16,164 research outputs found
CARBayes: an R package for Bayesian spatial modeling with conditional autoregressive priors
Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping
Using prior information to identify boundaries in disease risk maps
Disease maps display the spatial pattern in disease risk, so that high-risk
clusters can be identified. The spatial structure in the risk map is typically
represented by a set of random effects, which are modelled with a conditional
autoregressive (CAR) prior. Such priors include a global spatial smoothing
parameter, whereas real risk surfaces are likely to include areas of smooth
evolution as well as discontinuities, the latter of which are known as risk
boundaries. Therefore, this paper proposes an extension to the class of CAR
priors, which can identify both areas of localised spatial smoothness and risk
boundaries. However, allowing for this localised smoothing requires large
numbers of correlation parameters to be estimated, which are unlikely to be
well identified from the data. To address this problem we propose eliciting an
informative prior about the locations of such boundaries, which can be combined
with the information from the data to provide more precise posterior inference.
We test our approach by simulation, before applying it to a study of the risk
of emergency admission to hospital in Greater Glasgow, Scotland
Boundary detection in disease mapping studies
In disease mapping, the aim is to estimate the spatial pattern in disease
risk over an extended geographical region, so that areas with elevated risks
can be identified. A Bayesian hierarchical approach is typically used to
produce such maps, which models the risk surface with a set of spatially smooth
random effects. However, in complex urban settings there are likely to be
boundaries in the risk surface, which separate populations that are
geographically adjacent but have very different risk profiles. Therefore this
paper proposes an approach for detecting such risk boundaries, and tests its
effectiveness by simulation. Finally, the model is applied to lung cancer
incidence data in Greater Glasgow, Scotland, between 2001 and 2005
Cluster detection and risk estimation for spatio-temporal health data
In epidemiological disease mapping one aims to estimate the spatio-temporal
pattern in disease risk and identify high-risk clusters, allowing health
interventions to be appropriately targeted. Bayesian spatio-temporal models are
used to estimate smoothed risk surfaces, but this is contrary to the aim of
identifying groups of areal units that exhibit elevated risks compared with
their neighbours. Therefore, in this paper we propose a new Bayesian
hierarchical modelling approach for simultaneously estimating disease risk and
identifying high-risk clusters in space and time. Inference for this model is
based on Markov chain Monte Carlo simulation, using the freely available R
package CARBayesST that has been developed in conjunction with this paper. Our
methodology is motivated by two case studies, the first of which assesses if
there is a relationship between Public health Districts and colon cancer
clusters in Georgia, while the second looks at the impact of the smoking ban in
public places in England on cardiovascular disease clusters
Identifying Clusters in Bayesian Disease Mapping
Disease mapping is the field of spatial epidemiology interested in estimating
the spatial pattern in disease risk across areal units. One aim is to
identify units exhibiting elevated disease risks, so that public health
interventions can be made. Bayesian hierarchical models with a spatially smooth
conditional autoregressive prior are used for this purpose, but they cannot
identify the spatial extent of high-risk clusters. Therefore we propose a two
stage solution to this problem, with the first stage being a spatially adjusted
hierarchical agglomerative clustering algorithm. This algorithm is applied to
data prior to the study period, and produces potential cluster structures
for the disease data. The second stage fits a separate Poisson log-linear model
to the study data for each cluster structure, which allows for step-changes in
risk where two clusters meet. The most appropriate cluster structure is chosen
by model comparison techniques, specifically by minimising the Deviance
Information Criterion. The efficacy of the methodology is established by a
simulation study, and is illustrated by a study of respiratory disease risk in
Glasgow, Scotland
An integrated Bayesian model for estimating the long-term health effects of air pollution by fusing modelled and measured pollution data: a case study of nitrogen dioxide concentrations in Scotland
The long-term health effects of air pollution can be estimated using a spatio-temporal ecological study, where the disease data are counts of hospital admissions from populations in small areal units at yearly intervals. Spatially representative pollution concentrations for each areal unit are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over grid level concentrations from an atmospheric dispersion model. We propose a novel fusion model for estimating spatially aggregated pollution concentrations using both the modelled and monitored data, and relate these concentrations to respiratory disease in a new study in Scotland between 2007 and 2011
A New Method for Estimating Dark Matter Halo Masses using Globular Cluster Systems
All galaxies are thought to reside within large halos of dark matter, whose
properties can only be determined from indirect observations. The formation and
assembly of galaxies is determined from the interplay between these dark matter
halos and the baryonic matter they host. Although statistical relations can be
used to approximate how massive a galaxy's halo is, very few individual
galaxies have direct measurements of their halo masses. We present a method to
directly estimate the total mass of a galaxy's dark halo using its system of
globular clusters. The link between globular cluster systems and halo masses is
independent of a galaxy's type and environment, in contrast to the relationship
between galaxy halo and stellar masses. This trend is expected in models where
globular clusters form in early, rare density peaks in the cold dark matter
density field and the epoch of reionisation was roughly coeval throughout the
Universe. We illustrate the general utility of this relation by demonstrating
that a galaxy's supermassive black hole mass and global X-ray luminosity are
directly proportional to their host dark halo masses, as inferred from our new
method.Comment: 6 pages, 4 colour figures. Accepted by MNRAS Letters. Data catalogue
available from the first autho
Bayesian cluster detection via adjacency modelling
Disease mapping aims to estimate the spatial pattern in disease risk across an area, identifying units which have elevated disease risk. Existing methods use Bayesian hierarchical models with spatially smooth conditional autoregressive priors to estimate risk, but these methods are unable to identify the geographical extent of spatially contiguous high-risk clusters of areal units. Our proposed solution to this problem is a two-stage approach, which produces a set of potential cluster structures for the data and then chooses the optimal structure via a Bayesian hierarchical model. The first stage uses a spatially adjusted hierarchical agglomerative clustering algorithm. The second stage fits a Poisson log-linear model to the data to estimate the optimal cluster structure and the spatial pattern in disease risk. The methodology was applied to a study of chronic obstructive pulmonary disease (COPD) in local authorities in England, where a number of high risk clusters were identified
Spatial clustering of average risks and risk trends in Bayesian disease mapping
Spatiotemporal disease mapping focuses on estimating the spatial pattern in disease risk across a set of nonoverlapping areal units over a fixed period of time. The key aim of such research is to identify areas that have a high average level of disease risk or where disease risk is increasing over time, thus allowing public health interventions to be focused on these areas. Such aims are well suited to the statistical approach of clustering, and while much research has been done in this area in a purely spatial setting, only a handful of approaches have focused on spatiotemporal clustering of disease risk. Therefore, this paper outlines a new modeling approach for clustering spatiotemporal disease risk data, by clustering areas based on both their mean risk levels and the behavior of their temporal trends. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland
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