Statistics Across Campuses

Continuous Time Capture-Recapture Date: 05 November 2020, Thursday Time: 9am AEDT / 11am NZDT Speaker:  Prof Richard Barker  (PVC, The University of Otago) Abstract: Motivated by field sampling of DNA fragments, we describe a general model for capture-recapture modeling of samples drawn one at a time in continuous-time. Our model is based on Poisson sampling where the sampling time may be unobserved. We show that previously described models correspond to partial likelihoods from our Poisson model and their use may be justified through arguments concerning $S$- and Bayes-ancillarity of discarded information. We demonstrate a further link to continuous-time capture-recapture models and explain observations that have been made about this class of models in terms of partial ancillarity. We illustrate application of our models using data from the European badger (\emph{Meles meles}) in which genotyping of DNA fragments was subject to error. Link:      https://anu.zo...

Bayesian hierarchical modeling and data fusion for multivariate speciated nitrogen in lakes Date: 30 October 2020, Friday Time: 10am Speaker: Dr Erin Schliep  (University of Missouri) Abstract: Concentrations of nitrogen provide a critical metric for understanding ecosystem function and water quality in lakes. However, varying approaches for quantifying nitrogen concentrations may bias the comparison of water quality across lakes and regions. Different measurements of total nitrogen exist based on its composition (e.g., organic versus inorganic, dissolved versus particulate), which we refer to as nitrogen species. Fortunately, measurements of multiple nitrogen species are often collected, and can therefore be leveraged together to inform our understanding of the controls on total nitrogen in lakes. We develop a multivariate hierarchical statistical model that fuses speciated nitrogen measurements obtained across multiple methods of reporting in order to improve our estimates of tot...

An introduction to Bayesian synthetic likelihood Date: 27 October 2020, Tuesday Time: 11am AEDT Speaker: Dr Leah South (Queensland University of Technology) Abstract: Many complex statistical models have intractable likelihoods, making standard methods for estimating the posterior distribution that use direct likelihood evaluation infeasible. In these contexts, the benefits of likelihood-free methods such as Bayesian synthetic likelihood (BSL) become apparent. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Relative to its competitor approximate Bayesian computation (ABC), BSL requires little tuning and less model simulations when the chosen summary statistic is high-dimensional. This talk will introduce the BSL method, several recent extensions and our R associated software. This is joint work with Chris Drovandi, Ziwen An, David Nott and Anthony Lee. The seminar i...

Generalized Whittle likelihood for Bayesian nonparametric spectral density estimation Date: 29 October 2020, Thursday Time: 9am AEDT / 11am NZDT  Speaker:   Prof Renate Meyer (The University of Auckland) Abstract: Most nonparametric Bayesian approaches use Whittle's likelihood to estimate the spectral density as the main nonparametric characteristic of stationary time series, as e.g. Choudhuri et al. (2004) and Rosen et al. (2012). However, the loss of efficiency of the nonparametric approach using Whittle's likelihood can be substantial. We show that the Whittle likelihood can be regarded as a special case of a nonparametrically corrected parametric likelihood which gives rise to a robust and more efficient Bayesian nonparametric spectral density estimate based on a generalized Whittle likelihood (Kirch et al. 2019). We prove that the posterior distribution based on the generalized Whittle likelihood and the nonparametric Bernstein-Dirichlet process prior is consistent for G...

Genome-Wide Association Studies and beyond Date: 22 October 2020, Thursday Time: 12pm AEDT / 9am AWST Speaker: A/Prof Nicola Armstrong  (Murdoch University) Abstract: White matter hyperintensities (WMHs) can be classified as deep (DWMH) and periventricular (PV) WMH dependent upon their anatomical location in relation to the lateral ventricle and subcortical space. This categorisation is thought to be reflected by etiological and clinical pathophysiological differences between DWMH and PVWMH. WMHs are associated with cognitive functional impairments and are strongly correlated with neurodegenerative and neuropsychiatric disorders including Alzheimer’s and vascular dementia. Heritability studies indicate significant (non-identical) heritability coefficients for DWMH and PVWMH. We recently carried out a GWAS in 24,571 participants from CHARGE, ENIGMA, and UK biobank (UKBB) for DWMH and PVWMH. Here I will give an overview of our (continuing) journey to understand the genetic underpi...

  Model-free Prediction and Regression: A Transformation-based Approach to Inference Date: Thursday  22  October 2020 Time: 11 am Speaker:  Professor  Dimitris  Politis  ( University of California at San Diego ) Abstract: Prediction has been traditionally approached via a model-based paradigm, i.e., (a) fit a model to the data at hand, and (b) use the fitted model in order to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation have freed practitioners from the limitations of parametric models, and paved the way towards the ‘big data’ era of the 21st century. Nonetheless, there is a further step one may take, namely going beyond even nonparametric models. The Model-Free Prediction Principle i...

Dynamic fibre samplers for linear inverse problems Date: 23 October 2020, Friday Time: 2pm Speaker:  Prof. Martin Hazelton  (University of Otago, New Zealand) Abstract: Statistical inverse problems occur when we wish to learn about some random process that is observed only indirectly. Inference in such situations typically involves sampling possible values for the latent variables of interest conditional on the indirect observations. This talk is concerned with linear inverse problems for count data, for which the latent variables are constrained to lie on a fibre (solution set for the linear system) comprising the integer lattice within a convex polytope (a bounded multidimensional polyhedron). An illustrative example arises in transport engineering where we observe vehicle counts entering or leaving each zone of the network, then want to sample possible interzonal patterns of traffic flow consistent with those entry/exit counts. Other areas of application include estima...

Approximate likelihood methods for stochastic differential equation models with high frequency sampling Date: 15 October 2020, Thursday Time: 10am   12pm Speaker:  Prof Andrew Wood  (ANU) Abstract: In most stochastic differential equation models the transition density is not available in closed form. This poses a serious challenge if we wish to adopt a likelihood-based approach to estimation and inference. The literature on this topic will be briefly reviewed. A two-step approach will then be described: (i) develop a small-time Ito-Taylor approximation to the sample path; and (ii) apply the so-called epsilon expansion to the Ito-Taylor approximation, leading to a closed-form approximation to the transition density, which can in turn be used to construct an approximate likelihood. My aim will be to discuss steps (i) and (ii) assuming no prior expertise. The epsilon expansion, which in a certain sense is a generalisation of the Edgeworth expansion, is due to Cox an...

Robust approaches to principal component analysis for high-dimensional and directional data Date: 16 October 2020, Friday Time: 4pm Speaker: Prof. Inge Koch  (The University of Western Australia) Abstract: Principal component analysis (PCA) is a widespread tool for selecting a smaller number of dimensions and key features in multivariate and high-dimensional data. More recently a number of variants of PCA have been developed including sparse PCA for high-dimensional data and robust PCA. In this talk we focus on PCA developments for multivariate and high-dimensional directional random vectors and data which have been transformed to live on the surface of the d-dimensional sphere. These random vectors are also know as special signs. For directional random vectors we review robust covariance-related matrices, including the sign and rank covariance matrices, and we present theoretical results of these and relate their relationships to the canonical population covariance matrix. For r...

AdaptSPEC-X: Spectral analysis of multiple nonstationary time series Date: 08 October 2020, Thursday Time: 10am Speaker:  Dr Michael Bertolacci  (University of Wollongong) Abstract: Time series that are realisations from nonstationarity processes occur frequently in data analysis, and one category of methods for dealing with this involves estimating the time varying mean and spectrum of the process. For naturally cyclical processes, such as rainfall or seasonal diseases, these techniques have the additional advantage that the spectrum is physically meaningful. We present a Bayesian method called AdaptSPEC-X for spectral estimation in the setting where multiple potentially nonstationary time series are available over a spatial field. The method takes advantage of the spatial dependencies to improve estimation of the time varying mean and spectrum, which also allows for prediction at unknown locations. We describe applications of the method to Australian rainfall data and measle...