Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this paper, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomised survey data with data from non-randomised, and therefore potentially biased, surveys; spatio-temporal extensions; spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programmes.Comment: Submitte

On The Inverse Geostatistical Problem of Inference on Missing Locations

The standard geostatistical problem is to predict the values of a spatially continuous phenomenon, $S(x)$ say, at locations $x$ using data $(y_i,x_i):i=1,..,n$ where $y_i$ is the realization at location $x_i$ of $S(x_i)$, or of a random variable $Y_i$ that is stochastically related to $S(x_i)$. In this paper we address the inverse problem of predicting the locations of observed measurements $y$. We discuss how knowledge of the sampling mechanism can and should inform a prior specification, $\pi(x)$ say, for the joint distribution of the measurement locations $X = \{x_i: i=1,...,n\}$, and propose an efficient Metropolis-Hastings algorithm for drawing samples from the resulting predictive distribution of the missing elements of $X$. An important feature in many applied settings is that this predictive distribution is multi-modal, which severely limits the usefulness of simple summary measures such as the mean or median. We present two simulated examples to demonstrate the importance of the specification for $\pi(x)$, and analyze rainfall data from Paran\'a State, Brazil to show how, under additional assumptions, an empirical of estimate of $\pi(x)$ can be used when no prior information on the sampling design is available.Comment: Under revie

Suppression of zinc dendrites in zinc electrode power cells

Addition of various tetraalkyl quarternary ammonium salts, to alkaline zincate electrolyte of cell, prevents formation of zinc dendrites during charging of zinc electrode. Electrode capacity is not impaired and elimination of dendrites prolongs cell life

INLA or MCMC? A Tutorial and Comparative Evaluation for Spatial Prediction in log-Gaussian Cox Processes

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We first describe the device of approximating a spatially continuous Gaussian field by a Gaussian Markov random field on a discrete lattice, and present a simulation study showing that, with careful choice of parameter values, small neighbourhood sizes can give excellent approximations. We then introduce the spatial log-Gaussian Cox process and describe MCMC and INLA methods for spatial prediction within this model class. We report the results of a simulation study in which we compare MALA and the technique of approximating the continuous latent field by a discrete one, followed by approximate Bayesian inference via INLA over a selection of 18 simulated scenarios. The results question the notion that the latter technique is both significantly faster and more robust than MCMC in this setting; 100,000 iterations of the MALA algorithm running in 20 minutes on a desktop PC delivered greater predictive accuracy than the default \verb=INLA= strategy, which ran in 4 minutes and gave comparative performance to the full Laplace approximation which ran in 39 minutes.Comment: This replaces the previous version of the report. The new version includes results from an additional simulation study, and corrects an error in the implementation of the INLA-based method

Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir

Julian Besag was an outstanding statistical scientist, distinguished for his pioneering work on the statistical theory and analysis of spatial processes, especially conditional lattice systems. His work has been seminal in statistical developments over the last several decades ranging from image analysis to Markov chain Monte Carlo methods. He clarified the role of auto-logistic and auto-normal models as instances of Markov random fields and paved the way for their use in diverse applications. Later work included investigations into the efficacy of nearest neighbour models to accommodate spatial dependence in the analysis of data from agricultural field trials, image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph

A Partial Likelihood for Spatio-temporal Point Processes

Spatio-temporal point process data arise in many fields of application. An intuitively natural way to specify a model for a spatio-temporal point process is through its conditional intensity at location x and time t, given the history of the process up to time t. Typically, this results in an analytically intractable likelihood. Likelihood-based inference therefore relies on Monte Carlo methods which are computationally intensive and require careful tuning to each application. We propose a partial likelihood alternative which is computationally straightforward and can be applied routinely. We apply the method to data from the 2001 foot-and-mouth epidemic in the UK, using a previously published model for the spatio-temporal spread of the disease

Clustering of equine grass sickness cases in the United Kingdom: a study considering the effect of position-dependent reporting on the space-time K-function

Equine grass sickness (EGS) is a largely fatal, pasture-associated dysautonomia. Although the aetiology of this disease is unknown, there is increasing evidence that Clostridium botulinum type C plays an important role in this condition. The disease is widespread in the United Kingdom, with the highest incidence believed to occur in Scotland. EGS also shows strong seasonal variation (most cases are reported between April and July). Data from histologically confirmed cases of EGS from England and Wales in 1999 and 2000 were collected from UK veterinary diagnostic centres. The data did not represent a complete census of cases, and the proportion of all cases reported to the centres would have varied in space and, independently, in time. We consider the variable reporting of this condition and the appropriateness of the space–time K-function when exploring the spatial-temporal properties of a ‘thinned’ point process. We conclude that such position-dependent under-reporting of EGS does not invalidate the Monte Carlo test for space–time interaction, and find strong evidence for space–time clustering of EGS cases (P<0.001). This may be attributed to contagious or other spatially and temporally localized processes such as local climate and/or pasture management practices