School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableBayesian likelihood-based regression for estimation of optimal dynamic treatment regimes(OXFORD UNIV PRESS, 2023-07-12)Abstract Clinicians often make sequences of treatment decisions that can be framed as dynamic treatment regimes. In this paper, we propose a Bayesian likelihood-based dynamic treatment regime model that incorporates regression specifications to yield interpretable relationships between covariates and stage-wise outcomes. We define a set of probabilistically-coherent properties for dynamic treatment regime processes and present the theoretical advantages that are consequential to these properties. We justify the likelihood-based approach by showing that it guarantees these probabilistically-coherent properties, whereas existing methods lead to process spaces that typically violate these properties and lead to modelling assumptions that are infeasible. Through a numerical study, we show that our proposed method can achieve superior performance over existing state-of-the-art methods.
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ItemNo Preview AvailableNonstationary Gaussian Process Discriminant Analysis With Variable Selection for High-Dimensional Functional Data(TAYLOR & FRANCIS INC, 2023-04-03)
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ItemNo Preview AvailableUncertainty Quantification in Depth Estimation via Constrained Ordinal Regression(SPRINGER INTERNATIONAL PUBLISHING AG, 2022)
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ItemA representation learning framework for detection and characterization of dead versus strain localization zones from pre-to post-failure(SPRINGER, 2022-08)Abstract Experiments have long shown that zones of near vanishing deformation, so-called “dead zones”, emerge and coexist with strain localization zones inside deforming granular media. To date, a method that can disentangle these dynamically coupled structures from each other, from pre- to post- failure, is lacking. Here we develop a framework that learns a new representation of the kinematic data, based on the complexity of a grain’s neighborhood structure in the kinematic-state-space, as measured by a recently introduced metric calleds-LID. Dead zones (DZ) are first distinguished from strain localization zones (SZ) throughout loading history. Next the coupled dynamics of DZ and SZ are characterized using a range of discriminative features representing: local nonaffine deformation, contact topology and force transmission properties. Data came from discrete element simulations of biaxial compression tests. The deformation is found to be essentially dual in nature. DZ and SZ exhibit distinct yet coupled dynamics, with the separation in dynamics increasing in the lead up to failure. Force congestion and plastic deformation mainly concentrate in SZ. Although the 3-core of the contact network is highly prone to damage in SZ, it is robust to pre-failure microbands but is decimated in the shearband, leaving a fragmented 3-core in DZ at failure. We also show how loading condition and rolling resistance influence SZ and DZ differently, thus casting new light on controls on plasticity from the perspective of emergent deformation structures. Graphic abstract
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ItemA Bayesian mixture model for clustering and selection of feature occurrence rates under mean constraints(WILEY, 2017-12)In this paper, we consider the problem of modeling a matrix of count data, where multiple features are observed as counts over a number of samples. Due to the nature of the data generating mechanism, such data are often characterized by a high number of zeros and overdispersion. In order to take into account the skewness and heterogeneity of the data, some type of normalization and regularization is necessary for conducting inference on the occurrences of features across samples. We propose a zero‐inflated Poisson mixture modeling framework that incorporates a model‐based normalization through prior distributions with mean constraints, as well as a feature selection mechanism, which allows us to identify a parsimonious set of discriminatory features, and simultaneously cluster the samples into homogenous groups. We show how our approach improves on the accuracy of the clustering with respect to more standard approaches for the analysis of count data, by means of a simulation study and an application to a bag‐of‐words benchmark data set, where the features are represented by the frequencies of occurrence of each word.
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ItemSpatial Regression with Covariate Measurement Error: A Semiparametric Approach(WILEY, 2016-09)Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.
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ItemOptimal allocation of PCR tests to minimise disease transmission through contact tracing and quarantine(ELSEVIER, 2021-12)PCR testing is a crucial capability for managing disease outbreaks, but it is also a limited resource and must be used carefully to ensure the information gain from testing is valuable. Testing has two broad uses for informing public health policy, namely to track epidemic dynamics and to reduce transmission by identifying and managing cases. In this work we develop a modelling framework to examine the effects of test allocation in an epidemic, with a focus on using testing to minimise transmission. Using the COVID-19 pandemic as an example, we examine how the number of tests conducted per day relates to reduction in disease transmission, in the context of logistical constraints on the testing system. We show that if daily testing is above the routine capacity of a testing system, which can cause delays, then those delays can undermine efforts to reduce transmission through contact tracing and quarantine. This work highlights that the two goals of aiming to reduce transmission and aiming to identify all cases are different, and it is possible that focusing on one may undermine achieving the other. To develop an effective strategy, the goals must be clear and performance metrics must match the goals of the testing strategy. If metrics do not match the objectives of the strategy, then those metrics may incentivise actions that undermine achieving the objectives.
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ItemBayesian variable selection for logistic regression(WILEY, 2019-10)Abstract A key issue when using Bayesian variable selection for logistic regression is choosing an appropriate prior distribution. This can be particularly difficult for high‐dimensional data where complete separation will naturally occur in the high‐dimensional space. We propose the use of the Normal‐Gamma prior with recommendations on calibration of the hyper‐parameters. We couple this choice with the use of joint credible sets to avoid performing a search over the high‐dimensional model space. The approach is shown to outperform other methods in high‐dimensional settings, especially with highly correlated data. The Bayesian approach allows for a natural specification of the hyper‐parameters.
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