: 12:15pm Friday 6 August 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The preliminary Honours and Postgraduate Diploma talks. 

Title: Overview of Mathematica for Education and Research

• Speakers: Cliff Hastings (Director, Academic Initiatives at Wolfram Research) and Kim Schriefer (Senior Member, International Business Development staff at Wolfram Research).
  
• Time & date: 3:00pm Tuesday 27 July 2010.
• Venue: Room 233 (R A Fisher Laboratory), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The Mathematica Seminars 2010 offer an opportunity to experience the applicability, ease-of-use, as well as the advancements of Mathematica 7 in education and academic research.
  These seminars will highlight the latest directions in technical computing with Mathematica, and the impact this technology has across a wide range of academic fields, from maths,  physics and biology to finance, economics and business. Those not yet familiar with Mathematica will gain an overview of the system and discover the breadth of applications it can address, while experts will get firsthand experience with recent advances in Mathematica like parallel computing, digital image processing, point-and-click palettes, built-in curated data, as well as courseware examples. 

Title: Admissibility of the Usual Confidence Interval in Linear Regression

• Speaker: Paul Kabaila, Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia.
  
• Time & date: 11.00 Friday 7 May 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Roughly speaking, a statistical procedure (e.g. a point estimator or a confidence interval) is said to be admissible if there is no other procedure that is at least as good for all possible parameter values and better for at least one parameter value. Admissibility is an important concept for a number of reasons, including the fact that there are some surprising examples of procedures that are not admissible. In this talk, we introduce the concept of admissibility by first considering point estimators. We then move on to the more difficult concept of admissibility of confidence intervals. We finish the talk by describing the new result presented in joint work with Khageswor Giri and Hannes Leeb: "Admissibility of the usual confidence interval in linear regression", Electronic Journal of Statistics, 4, 300 − 312 (2010).

Title: Multivariate Process Capability Analysis

• Speaker: Dr. Mali Adollahian, School of Mathematical and Geospatial Sciences RMIT.
  
• Time & date: 11.00 Friday 16 April 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: In real world quality characteristics describing a product are often interrelated with each other and do not follow a normal distribution. This non-normality and correlated characteristics of multivariate data poses a challenge to researchers to investigate accurate and effective process performance yardstick in the area of quality control.
  
  Multivariate capability measures that are currently employed, except for a handful of cases, depend intrinsically on the underlying multivariate data being normally distributed.
  
  We will present different methods to investigate a suitable multivariate performance measure. In the first section we will deploy geometric distance introduced by Wang (Wang 2006) to reduce the dimensionality of the correlated non-normal multivariate data and then fit Burr distribution to the geometric distance variable. The optimal parameters of the fitted Burr distribution will be estimated using different numerical techniques. The proportion of non-conformance (PNC) will be used as a criterion for process performance measurements.
  
  We will introduce an innovative approach for a multivariate capability index based on the Generalized Covariance Distance (GCD). This proposed approach is easy to use by frontline managers and quality practitioners. Another novelty introduced in this methodology is to approximate the distribution of these distances by a Burr XII distribution and then estimate its parameters using different numerical techniques. Examples based on real manufacturing process data are also presented which demonstrate that the proportion of nonconformance using proposed GCD method is very close to the actual proportion of nonconformance value.

Title: Animal (ewes and lambs) production from native pastures in North East Victoria

• Speaker: Sorn Norng, Department of Primary Industries.
  
• Time & date: 12.00 Friday 12 March 2010.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Native pastures have traditionally been grazed with Merino wethers for wool production. With declining returns from wool production, there is need for considering alternative uses of these native pastures that are both economically-viable and environmentally-responsible. One option is to use these native pastures for prime lamb production by joining Merino ewes to a terminal sire. An ongoing experimental study at Rutherglen is evaluating the relative benefits of four different grazing management strategies for lamb production. A satisfactory analysis should account for any imbalance and unequal replication, the nested and temporal structure present in the design, and to offer results that address the experimental aims which are interpretable to the scientist.  This talk summarises the statistical approaches used to analyse the available data from this study and to present some preliminary results.

Title: Development of optimal designs for population pharmacokinetic studies of artesunate

Kris Jamsen

• Speaker: Kris Jamsen, The University of Melbourne.
  
• Time & date: 11.00am Friday 20 November.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Effective treatment of malaria requires that the dose and frequency of administration of the antimalarial drug provide drug concentrations over time (known as the 'pharmacokinetic profile') sufficient to kill all of the parasites in the body. Population pharmacokinetic (PK) studies determine the PK profiles in the patient populations by using complex statistical models that allow sparse data from patients where intensive blood sampling is not feasible. Currently, population PK studies of antimalarial drugs are designed without formally considering the statistical models that are fitted to the data, which could lead to designs where it is impossible to estimate the target PK parameters, wasting time and money. We have developed and evaluated designs for future population PK studies of artesunate using optimal design theory [1], which analytically determines a design (i.e. a set of blood sampling times) that maximizes the precision of the PK parameters considering the practical constraints of sampling the patients. The designs include the high risk groups, pregnant women and children, for whom there is very little PK data available.
  1. Retout S, Duffull S, Mentre F. Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs. Comput Methods Programs Biomed 65(2): 141-151, 2001.

Title: Estimation for Non-negative Le´vy-driven CARMA Processes

Peter Brockwell

• Speaker: Prof. Peter Brockwell, Colorado State University and The University of Melbourne.
  
• Time & date: 11.00am Friday 23 October.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Continuous-time autoregressive moving average (CARMA) processes with a non-negative kernel and driven by a non-decreasing Le´vy process constitute a useful and very general class of stationary, non-negative continuous-time processes which have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis and Yang (J. Appl. Prob., 2007) derived efficient estimates of the parameters of a non-negative Le´vy -driven CAR(1) (or stationary Ornstein-Uhlenbeck) process and showed how the realization of the underlying Le´vy process can be estimated from closely-spaced observations of the process itself. In this talk we show how the ideas of that paper can be generalized to higher order CARMA processes with non-negative kernel, the key idea being the decomposition of the CARMA process into a sum of dependent Ornstein-Uhlenbeck processes. (Joint work with Richard Davis and Yu Yang.)

Title: Volatility in the Black-Scholes formula

• Speaker: Dr Kais Hamza, Monash University.
  
• Time & date: 11.00am Friday 6 November 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This talk addresses the question of whether a model for stock price exists that is consistent with the Black-Scholes formula. The results will also be extended to Bachelier and similar formulae.

Title: Distributions of quadratic functionals of the ordinary and fractional Brownian motions

Katsuto Tanaka

• Speaker: Prof. Katsuto Tanaka, Hitotsubashi University, Japan.
  
• Time & date: 10.30am Wednesday 16 September 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: I discuss distributions of quadratic functionals of the ordinary Brownian motion (Bm) and fractional Bm. As far as the ordinary Bm is concerned, quadratic functionals were earlier suggested by several authors as test statistics for goodness of fit tests. Recently, such functionals were used in time-series based econometrics. In this talk I demonstrate how to derive and compute the distributions of such functionals by using various examples. I also discuss ratios of such functionals. Moreover I discuss quadratic functionals of the fractional Bm, but it turns out that the case of the fractional Bm is difficult and there remain some problems to be solved.

Title: A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets

Connie Li Wai Suen

• Speaker: Connie Li Wai Suen, La Trobe University.
  
• Time & date: 11.00am Friday 18 September 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Principal Component Analysis (PCA) is a widely-used tool in multivariate analysis. Although much has been done in regards to sensitivity analysis and the development of influence diagnostics for the eigenvector estimators that define sample principal components, little, if any, has been done in this setting regarding sample principal components themselves. We develop a sensitivity measure for principal components associated with the covariance matrix that is very much related to the influence function (Hampel, 1974). This influence measure is based on the average squared canonical correlation and differs from existing measures in that it assesses influence of certain observational types on the sample principal components. We use this measure to derive an influence diagnostic that satisfies two key criteria being (i) it detects influential observations with respect to subsets of sample principal components and (ii) is efficient to calculate even in high dimensions. We use microarray datasets to show that our measure satisfies both criteria.

Title: Applications of Meta-regression using Maximum Likelihood

Michael Malloy

• Speaker: Michael Malloy, La Trobe University.
  
• Time & date: 11.00am Friday 18 September 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: An analysis of clinical trials using meta-regression is a practice which is not only of great importance to the medical world, but other research fields as well. This talk will discuss the application of meta-regression using maximum likelihood in the statistical software package R. A generalized linear model (GLM) is assumed from which maximum likelihood estimates using an inbuilt minimiser function are obtained. We then describe how to compute the Hessian matrix for a GLM from which approximate variances of the coefficients are achieved. Real life data examples will be provided.
  

Title: Expansions and variance inequalities of Poisson functionals

• Speaker: Prof. Guenter Last, University of Karlsruhe.
  
• Time & date: 11.00am Friday 11 September 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The Poisson process is a fundamental object of probability theory and is important for both theory and applications. It can be defined on arbitrary measurable spaces. In the first part of the talk we discuss some basic properties of this process. Then we proceed with an explicit Fock space representation for Poisson processes in terms of iterated difference operators. Some interesting consequences of this representation are the Wiener-Ito chaos expansion and variance inequalities for square integrable functions of the Poisson process. The talk is based on joint work with Mathew Penrose (Bath).

Title: Multifractality of Products of Geometric Ornstein-Uhlenbeck Type Processes

N. N. Leonenko

• Speaker: Prof. N. N. Leonenko, Cardiff University, UK.
  
• Time & date: 11am Friday 14 August 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: This is joint work with V.V. Anh (Queensland University of Technology, Brisbane) and N.-R. Shieh (National Taiwan University, Taipei).
  
  We consider multifractal products of stochastic processes as defined in Mannersalo et al. (2002), but we provide a new interpretation of the conditions on the mean, variance and covariance functions of the resulting cumulative processes in terms of the moment generating functions. We show that the logarithms of the corresponding limiting processes have an infinitely divisible distribution such as the gamma and variance gamma distributions (resulting in the log-gamma and log-variance gamma scenarios respectively), the inverse Gaussian and normal inverse Gaussian distributions (yielding the log-inverse Gaussian and log-normal inverse Gaussian scenarios respectively). We describe the behaviour of their q-th order moments and Rényi functions, which are non-linear, hence displaying their multifractality. A property on the dependence structure of the limiting processes, leading to their possible long-range dependence, is also obtained.
  
  We consider very different scenarios such as the log-gamma and log-inverse Gaussian scenarios as typical examples of our approach. We should also note some related results by Barndorff-Nielsen and Schmiegel (2004) who introduced some Lévy-based spatiotemporial models for parametric modelling of turbulence. Log-infinitely divisible scenarios related to independently scattered random measures were introduced in Bacry and Muzy (2003) and others. We should note that Chris Heyde (1999) proposed to use a multifractality into risky asset model with fractal activity time (see also Heyde and Leonenko (2005)).
  
  Similar results can be obtained for the multifractal products of stationary diffusion processes (Anh, Leonenko and N.-R. Shieh (2009b)) and birth-death processes processes (Anh, Leonenko and N.-R. Shieh (2009a)).
  

  
  References
  V.V. Anh, N.N. Leonenko and N.-R. Shieh (2008) Multifractality of products of geomertic Ornstein-Uhlenbeck type processes, Adv. Appl. Prob., 40, 1129-1156.
  V.V. Anh, N.N. Leonenko and N.-R. Shieh (2009a) Multifractal scaling of products of birth-death processes, Bernoulli, 15 (2), 508-531
  V.V. Anh, N.N. Leonenko and N.-R. Shieh (2009b) Multifractal products of stationary diffusion processes, Stochastic Analysis and Applications, 27, 475-499
  E. Bacry and J.F. Muzy (2003) Log-infinitely divisible multifractal processes, Comm. Math. Phys., 236, 449.475

Title: Honours Thesis Presentations

• Time & date: 2pm Friday 7 August 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Honours students will give presentations detailing work that they covered in their thesis topic.
  

Title: Testing the equality of error distributions from k independent GARCH models

Ajay Chandra

• Speaker: Ajay Chandra, Department of Mathematics and Statistics, La Trobe University.
  
• Time & date: 11.00am Friday 17 July 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: We study the problem of testing the null hypothesis that errors from k independent parametrically specified generalized autoregressive conditional heteroskedasticity (GARCH) models have the same distribution versus a general alternative. First we establish the asymptotic validity of a class of linear test statistics derived from the k residual-based empirical distribution functions. A distinctive feature is that the asymptotic distribution of the test statistics involves terms depending on the distributions of errors and the parameters of the models, and weight functions providing the flexibility to choose scores for investigating power performance. A Monte Carlo study assesses the asymptotic performance of the Wilcoxon and Van der Waerden tests in terms of empirical size and power in finite samples. The results demonstrate that the proposed tests have overall reasonable size and their power is particularly high when the assumption of Gaussian errors is violated.
  

Title: Kullback-Leibler Information for Model Selection and Comparison in Logistic Linear Models

Guoqi Qian

• Speaker: Guoqi Qian, Department of Mathematics and Statistics, University of Melbourne.
  
• Time & date: 11.30am Friday 5 June 2009.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: We consider two issues involved in model selection:
  (1) Model selection starts with a proposed model class, and it is often unrealistically assumed that the true model generating the data belongs to this model class.
  Then what would happen to model selection if the true model is not in the proposed model class? In other words, how to quantify the model selection bias in the situation of model class mis-specification?
  (2) Model selection often ends up with a selected optimum model minimizing or maximizing a numeric selection criterion function. But it does not or is not able to provide a measure of variability or uncertainty involved in model selection. Such a measure, if available, would be very useful in determining models which are indistinguishable from the optimum model.

  
  We have developed new estimators of Kullback-Leibler information to address these two issues. Our work will be presented in the context of logistic regression model selection but can be extended to other model selection problems.

Title: Variance stabilisation approach to meta-analysis: combining the evidence

Elena Kulinskaya

• Speaker: Elena Kulinskaya, Director of Statistical Advisory Service, Imperial College, London.
  
• Time & date: 11am Wednesday 26 November 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: In the traditional fixed effects model (FEM) of meta analysis, given the estimated effects from K studies θ1,…, θK , with θi ~N(θ, σi2) , the combined effect θ is estimated as the weighted mean θest =(wi θ1+…+ wK θK)/W ~N(θ ,1/ W ) , where wi=σi-2 and W= (w1+…+ wK ). If the homogeneity of the effects is rejected, the random effects model can be used: θi ~N(θ, σi-2 +τ2). (Sutton et al, 2000).
  
  When the variance stabilizing transformation (vst) is applied to the estimated effects, we deal instead with the transformed standardised effects K(δi). They are estimated by κi =ni-1/2h(Si) ~N(K(δ),1/ni) and can be added with known weights ni in meta-analysis (Kulinskaya, Morgenthaler and Staudte, 2008).
  
  Given variance stabilized statistics from K studies T1,…,TK , with T1 ~N(ni1/2 κ ,1) , the combined effect κest=(n1 κ1+…+nK κK))/ N ~N(K(δ),1/ N ) where N= n1 +…+nK. The back-transformation is used to obtain the inference on the standardised effects δ. If the homogeneity of the transformed effects is rejected, the random transformed effects model can be used: κ i ~N(κ , ni-1 +τ2).
  
  When there are no nuisance parameters (as in the 1-sample Binomial or Poisson case) these two approaches to meta analysis are equivalent. In the general case, the variance stabilization approach can be used even when the inference on the original, non-standardised effects is of primary interest. In this case the optimal weights depend on the nuisance parameters. An example is the variance stabilizing arcsine transformation for the difference in absolute risks, with the average risk as the nuisance parameter.

Title: On the Asymptotic Variance of Vacancy for Boolean Models with Grain Distortions

Christian Rau

• Speaker: Christian Rau, School of Mathematical Sciences, Monash University.
• Time & date: 11am Friday 14 November 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: A Boolean model is a spatial coverage process whose driving point process is homogeneous Poisson, and whose attached random sets, or grains, are independent and identically distributed (i.i.d). Apart from a host of traditional applications, Boolean models have been employed recently in the modelling of sensor networks, which motivated this research. The asymptotic variance of vacancy (AVV) in the Boolean model is defined by letting the intensity of the Poisson process diverge to infinity, and simultaneously scaling the grains to become small. We consider optimality and continuity properties of the AVV when the grains are subject to i.i.d. distortions, which includes rotations and shearings as special cases. An important role in the formulation and derivation of our results is played by notions of symmetry well known from multivariate analysis and stochastic simulation, such as conjugation-invariance and group models. This is joint work with Sung Nok Chiu, Hong Kong Baptist University.

Title: Honours Thesis Presentations

• Time & date: 1pm Friday 31 October 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Six honours student will give a 20 minute presentation detailing work that they covered in their thesis topic.

Title: Multiscale Simulation of Biochemical Systems

Linda Petzold

• Speaker: Linda Petzold, University of California Santa Barbara.
  
• Time & date: 2pm Friday 22nd July 2008.
• Venue: SEMS meeting room 221, Physical Sciences 1, La Trobe University, Melbourne Campus.
• Abstract: In microscopic systems formed by living cells, the small numbers of some reactant molecules can result in dynamical behavior that is discrete and stochastic rather than continuous and deterministic. An analysis tool that respects these dynamical characteristics is the stochastic simulation algorithm (SSA). Despite recent improvements, as a procedure that simulates every reaction event, the SSA is necessarily inefficient for most realistic problems. There are two main reasons for this, both arising from the multiscale nature of the underlying problem: (1) the presence of multiple timescales (both fast and slow reactions); and (2) the need to include in the simulation both chemical species that are present in relatively small quantities and should be modeled by a discrete stochastic process, and species that are present in larger quantities and are more efficiently modeled by a deterministic differential equation. We will describe several recently developed techniques for multiscale simulation of biochemical systems, and outline some of the future challenges.

Title: Bayesian Methods in Software Testing and Capability Maturity Model

• Speaker: Salilesh Mukhopadhyay, Feasible Solution Inc, USA.
  
• Time & date: 2pm Friday 4 July 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: Most of the time the testing phase of the application does not allow an end-to-end testing with all the interfaces up and running in QA environment. To remedy the situation the common practice is to have coverage analysis with appropriate risk mitigation in Finacial (large) applications mainly. However the testing scenarios of E-Commerce, Business to Business Models, Electronic Raw Material Acquisition, Auction Engines are not at all different. The present paper provides a statistical analysis of the scenarios and calculates the associated risk for each phase of testing cycle like, Unit, System Integration Testing, End-to-End Testing, UAT.
  
  The purpose of the present paper is to provide an outline of Bayesian Methods (Prior and Posterior analysis) in Software testing with special emphasize on Capability Maturity Model. Different types of testing scenarios will be analysed for each phase of testing like Unit testing, System Integration Testing, End-to-End Testing, User Acceptance Testing and post production maintenance Testing. Manual and Automated testing will be discussed in details for stable QA environment. Finally the benefits of using quantitative analysis to mitigate the associated risk in each phase will be discussed in details.

Title: The Coverage Probability of Confidence Intervals in 2r factorial Experiments after Preliminary Hypothesis Testing

• Speaker: Khageswor Giri, Department of Mathematics and Statistics, La Trobe University.
  
• Time & date: 2pm Friday 23 May 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: We consider a 2r factorial experiment with at least two replicates. Our aim is to find a confidence interval for θ, a specified linear combination of regression parameters. We suppose that preliminary hypothesis tests are carried out sequentially beginning with the rth order interaction. After these preliminary hypothesis tests, a confidence interval for θ with nominal coverage 1-α is constructed under the assumption that the selected model is given to us a priori. We call this the naïve 1-α confidence interval for θ. We describe a new efficient Monte Carlo method, which employs conditioning for variance reduction, for estimating the minimum coverage probability of the naive confidence interval. The application of this method is demonstrated in the context of a 23 factorial experiment with 2 replicates and a particular contrast θ of interest. The naive confidence interval, with nominal coverage probability 0.95, has minimum coverage probability that is, to a good approximation, 0.464. This shows that the naive confidence interval is completely inadequate.

Title: Variance stabilizing the risk difference to obtain confidence intervals for effects and effect sizes

Robert Staudte

• Speaker: Associate Professor, Dr Robert Staudte, Department of Mathematics and Statistics, La Trobe University.
  
• Time & date: 2pm Friday 16 May 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: I will be discussing the study of dimension reduction of high dimensional data for binomial response variable data sets when the number of individuals sampled is less than the number of measurement variables. The application of principle component analysis as a prestep to Sliced Inverse Regression and Sliced Average Variance Estimation will be presented. In this setting in order to produce an efficient algorithm, an approximation technique using first and second order perturbations is suggested as a one step eigen-analysis in the cross-validation step of the classification of the binomial response variable data sets.

Title: Approximating cross-validation results for binary classification methods preceded by principal component dimension reduction

Mitra Jazayeri

• Speaker: Mitra Jazayeri, Department of Mathematics and Statistics, La Trobe University.
  
• Time & date: 2pm Friday 9 May 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The usual estimator of the risk difference is variance stabilized, conditionally on an estimated weighted average of the unknown risks. This leads to conditional confidence intervals for the standardized risk difference, and hence for a correlation effect size. In addition, it leads to confidence intervals for the risk difference itself, with more accurate unconditional coverage than those obtained by standard asymptotic methods, as shown by simulations studies. Methods for combining the results of several studies are presented, and illustrated on nine independent randomized clinical trials of the effect of diuretics on pre-eclampsia.

Title: On Survival Equivalence Function

• Speaker: Prof. T. K. Pogany, University of Rijeka, Croatia .
  
• Time & date: 2pm Friday 29 February 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: The reliability of composite systems is improved by decreasing the argument of the associated survival function in the case of general positive i.i.d. random life components connected in series (paralell). The gamma-Weibull distribution has been recently introduced by Leipnik and Pearce. The density function, the probability distribution function and the characteristic function are of is expressed in terms of the confluent Fox-Wright generalization of the hypergeometric function, and its incomplete variant. The composite series (paralell) systems reliability is presented taking for the case study system components having gamma-Weibull life distribution.

Title: Parameter Estimation and Bias Correction for Diffusion Processes

Song Xi Chen

• Speaker: Prof. Song Xi Chen, Department of Statistics, Iowa State University.
  
• Time & date: 2pm Friday 7 March 2008.
• Venue: Room 310 (Access Grid Room), Physical Sciences 2, La Trobe University, Melbourne Campus.
• Abstract: This lecture considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter as observed in many empirical studies, we develop expansions for the bias and variance of parameter estimators for two mostly employed interest rate processes. A parametric bootstrap procedure is proposed to correct bias in parameter estimation of general diffusion processes with a theoretical justification. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates for both univariate and multivariate processes. The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study on a Fed fund rate data.