Department of Statistics Seminars

Phase transitions in loss networks

This talk is part of the mini-workshop in probability and statistical physics. The talk will be given jointly by Ilze and Benny.

Loss networks have been widely used in modelling telecommunications networks. In this talk we consider loss networks with a tree structure, supporting both single-link and multi-link connections. Such networks may exhibit phase transitions as the arrival rates for multi-rate connections increase. We will discuss how the phase transitions are affected by changes in network structure -- changes in capacity, connectivity, some degree of asymmetry, and the addition of controls.

Degenerate Random Environments

This is part of a mini-workshop in probability and statistical physics.

We discuss joint work with Prof. Tom Salisbury on certain kinds of random graphs. These models are similar to percolation models but also have important differences, including the notion of "Markolation" versus percolation. We will focus on some of the more interesting examples and see that there are phase transitions as we vary the parameters of the model(s).

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

What is Quantum Field Theory?

We will take a brief walk through the history of quantum field theory and then branch off into connections with down to earth problems involving self-avoiding walk.

The connection to quantum field theory is one way to prove results on the end-to-end distance of the typical self-avoiding walk as a function of the number of steps in the walk.

David Brydges is a former president of the International Association for Mathematical Physics and a Fellow of the Royal Society of Canada, with a Canada Research Chair at the University of British Columbia. He has made fundamental contributions to both mathematical physics and probability, including the development of Wilson's Renormalisation Group and the invention of the Lace Expansion.

http://www.math.ubc.ca/~db5d/

Many-core statistical inference of stochastic processes: a bright computational future

Massive numerical integration plagues the statistical inference of partially observed stochastic processes. An important biological example entertains partially observed continuous-time Markov chains (CTMCs) to model molecular sequence evolution. Joint inference of phylogenetic trees and codon-based substitution models of sequence evolution remains computationally impractical. Parallelizing data likelihood calculations is an obvious strategy; however, across a cluster-computer, this scales with the total number of processing cores, incurring considerable cost to achieve reasonable run-time.

To solve this problem, I describe many-core computing algorithms that harness inexpensive graphics processing units (GPUs) for calculation of the likelihood under CTMC models of evolution. High-end GPUs containing hundreds of cores and are low-cost. These novel algorithms are particularly efficient for large state-spaces, including codon models, and large data sets, such as full genome alignments where we demonstrate up to 150-fold speed-up. I conclude with a discussion of the future of many-core computing in statistics and touch upon recent experiences with massively large and high-dimensional mixture models.

http://www.biomath.ucla.edu/msuchard/

Comparing Trees using Distances, Trees and Multidimensional Scaling

Distances between trees have useful applications in combining phylogenetic trees built from multiple genes and in studying trees built from bootstrap samples and Bayesian posterior distributions.

Until recently, computations of the distance between trees was intractable. We have developed an R package to compute the distance between trees based on a polynomial algorithm by M. Owen and S. Provan.

Using this distance we are able to project trees from data with varying mutation rates, compare hierarchical clustering trees for Microarrays, and study influence functions for the data used to build the trees.

The main tool for using the distances is multidimensional scaling, although the original tree metric delivers a treespace which is not Euclidean, it is itself negatively curved, the Euclidean approximations provided by MDS are very useful for making low dimensional graphics of tree projections.

(This is joint work with John Chakerian)

http://www-stat.stanford.edu/~susan/

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