Schedule
You can see the schedule for the students' conference below. Once the abstracts are added, you can find them here. If the submitted abstract of your talk is not listed here, please contact us.
Keynote Speaker
Professor Aihua Xia,
Professor, School of Mathematics and Statistics,
The University of Melbourne.
Talk Title: Modelling the extinction time of an epidemic
10.00 a.m. - 11.00 a.m.
Abstract:
The modelling of COVID-19 has been of significant interest in the last eight months and the classical SIR epidemic model is clearly inadequate in answering questions around COVID-19. I will begin my talk with an introduction of the law of small numbers and use it to estimate the number of infects of COVID-19 in Wuhan. The Poisson law of small numbers is then used to build a model which allows the virus establishes itself within a host for a random time (incubation period) before they become infectious. We show that when the person-to-person contact rate of a population in which a disease has been spreading is lowered sufficiently, the disease is headed to extinction and asymptotic results and bounds of the extinction time can be established. This talk is based on a joint work with D. J. Daley.
Schedule for the Fourth Victorian Research StudentsVRSMiPS IV Talk Titles and Abstracts
Scheduling staff shifts of a blood donor centre
11.00 a.m. – 11.20 a.m.
Achini Erandi Madduma Wellalage, The University of Melbourne
Abstract:
In Australian Red Cross Lifeblood (ARCL), blood collections mostly depend on voluntary blood donors who donate blood without any remuneration. Therefore, it is important to provide a better service to convince donors to actively stay until the end of the donation process and return regularly to donate blood. A well-managed staff is required to make the donor flow efficient. Hence, our research question is how to schedule staff shifts effectively while minimising the waiting times spent by donors during the blood donation.
Fast inference methods for factor copulas
11.25 a.m. – 11.45 a.m.
Alex Verhoijsen, The University of Melbourne
Abstract:
Factor copula models provide a flexible tool to model dependence in high dimensions by assuming latent factors are the source of dependence between observable variables. However, their estimation procedure quickly becomes computationally cumbersome when the dimension becomes large. We propose a fast inference method to reduce the computational burden in estimation methods for factor copulas. This is done by removing the need for numerical integration. Our method uses factor analysis to obtain approximations for the unobservable factors that cause dependence between the observable variables. We show that this method improves on existing methods. Moreover, existing methods only work for one-factor copula models, while our proposed method can handle multi-factor copula models. We show that for high-dimensional datasets, the computational time decreases substantially. While standard maximum likelihood performs better than our method in terms of RMSE, this difference quickly becomes smaller with increasing dimension.
Stochastic Matching Models: FCFS, Double Auctions and Beyond
11.50 a.m. – 12.10 p.m.
Behrooz Niknami, The University of Melbourne
Abstract:
Stochastic Matching Models concern themselves with queueing networks where customers and servers are assigned to each other via some compatibility structure and orders are processed using some priority regime. Often the difference between customers and servers are blurred by neglecting service times in favour of streams of server arrivals. Recently, novel product form invariant distributions have been established for various such models under the First come First Serve (FCFS) priority regime. However, there is still much to be learned of other priorities, an example of which is the Double Auction priority employed in stock markets. We will explore these models in this talk and attempt to see what can be said matching models with double auction priority, perhaps by appealing to what is known already about FCFS priority models.
Virtual Lunch Break + Collaboration Time
Analysis of Multifractal and Monofractal Spherical Random Fields with Cosmological Applications
1.15 p.m. – 1.35 p.m.
Ravindi Nanayakkara, La Trobe University
Abstract:
The Rényi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the Rényi function is known explicitly. The theoretical part of the article presents multifractal random fields on the sphere and develops specific models where the Rényi function can be computed explicitly. For all considered models explicit expressions of their multifractal spectrum are obtained. Properties of the models and dependencies of their characteristics on parameters are investigated. Then these results are applied to the Cosmic Microwave Background Radiation data collected from the Planck mission. The main statistical model used to describe these data in the literature is isotropic Gaussian fields. We present numerical multifractality studies and methodology based on simulating random fields, computing the Rényi function and the multifractal spectrum for different scenarios and actual CMB data. The obtained results can also find numerous potential applications for other geoscience, environmental and directional data.
Strong Law of Large Numbers for Functionals of Random Fields with Unboundedly Increasing Covariances
1.40 p.m. – 2.00 p.m.
Illia Donhauzer, La Trobe University
Abstract:
The talk is about the Strong Law of Large Numbers for integral functionals of random fields with unboundedly increasing covariances. The case of functional data and increasing domain asymptotics is considered. Conditions on covariance functions such that the Strong Law of Large Numbers holds true will be presented. The considered scenarios include non-stationary random fields. The discussion about applications to weak and long-range dependent random fields and numerical examples will be shown.
Improving Dimension Reduction outcomes using Optimal Response Transformations
2.05 p.m. – 2.25 p.m.
Marina Masioti, La Trobe University
Abstract:
This talk presents a way to improve dimension reduction estimates using optimal response transformations. Dimension reduction is required in order for us to view and study the relationship between a response and multiple explanatory variables in a lower-dimensional setting. We employ simple, one-parameter response transformations, where a tool known as the influence function is used to choose the optimal parameter value of the transformation. This method is applied to the Principal Hessian Directions (pHd) Analysis and the Ordinary Least Squares (OLS) methods for dimension reduction. We show how this method works under the Single-Index Model (SIM) and also provide an Iterative version of the method for Multiple-Index models. Our simulations highlight excellent performance.
Latent Voter Model on Locally Tree-Like Random Graphs
2.30 p.m. – 2.50 p.m.
Ran Huo, The University of Melbourne
Abstract:
We study a latent voter model introduced by Lambiotte, Saramaki, and Blondel in (2009). In our model, each individual owns one of two types of technology, say an iPad or a Microsoft Surface tablet. We study this model on random graphs (generated by the configuration model) with bounded degrees. Individuals at times of a rate one Poisson process pick a neighbor at random and imitate their opinion (i.e. choice of devices). However, it is unlikely that someone who has recently bought a new tablet computer will replace it, so we introduce latent states in which individuals will not change their opinion. However, this latent period is short and expires at a constant rate. Our first result is that if time is speed up then the fraction of each opinion converges to a fixed point of ODE as t goes to infinity. This is proved using ideas of Cox, Durrett, and Perkins (2013). One constructs a dual process that is a coalescing random walk plus branching. Using this result, we can show that the latent voter model has a quasi-stationary state in which opinion 1 has probability approximately 1/2 and persists in this state for a time that is longer than any polynomial of the size of the population. Thus, even a very small latent period drastically changes the behavior of the voter model.
Virtual Coffee Break + Collaboration Time
Explaining, exploring, and clustering with non-linear and complex data
3.15 p.m. – 3.35 p.m.
Daniel Fryer, The University of Queensland
Abstract:
Complex and non-linear data pose some of the most relevant and compelling statistical challenges of our time. In this talk, I will focus on two different challenges: exploring dependence structures in non-linear data, in the context of supervised machine learning, with the intention to attribute dependence on the response variable “fairly” amongst a number of explanatory features (1); and adapting “flat” classical optimisation algorithms to suit curved spaces, with non-Euclidean Riemannian metrics (2). In particular, I will introduce the Shapley value – a method of fair payoff distribution arising from the mathematical theory of cooperative games – and show how this technique can be used to break ground on item (1). Then, I will talk briefly about the log-Cholesky Riemannian metric, and how a simple transformation allows us to efficiently adapt the Euclidean k-means algorithm to the convex cone of symmetric positive definite matrices, thus breaking ground on item (2). The latter technique will be demonstrated with an application to clustering of time-series in a sequence of synthetic aperture radar images.
Identify the effect for shorebirds from the fox eradication program in Philip Island using changepoint methods
3.40 p.m. – 4.00 p.m.
Udani Wijewardhana, Swinburne University
Abstract:
In the past fox predation was the greatest land-based threat to the long-term viability of the shorebird colonies on Phillip Island, Victoria, Australia. Regular fox control for 20 years up to 2006 had reduced the fox population, but shorebirds continued to be decimated. Therefore, a fox eradication program was put in place in 2006. There were three phases to this program called knock-down, clean-up and post-eradication. An effective knock-down was declared in 2011. The impact of these measures for local shorebirds has never been thoroughly assessed. This study aims to track the effects of the fox eradication program on abundance measures for six local shorebird species found on Philip Island. We have used annual citizen science data for 2002 to 2017 extracted from the Atlas of Living Australia, adjusted for possible confounding variables such as resident human population. We have used two statistical methods to assess the impact of the fox eradication program which are changepoint analysis and INLA modelling. The INLA model has proved that there has been a significant increase in sightings of shorebirds and the changepoints identified by the four changepoint methods has helped to confirm the significant changes in shorebird numbers after at least one of the first two phases of the fox eradication program.
Skorokhod planar embedding
4.05 p.m. – 4.25 p.m.
Maher Boudabra, Monash University
Abstract:
If µ is a distribution, is there a planar domain U for which the real part of a stopped planar Brownian motion upon exiting U has the distribution µ? The problem is often called the planar Skorokhod embedding problem. We show the problem is solvable (under some requirements) as well as a uniqueness criterion of the domain.
The historical voter model
4.30 p.m. – 4.50 p.m.
Tim Banova, The University of Melbourne
Abstract:
In the past three decades, many high-dimensional spatial occupation models arising in statistical physics have been proven, or are conjectured, to converge weakly to super-Brownian motion, a measure-valued process which can be viewed as the scaling limit of branching random walk. More recently, the focus has shifted to proving convergence of the so-called historical processes associated with these models to the scaling limit historical Brownian motion; this was carried out for lattice trees in upcoming work. This talk summarises an approach for proving f.d.d convergence of historical processes via quantities known as detailed r-point functions, before applying it to the historical voter model.