Statistics Across Campuses

A gentle introduction to string-count distributions in random texts  Date: Thursday 25 February 2021 Time: 10am Speaker: Dr Ben O'Neill (ANU) Abstract: An interesting problem that arises in genetic analysis and other contexts is determining the exact or approximate probability distribution of the “string-count” giving the number of occurrences of a fixed character string in a random “text” (i.e., a random vector of symbols). The simplest case of interest is when the symbols in the text are IID categorical random variables. The prima facie simplicity of this problem sometimes attracts the attention of novice analysts, buoyed by the fact that it is easy to compute the probability of a match in the simple case where the length of the text is the same as the length of the string. (And of course, if the text is shorter than the string then the problem is trivial!) However, when the length of the text is larger than the length of the string, the problem becomes complicated, owing to ...

My experience of Bayesian Inference and Deep Learning Date: 26 February 2021, Friday Time: 4pm AEDT Speaker: A/Prof. Richard Xu (University of Technology Sydney) Abstract:  In a research environment where deep learning methods dominate, Bayesian framework still plays a vital role. In this talk, I will first illustrate Bayesian inference through a small tutorial. Then I will describe some of the latest research results (including some of my own works), in which Bayesian inference has been used to explain and assist (and assisted by) deep learning. Finally, I will give some thoughts on the future of Bayesian inference. Bio: Richard Yi Da Xu is an Associate Professor at the University of Technology, Sydney (UTS). He leads a team of 25 people, includes postdoc, PhD students, and data engineers; His primary research is in machine learning and artificial intelligence. Richard published at many top international conferences, including AAAI, IJCAI, ECAI, ECCV, AI-STATS and ICDM as well as...

Dealing with detection error in site occupancy and abundance surveys: what can we do with a single survey? Date: 04 December 2020, Friday Time: 10am AEDT  Speaker: Prof Subbash Lele  (University of Alberta) Abstract: Site occupancy probabilities and abundance of target species are commonly used in various ecological studies. Detection error introduces bias in the estimators of site occupancy. Existing methods for estimating occupancy probability in the presence of detection error use replicate surveys. These methods assume either population closure, i.e. the site occupancy status remains constant across surveys or a structured dependence across surveys. The practical difficulties with replicate surveys are well known. Statistically, the closure assumption is seldom satisfied and the dependence structure can be difficult to model. The cost of replicate surveys can be prohibitive and they may be logistically prohibitive.  Given these practical difficulties, we ask the ...

Computing Bayes: Bayesian Computation from 1763 to the 21st Century Date: 19 November 2020, Thursday Time: 10.30am AEDT Contact the organizer: Andriy Olenko a.olenko@latrobe.edu.au Speaker: Prof Gael M. Martin (Monash University) Abstract: The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian inference, with the rules of probability used to transform prior probability distributions for all unknowns - models, parameters, latent variables - into posterior distributions, subsequent to the observation of data. Conducting Bayesian inference requires the evaluation of integrals in which these probability distributions appear. Bayesian computation is all about evaluating such integrals in the typical case where no analytical solution exists. This paper takes the reader on a chronological tour of Bayesian computation over the past two and a half centuries. B...

Change-set analysis for spatial clustering in environmental health Date: 20 November 2020, Friday Time: 10am AEDT  Speaker: Prof Jun Zhu  (University of Wisconsin-Madison) Abstract: Mapping of disease incidence is of importance to environmental health. In this talk, we consider identification of clusters of spatial units with elevated disease rates and develop a new approach that estimates the relative disease risk in association with potential environmental risk factors and simultaneously identifies clusters corresponding to elevated risks. A heterogeneity measure is proposed to enable the comparison of a candidate cluster and its complement under a pair of complementary models. A quasi-likelihood procedure is developed for estimating the model parameters and identifying the clusters. An advantage of our approach over traditional spatial clustering methods is the identification of clusters that can have arbitrary shapes due to abrupt or non-contiguous changes while accounting...

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...