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Tilman M. Davies
University of Otago
32Publications
9H-index
358Citations
Publications 32
Newest
#1Richard Elson (UEA: University of East Anglia)
#2Tilman M. Davies (University of Otago)H-Index: 9
Last.Iain R. Lake (UEA: University of East Anglia)H-Index: 33
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Abstract Identifying geographical areas with significantly higher or lower rates of infectious diseases can provide important aetiological clues to inform the development of public health policy and interventions designed to reduce morbidity. We applied kernel smoothing to estimate the spatial and spatio-temporal variation in risk of STEC O157 infection in England between 2009 and 2015, and to explore differences between the residential locations of cases reporting travel and those not reporting...
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#1Suman Rakshit (Curtin University)H-Index: 3
#2Tilman M. Davies (University of Otago)H-Index: 9
Last.Adrian Baddeley (Curtin University)H-Index: 35
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4 CitationsSource
#1Tilman M. Davies (University of Otago)H-Index: 9
#2Andrew B. Lawson (MUSC: Medical University of South Carolina)H-Index: 35
ABSTRACTSpatial point pattern data sets are commonplace in a variety of different research disciplines. The use of kernel methods to smooth such data is a flexible way to explore spatial trends and make inference about underlying processes without, or perhaps prior to, the design and fitting of more intricate semiparametric or parametric models to quantify specific effects. The long-standing issue of ‘optimal’ data-driven bandwidth selection is complicated in these settings by issues such as hig...
3 CitationsSource
#1Tilman M. Davies (University of Otago)H-Index: 9
#2Claire R. Flynn (Wellington Management Company)H-Index: 1
Last.Martin L. Hazelton (Massey University)H-Index: 26
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Abstract Implementation of the spatially adaptive kernel estimator relies on choice of a ‘global bandwidth’. We derive the closed-form asymptotic bias for this estimator with the aim of developing relevant selectors, and note non-uniform convergence hinders its usability for this purpose.
4 CitationsSource
#1Tilman M. Davies (University of Otago)H-Index: 9
#2Adrian Baddeley (Curtin University)H-Index: 35
Kernel smoothing of spatial point data can often be improved using an adaptive, spatially varying bandwidth instead of a fixed bandwidth. However, computation with a varying bandwidth is much more demanding, especially when edge correction and bandwidth selection are involved. This paper proposes several new computational methods for adaptive kernel estimation from spatial point pattern data. A key idea is that a variable-bandwidth kernel estimator for d-dimensional spatial data can be represent...
6 CitationsSource
#1Tilman M. Davies (University of Otago)H-Index: 9
#2Jonathan C. Marshall (Massey University)H-Index: 14
Last.Martin L. Hazelton (Massey University)H-Index: 26
view all 3 authors...
9 CitationsSource
#1Tilman M. DaviesH-Index: 9
Last.Martin L. HazeltonH-Index: 26
view all 3 authors...
Kernel smoothing is a highly flexible and popular approach for estimation of probability density and intensity functions of continuous spatial data. In this role it also forms an integral part of estimation of functionals such as the density-ratio or "relative risk" surface. Originally developed with the epidemiological motivation of examining fluctuations in disease risk based on samples of cases and controls collected over a given geographical region, such functions have also been successfully...
#1Tilman M. Davies (University of Otago)H-Index: 9
#2Philip W. Sheard (University of Otago)H-Index: 17
Last.Jon Cornwall (Victoria University of Wellington)H-Index: 11
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#1Tilman M. Davies (University of Otago)H-Index: 9
#2Khair Jones (Massey University)H-Index: 1
Last.Martin L. Hazelton (Massey University)H-Index: 26
view all 3 authors...
The spatial relative risk function is now regarded as a standard tool for visualising spatially tagged case-control data. This function is usually estimated using the ratio of kernel density estimates. In many applications, spatially adaptive bandwidths are essential to handle the extensive inhomogeneity in the distribution of the data. Earlier methods have employed separate, asymmetrical smoothing regimens for case and control density estimates. However, we show that this can lead to potentiall...
11 CitationsSource
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