Wednesday 19 February 2020, 1:30pm to 2:30pm
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Open toPostgraduates, Staff
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Short 15 minute talks from Emma Simpson, Aaron Lowther, and Tom Burnett
Conditional modelling of spatio-temporal extremes for Red Sea surface temperatures
Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration of spatio-temporal extensions. This neglects an important feature of extreme events: their evolution over time. Many existing models for the spatial case are limited by the number of locations they can handle; this impedes extension to space-time settings, where models for higher dimensions are required. Moreover, the spatio-temporal models that do exist are restrictive in terms of the range of extremal dependence types they can capture. Recently, conditional approaches for studying multivariate and spatial extremes have been proposed, which enjoy benefits in terms of computational efficiency and an ability to capture both asymptotic dependence and asymptotic independence. We extend this class of models to a spatio-temporal setting, conditioning on the occurrence of an extreme value at a single space-time location. We apply our model to Red Sea surface temperatures, demonstrating how it can be used to assess the risk of coral bleaching attributed to high water temperatures over consecutive days.
Adding treatment arms to a trial in progress.
Multi-Arm Multi-Stage (MAMS) trials are an efficient tool for the comparison of several treatments with a control. Suppose a new treatment becomes available at some stage of a trial already in progress. There are clear benefits to adding the treatment to the current trial for comparison, but how do we do this?As flexible as the MAMS framework is, it requires pre-planned options for how the trial proceeds at each stage in order to control the familywise error rate. Thus, as with many adaptive designs, we may not make unplanned design modifications. The conditional error approach allows unplanned design modifications while maintaining the error rate. We extend this to allow the incorporation of new treatments into the trial in progress. Using a single stage two-arm trial, we demonstrate the principals of incorporating additional hypotheses into the testing structure. With this framework for adding treatments and hypotheses in place, we show how to update the testing procedure for a MAMS trial in progress to incorporate additional treatment arms. Through simulation, we illustrate the operating characteristics of such procedures.
An overview of my research and interests
In this short talk I will give a brief summary of the methodology that we developed in my thesis and discuss my research interests. The work in my thesis focused on selecting predictors for multiple response variables simultaneously. We were motivated by an industrial application which meant that interpretable modelswere highly desirable. Using a generalisation of the best-subset selection procedure, we were able to select predictors simultaneously and fit sparse, interpretable models. We implement the generalised best subset procedure by solving a sequence of mixed integer quadratic optimisation programs. Our method was applied to time series data using an iterative two-step approach, first estimating the regression coefficients and then the temporal correlation in the regression residuals.
More detailed information can be found on arXiv: https://arxiv.org/abs/2001.02883
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