Statistics Across Campuses

Metric number theory via geometry and dynamics: Mahler to Margulis Joint Stochastic and Mathematics colloquium at La Trobe University. Speaker: Dr Mumtaz Hussain, La Trobe University Time & Date: 11:00am Thursday 25 June 2020   Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Venue: zoom meeting, see details below Abstract: There are two well-known approaches in solving the measure theoretic problems in Diophantine approximation.  The metrical approach arise from the geometry of numbers and the ergodic theoretic approach arise from the dynamics on the space of lattices. One of the main ingredients in the geometry of numbers is the usage of Borel-Cantelli lemmas from probability theory. Dynamics on the space of lattices rely on the Dani correspondence principle (1985) which was extensively  developed further by Margulis and Kleinbock.  I will discuss both of these approaches and along the way discuss some well-known results such as the resol...

Analysis of repeated categorical ratings: going beyond inter-rater agreement. Statistics and Stochastic colloquium at La Trobe University. Speaker: Dr Damjan Vukcevic, University of Melbourne Time & Date: 12:00pm Thursday 18 June 2020 Venue: zoom meeting, see details below Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Abstract: A common task in health and medicine is the classification of patient information into one of several categories by a trained expert. This could include assessing the presence and type of a tumour from a medical image or providing a disease diagnosis from a series of medical tests. Often such judgements are hard to make and error prone: two experts may rate the same scenario differently or the same expert may provide alternative ratings of the same scenario when rating it multiple times on different occasions. Analysing the performance of such expert ‘raters’, and the accuracy of their ‘ratings’ across a series of ‘items’, is a comm...

Estimation of Graphical Models for a class of Multivariate Skew-Symmetric Distributions Date: 26 June 2020, Friday Time: 4pm Speaker: Dr Linh Nghiem (ANU) Abstract: We consider the problem of estimating graphical models for data generated from a class of multivariate skew symmetric distributions, which can be used to model multivariate data with both moderate skewness and heavy tails. Conditional independence between any component requires both the corresponding element of the inverse covariance matrix and the product of the two corresponding components in the shape vector to be zero. Utilizing new properties of the conditional expectation in this class of distributions, we propose a novel two-step nodewise approach to estimate the graphical model. For each nodewise regression, we first fit a linear model using least squares, and then fit a one-component projection pursuit regression on the residual obtained from the first step. The graph is estimated by thresholding an app...

Spatial Confounding in GEEs Date: 19 June 2020, Friday Time: 4pm Speaker: Dr Francis Hui (ANU) Abstract: Generalized Estimating Equations (GEEs) are a popular tool in many scientific disciplines for investigating the effects of covariates on the mean of a response. In the context of spatial analysis, GEEs rely on specifying a regression model for the marginal mean, a variance function, and a working correlation matrix characterizing the spatial correlation between observations. One of the key features of GEEs is that estimation of the covariate effects is robust to misspecification of the (spatial) working correlation matrix. That is, the choice of working correlation only affects efficiency and not the consistency (effectively, the target) of the GEE estimator.  In this talk, we introduce and explore the concept of spatial confounding in GEEs. Specifically, we show that in settings where the covariates included in the GEE are (also) spatially correlated, the choi...

Bayesian modelling of complex trajectories: a case study of covid-19 Date: 12 June 2020, Friday Time: 2 pm Speaker: Prof. Kerrie Mengersen (Queensland University of Technology) Abstract: Since the initial outbreak in Wuhan (Hubei, China) in December 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus responsible for coronavirus disease 2019 (COVID-19), has rapidly spread to cause one of the most pressing challenges facing our world today: the COVID-19 pandemic. Within four months of the first reported cases, more than two and a half million cases were confirmed with over two hundred thousand deaths globally, and many countries had taken extreme measures to stop the spread. Although Bayesian models of epidemics are well known in the literature, modelling COVID-19 has been problematic because of the complexity of control responses that were implemented to contain the spread of the disease in different countries. In this presentation, I will describ...