Department of Statistics Seminars

Fast goodness-of-fit tests for copulas

Copulas are increasingly used to model multivariate distributions with continuous margins. The first half of the talk will be devoted to a non-technical presentation of the principles behind this very general approach and to the different steps involved in the modeling process. In the second half, recent results on goodness-of-fit testing for copulas will be presented. This is joint work with Jun Yan (University of Connecticut) and Mark Holmes.

http://www.stat.auckland.ac.nz/~ivan/

3rd Generation Bioinformatics - its up to you guys

Near Matches and Applications

When two judges rank the same n objects, we say a ``near match of order k'' occurs on the i-th object if their ranks for this, are close to within k. Of interest is the number of near matches in such a context, and its large-sample distribution. Applications to a nonparametric test in randomized block designs and to a new measure of association will be presented, along with some efficiency comparisons.

http://www.pstat.ucsb.edu/faculty/jammalam/

Some principles of flows and steps in designing tertiary statistics curricula for learning

NOTE ROOM CHANGE: THIS TALK IS NOW IN ROOM 279

We propose some principles of flow and steps in progression in teaching tertiary statistics, and discuss their roles in facilitating student learning. Many excellent principles for teaching statistics have been advocated and developed over the past two decades. These include data- and context-driven approaches using real data and situations with which students can identify; emphasis on concepts and statistical thinking; use of technology and graphics; incorporation of active and experiential learning; and development of rich and alternative assessment methods. Calls for tertiary educators to identify learning objectives, and to align assessment with those objectives, appear in both general and discipline-specific higher education literature. Although there is strong awareness of the importance of the `story' in learning statistics, less explicit attention has been given to course progression and the alignment of progression, of both content and learning stages, with objectives. Such attention is particularly important in statistics, with its conceptual, interpretative and communication demands, underpinned by sound quantitative models, techniques and problem-solving. Combining our proposed additional principles with those described above, we show how the same principles can give rise to distinct `first' courses in tertiary statistics through alignment with slightly different learning objectives. We also discuss the advantages of overt awareness of these principles in constructing later courses for optimal student learning. We advocate that greater explicit attention to principles of flow and appropriately-spaced learning stages will assist in the next steps in statistical education reform, in considering progression of content, of development of student learning and of advancement beyond the first course.

http://www.scitech.qut.edu.au/about/staff/mathsci/statistics/macgillivrayh.jsp

Spatial-temporal Poisson cluster models of rainfall: Applications and further developments

Spatial-temporal models of rainfall based on Poisson cluster processes are discussed. The application of the models in large urban drainage engineering projects (e.g. Auckland City, Glasgow, and Thames, London) is described. Further developments based on superposing multiple Poisson processes to represent different types of precipitation (e.g. convective and stratiform rain) are then given. Ways of reducing model parameters for multiple types of storms are considered, which include using a continuous probability distribution for storm types z and functional relationships between key parameters based on z. Using a uniform distribution for z, statistical properties up to third order are derived, and used to fit a Neyman-Scott Poisson cluster model to a 60-year record of hourly rainfall data taken from a site near Wellington. The performance of the fitted model is assessed by comparing observed and simulated extreme values over a range of time scales.

http://www.massey.ac.nz/~pscowper/

Estimating Diagnostic Test Likelihood Ratios

Let p1 and p2 represent the individual probabilities of response to a particular diagnostic test in two subpopulations consisting of diseased and disease-free individuals, respectively. In the terminology of diagnostic testing, p1 is called the sensitivity of the given test, and p2 is the probability of a false positive error, i.e., the complement of 1-p2, which is the test specificity.

Since 1975, the ratios r+ = p1/p2 and r- = (1-p1)/(1-p2) have been of particular interest to advocates of evidence-based medicine. These functions of sensitivity and specificity have been called the ``likelihood ratio of a positive test result" and the ``likelihood ratio of a negative test result," respectively.

We describe methods of deriving individual interval estimates of r+ and r-, and a simultaneous confidence region for both ratios. Using various performance characteristics of these confidence intervals, we compare our estimates with methods of interval estimation in common use. Via examples from various studies of diagnostic tests, we illustrate the merits of our computationally simple methods of deriving interval estimates of these medically relevant characteristics of diagnostic tests. As time permits, various extensions of the simplest version of this problem will also be discussed and illustrated with examples.

http://www.stats.uwaterloo.ca/Faculty/Matthews.shtml

On vector generalized linear and additive models and all that

The first half of this talk will give a broad overview of the project I have been working on over the last decade or so. It will mainly survey the classes of vector generalized linear and additive models (VGLMs/VGAMs) which are very large and contains many statistical models. For example, univariate and multivariate distributions, categorical data analysis, time series, survival analysis, extreme value analysis, mixture models, correlated binary data, and nonlinear regression. The framework will be tied in with my VGAM package for R. There are some natural extensions, e.g., reduced-rank ideas that perform ordination (a useful technique in ecology). The second half of this talk will focus on two sub-topics:

the xij problem and quantile/expectile regression. The former is useful for fitting a multinomial logit model where there are covariates specific to each alternative. Applications of the latter are becoming widespread in many fields.

http://www.stat.auckland.ac.nz/~yee/

Developing Statistical Perception

Statistics is typically portrayed as a set of methods for collecting and analyzing data. But more fundamentally, statistics is a way of seeing the world. I describe our efforts to understand the perceptions and ideas young students bring to bear on data and how we work to shape students' perceptions to make them more expert like.

To facilitate learning, we have built into the data visualization software, TinkerPlots, tools that support and then build on novice perceptions. More recently, we have added modeling capabilities which students use to create and explore ``worlds'' of their own making. In this way, we hope to develop the crucial understanding that statistics is not only about seeing, but also about questioning what we see.

http://www.umass.edu/srri/serg/staff/cliff.html

Mixtures, modes, and clusters

This talk will have three main sections. The first part of the talk will be concerned with the mathematical properties of a mixture of normal densities, focusing on the modes of the mixture. The second part will then describe a method of clustering data hierarchically based on the modes of a kernel density estimator.

The final section will be a sweep across a range of inferential issues that arise when the clustering method is used in higher dimensions, where the role of bandwidth parameters becomes more crucial. This last part is ongoing research, and so will have multiple open questions.

http://www.stat.psu.edu/people/faculty/lindsay.html

Resampling methods in change-point analysis

Real life data series are frequently not stable but exhibit changes in parameters at unknown time points. We encounter changes (or the possibility thereof) everyday in such diverse fields as economics, finance, medicine, geology, physics and so on. Therefore the detection, location and investigation of changes is of special interest. Change-point analysis provides the statistical tools (tests, estimators, confidence intervals). Most of the procedures are based on distributional asymptotics, however convergence is often slow -- or the asymptotic does not sufficiently reflect dependency. Using resampling procedures we obtain better approximations for small samples which take possible dependency structures more efficiently into account.

In this talk we give a short introduction into change-point analysis. Then we investigate more closely how resampling procedures can be applied in this context. We have a closer look at a classic location model with dependent data as well as a sequential location test, which has become of special interest in recent years.

http://mspcdip.mathematik.uni-karlsruhe.de/~ckirch/

Exploring student histories

The prerequisites for the paper STATS 220 are EITHER one stage 1 Statistics paper OR one stage 1 Computer Science paper. Because STATS 220 contains several computing topics, there has been an anxiety that final results would reveal a bimodal distribution, with the Comp Sci students doing well and the Stats students doing not so well, BUT this doomsday scenario has never actually eventuated.

Does this mean that the quality of the teaching in STATS 220 is so high that the students' past history counts for naught? Or is it possible that the students' backgrounds cannot be so neatly classified as the Computer Scientists versus the Statisticians? Without data, it is very hard to tell.

This year, it became possible to obtain reports on students histories - which papers they have taken in the past - which provided an opportunity to explore this question in a rational manner.

This talk will outline a simple exploration of the backgrounds of the students in the 2009 STATS 220 class. The focus will be on problems (and solutions) with data preparation and on graphical displays of the data.

http://www.stat.auckland.ac.nz/~paul/