Problem-driven spatio-temporal analysis and implications for postgraduate statistics teaching

The paper uses two case-studies, one in public health surveillance the other in veterinary epidemiology, to argue that the analysis strategy for spatio-temporal point process data should be guided by the scientific context in which the data were generated and, more particularly, by the objectives of the data analysis. This point of view is not specific to the point process setting and, in the author’s opinion, should influence the way that statistics is taught at postgraduate level in response to the emergence and rapid growth of data science

Families of covariance functions for bivariate random fields on spheres

This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory

A spatial analysis of giardiasis and cryptosporidiosis in relation to public water supply distribution in North West England

Giardia and Cryptosporidium are both waterborne parasites and leading causes of gastroenteritis. Although specimens from diarrhoeic patients are routinely examined for Cryptosporidium, they are often not examined for Giardia so many cases go undiagnosed. Since 2002, all faecal specimens in Central Lancashire have been tested for infection with Giardia and Cryptosporidium. The aim of this paper is to gain insight into the factors contributing to giardiasis and cryptosporidiosis, including evidence of transmission via drinking water. Our analysis found a higher risk of both conditions for young children and a second peak in risk of giardiasis in adults. There was a significantly higher risk of giardiasis for males and a higher risk of cryptosporidiosis for females. The geographical location was significant, with an increased risk in the north. Residence in an area with increased supply from one water treatment works was a significant predictor for cryptosporidiosis. © 2018 Elsevier Lt

Statistical Analysis of Surface Reconstruction Domains on InAs Wetting Layer Preceding Quantum Dot Formation

Surface of an InAs wetting layer on GaAs(001) preceding InAs quantum dot (QD) formation was observed at 300°C with in situ scanning tunneling microscopy (STM). Domains of (1 × 3)/(2 × 3) and (2 × 4) surface reconstructions were located in the STM image. The density of each surface reconstruction domain was comparable to that of subsequently nucleated QD precursors. The distribution of the domains was statistically investigated in terms of spatial point patterns. It was found that the domains were distributed in an ordered pattern rather than a random pattern. It implied the possibility that QD nucleation sites are related to the surface reconstruction domains

Modelling eggshell maculation

The eggshells of many avian species are characterised by distinctive patterns of maculation, consisting of speckles, spots, blotches or streaks, the spatial-statistical properties of which vary considerably between (and often within) species. Understanding the mechanisms underlying the production of eggshell maculation would enable us to explore the costs and constraints on the evolution of maculation patterns, but as yet this area is surprisingly understudied. Here I present a simple model of eggshell maculation, which is based on the known biology of pigment deposition, and which can produce a range of realistic maculation patterns. In particular, it provides an explanation for previous observations of maculation heterogeneity and diversity, and allows testable predictions to be made regarding maculation patterns, including a possible signalling role

Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

A statistical model to describe longitudinal and correlated metabolic risk factors: the Whitehall II prospective study.

Background Novel epidemiology models are required to link correlated variables over time, especially haemoglobin A1c (HbA1c) and body mass index (BMI) for diabetes prevention policy analysis. This article develops an epidemiology model to correlate metabolic risk factor trajectories. Method BMI, fasting plasma glucose, 2-h glucose, HbA1c, systolic blood pressure, total cholesterol and high density lipoprotein (HDL) cholesterol were analysed over 16 years from 8150 participants of the Whitehall II prospective cohort study. Latent growth curve modelling was employed to simultaneously estimate trajectories for multiple metabolic risk factors allowing for variation between individuals. A simulation model compared simulated outcomes with the observed data. Results The model identified that the change in BMI was associated with changes in glycaemia, total cholesterol and systolic blood pressure. The statistical analysis quantified associations among the longitudinal risk factor trajectories. Growth in latent glycaemia was positively correlated with systolic blood pressure and negatively correlated with HDL cholesterol. The goodness-of-fit analysis indicates reasonable fit to the data. Conclusions This is the first statistical model that estimates trajectories of metabolic risk factors simultaneously for diabetes to predict joint correlated risk factor trajectories. This can inform comparisons of the effectiveness and cost-effectiveness of preventive interventions, which aim to modify metabolic risk factors