Statistics Across Campuses

  Large Spatial Data Modeling and Analysis: A Krylov Subspace Approach Date: 15 October 2020, Thursday Time: 12.00pm Speaker: Dr Tingjin Chu (University of Melbourne )   Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Abstract: Estimating the parameters of spatial models for large spatial datasets can be computationally challenging, as it involves repeated evaluation of sizable spatial covariance matrices. In this paper, we aim to develop Krylov subspace based methods that are computationally efficient for large spatial data. Specifically, we approximate the inverse and the log-determinant of the spatial covariance matrix in the log-likelihood function via conjugate gradient and stochastic Lanczos on a Krylov subspace. These methods reduce the computational complexity from $O(N^3)$ to $O(N^2)$ and $O(N\log N)$ for dense and sparse matrices, respectively. Moreover, we quantify the difference between the approximated log-likelihood function and the original log-li...

  Multi-type age-structured population model Date: 01 October 2020, Thursday Time: 12.00pm   Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Speaker: Dr Jie Yen FAN (Monash University) Abstract: Population process in general setting, where each individual reproduces and dies depending on the state (such as age and type) of the individual as well as the entire population, offers a more realistic framework to population modelling. Formulating the population dynamics as a measure-valued stochastic process allows us to incorporate such dependence. We describe the dynamics of a multi-type age-structured population as a measure-valued process , and obtain its asymptotics, in particular, t he law of large numbers and the central limit theorem. Joint work with Kais Hamza, Peter Jagers and Fima Klebaner. Link: https://latrobe.zoom.us/j/98357628534  

  Leveraging Pleiotropy effect from genome-wide association studies using Sparse Group Models Date:  Friday 2  October 2020 Time: 3 pm Speaker:  Prof Benoit Liquet-Weiland (Macquarie University) Abstract: Genome-wide association studies (GWAS) focus on testing association between millions of genetic markers (or single nucleotide polymorphisms, SNPs) and a phenotype in an agnostic way, where every SNP is tested independently from the other SNPs for association with the phenotype. One major finding from GWAS era is that pleiotropy – that occurs when one gene influence two or more unrelated traits - is a widespread phenomenon in human complex traits. Several methods were proposed to combine results across studies of different phenotypes in order to improve the power of detecting pleiotropic associations at SNP level. It is well established that incorporating prior biological knowledge as gene or biological pathways structures to consider complex mechanisms can help to d...

Testing for principal component directions under weak identifiability Date: 02 October 2020, Friday Time: 4pm Speaker: Prof Davy Paindaveine (Université Libre de Bruxelles) Abstract: We consider the problem of testing the null hypothesis that the first principal direction coincides with a given direction in the multivariate Gaussian model. In the classical setup where eigenvalues are fixed, the likelihood ratio test (LRT) and the Le Cam optimal test for this problem are asymptotically equivalent under the null hypothesis, hence also under sequences of contiguous alternatives. We show that this equivalence does not survive asymptotic scenarios where the ratio of both leading eigenvalues goes to one faster than the inverse of root-n. For such scenarios, the Le Cam optimal test still asymptotically meets the nominal level constraint, whereas the LRT severely overrejects the null hypothesis. Consequently, the former test should be favored over the latter one whenever the two largest sampl...

Multiply robust imputation procedures for the treatment of item nonresponse in surveys. Date: 18 September 2020, Friday Time: 10am Speaker: Prof David Haziza (University of Ottawa) Abstract: Every time data are collected, it is virtually certain that we will face the problem of missing data. Missing data are undesirable because they make estimates vulnerable to nonresponse bias. In surveys, it is customary to distinguish unit nonresponse from item nonresponse. The former occurs when no usable information is collected on a sample unit, whereas the latter is characterized by the absence of information limited to some survey variables only. Unit nonresponse is usually handled through weight adjustment procedures methods. Item nonresponse is typically treated by some form of single imputation, whereby one replacement value is used to fill in for the missing value. In this presentation, we will describe multiply robust imputation procedures in finite population sampling. In practice, multi...

  Estimating a Covariance Function from Fragments of Functional Data Date:  Friday 11  September 2020 Time: 3 pm Speaker:  Professor Aurore Delaigle (University of Melbourne) Abstract: Functional data are often observed only partially, in the form of fragments. In that case, the standard approaches for estimating the covariance function do not work because entire parts of the domain are completely unobserved. In previous work, Delaigle and Hall (2013, 2016) have suggested ways of estimating the covariance function, based for example on Markov assumptions. In this work, we take a completely different approach which does not rely on such assumptions. We show that using a tensor product approach, it is possible to reconstruct the covariance function using observations located only on the diagonal of its domain. Zoom Link:   https://macquarie.zoom.us/j/91597976300?pwd=WVpyVEdtUXhKSEJjbHV2TVVWTXExdz09