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

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

RFID Smart Shelves

Nella presente tesi verrà trattato il tema della localizzazione in ambienti indoor mediante la tecnologia RFID (Radio Frequency IDentification): i primi sistemi RFID furono caratterizzati da semplici funzioni di identificazione a distanza di oggetti, persone o animali, mediante comunicazioni a radio frequenza tra le etichette elettroniche, o Tag, ad essi applicate ed un Reader. In tempi recenti sono entrati in via di sviluppo sistemi che utilizzano questa tecnologia non solamente per rilevare la presenza di un oggetto all’interno di un certo volume, ma anche per localizzare tale oggetto mediante stima delle coordinate del Tag ad esso applicato. Questo lavoro è rivolto alle cosiddette “Smart Shelves”, ovvero la realizzazione di scaffali per libri e vestiario, cassetti per medicinali, credenze o ripiani di frigorifero etc. che siano in grado di localizzare i Tag applicati agli oggetti al loro interno mediante comunicazione con antenne Reader; in particolare ci soffermeremo dettagliatamente sulla progettazione di un cassetto intelligente, ad esempio per medicinali, con lo scopo di introdurre delle linee guida di progetto da poter utilizzare nella localizzazione di Tag in questo particolare scenario. Sarà adottata la tecnologia RFID alle frequenze UHF (860MHz), unitamente all’impiego di Tag passivi e si analizzeranno quegli algoritmi che, partendo dalla disponibilità dell’informazione RSSI (Received Signal Strength Indication), permettano la localizzazione di Tag su una superficie bidimensionale

Geostatistical methods for disease prevalence mapping

Geostatistical methods are increasingly used in low-resource settings where disease registries are either non-existent or geographically incomplete. In this thesis, which is comprised of four papers, we address some of the common issues that arise from analysing disease prevalence data. In the first paper we consider the problem of combining data from multiple spatially referenced surveys so as to account for two main sources of variation: temporal variation, when surveys are repeated over time; data-quality variation, e.g. between randomised and non-randomised surveys. We then propose a multivariate binomial geostatistical model for the combined analysis of data from multiple surveys. We also show an application to malaria prevalence data from three surveys conducted in two consecutive years in Chikwawa District, Malawi, one of which used a more economical convenience sampling strategy. In the second paper, we analyse river-blindness prevalence data from a survey conducted in 20 African countries enrolled in the African Programme of Onchocerciasis Control (APOC). The main challenge of this analysis is computational, as a binomial geostatistical model has to be fitted to more than 14,000 village locations and predictions carried out on about 10 millions locations across Africa. To make the computation feasible and efficient, we then develop a low rank approximation based on a convolution-kernel representation which avoids matrix inversion. The third paper is a tutorial on the use of a new R package, namely “PrevMap”, which provides functions for both likelihood-based and Bayesian analysis of spatially referenced prevalence data. In the fourth paper, we present some extensions of the standard geostatistical model for spatio-temporal analysis of prevalence data and modelling of spatially structured zero-inflation. We then describe three applications that have arisen through our collaborations with researchers and public health programmers in African countries

On the goodness-of-fit of generalized linear geostatistical models

We propose a generalization of Zhang’s coefficient of determination to generalized linear geostatistical models and illustrate its application to river-blindness mapping. The generalized coefficient of determination has a more intuitive interpretation than other measures of predictive performance and allows to assess the individual contribution of each explanatory variable and the random effects to spatial prediction. The developed methodology is also more widely applicable to any generalized linear mixed model

Basic urban services fail to neutralise environmental determinants of ‘rattiness’, a composite metric of rat abundance

Globally, low-income urban communities suffer from poor provision of services and degraded environments, favouring opportunistic zoonotic reservoirs, such as rats. Large-scale infrastructural improvements in these contexts are limited, but targeted control of disease reservoirs has sometimes been achieved. A starting point for the targeted control of rats is assessing the impact of existing basic services on rat abundance. However, there is no gold-standard metric for rat abundance, and studies have used different or multiple metrics. Here, therefore, in four low-income urban Brazilian communities, we address the question of whether basic urban services (BUS) – trash collection, rodenticide application and health community agent visits – affect rat abundance, through the first application of the rattiness modelling framework. This recently-developed geostatistical method combines multiple abundance metrics (here, three) to generate rattiness, a proxy for rat abundance, a spatially-continuous latent process common to all metrics. In a cross-sectional study, we exploited spatial heterogeneities in BUS to evaluate its association with the presence of rat signs, rat marks on track plates, and live-trapped rats, and with rattiness, which combined these three imperfect metrics. Rattiness proved to be a useful tool for pooling information among the three metrics and was associated with a greater range of baseline predictors than any single metric. Rat signs and rattiness were positively associated with higher levels of BUS provision and environmental variables known to provide resources for rats. The strong association of baseline environmental variables with rat abundance highlights the need for targeted, small-scale environmental modifications to reduce resources for rats