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Bayesian Disease Mapping Models
Published in Andrew B. Lawson, Using R for Bayesian Spatial and Spatio-Temporal Health Modeling, 2021
An alternative specification involves only one random effect for both CH and UH. This can be achieved by specifying a prior distribution having two parameters governing these effects. For example, the covariance matrix of an MVN prior distribution can be parametrically modelled with such terms (Diggle et al., 1998; Wikle, 2002). This approach is akin to universal Kriging (Wackernagel, 2003; Cressie, 1993), which employs covariance models including variance and covariance range parameters. It has been dubbed “generalized linear spatial modeling.” A software library is available in R (geoRglm). Usually, these parameters define a multiplicative relation between CH and UH. For the full Bayesian analysis of this model, use is often made of posterior sampling algorithms.
Spatial Models
Published in Virgilio Gómez-Rubio, Bayesian Inference with INLA, 2020
As a preliminary analysis of this dataset, kriging will be used to obtain an estimation of the concentration of zinc in the study region. In particular, universal kriging (Cressie, 2015; Bivand et al., 2013) will be used in order to include covariates in the prediction.
Extreme Events, Population, and Risk: An Integrated Modeling Approach
Published in Vyacheslav Lyubchich, Yulia R. Gel, K. Halimeda Kilbourne, Thomas J. Miller, Nathaniel K. Newlands, Adam B. Smith, Evaluating Climate Change Impacts, 2020
Lelys Bravo de Guenni, Desireé Villalta, Andrés Sajo-Castelli
In this framework, the hazard model component was treated as a spatiotemporal prediction problem from rainfall point measurements y(s1), y(s2), …, y(sg) observed in locations s1, s2, …, sg. These measurements are considered realizations from a set of random variables Y(s1), Y(s2), …, Y(sg). We wish to estimate a spatial random field Y(s) in a new set of ungauged locations This problem is traditionally known as kriging or spatial prediction. Following Le and Zidek (2006), the spatiotemporal prediction problem can be written as follows. Assume Yt a p-dimensional vector of the random field at time t. Assume data at the first u coordinates are not available, while the next g observations are known. Vector Yt can be partitioned as where corresponds to the u ungauged locations while, corresponds to the gauged g locations. We can assume that random variables {Yt} are time independent, and the data vector follows a Gaussian distribution of the form where Np(ztB, Σ) denotes a normal p-variate distribution with mean μ = ztB and variance-covariance matrix Σ; is a k-dimensional row vector of covariates, and B is a k × p dimension matrix of regression coefficients, with p = u + g. Matrix B can be written as The partitions of matrix B and vector Yt are in agreement in the sense that covariates can change with time, but should be constant for all locations. On the other hand, regression coefficients β's can vary for the different locations.
Impact of missing data on the prediction of random fields
Published in Journal of Applied Statistics, 2020
Abdelghani Hamaz, Ouerdia Arezki, Farida Achemine
Assuming that X is only observed at a finite number of points D. The basic idea of Kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. Kriging belongs to the family of linear least squares estimation methods, and estimates values at unobserved location as a weighted average of the neighboring observed values. The determination of unknown weights requires specification of a parametric model for the covariance structure with few parameters. In practice, the model for the covariance is selected from a list of available models and then its parameters are estimated from the observed data 9] and might suffer from the problem of model misspecification. Some work has been done by using the nonparametric methods of estimating a multivariate covariance function, cf. [10,13]. Another drawback of this method is that the assumption of similar dependence structure at all the points may not hold true when the data is highly irregular. Hence, developing a prediction method which makes minimal assumptions on the covariance structure and its data driven is a major challenge for prediction on random fields.
Measurement and mapping of the electromagnetic radiation in the urban environment
Published in Electromagnetic Biology and Medicine, 2020
Jin Liu, Minhong Wei, Huafang Li, Xin Wang, Xiaoyu Wang, Song Shi
Since measurement results can hardly be sufficient to cover every corner of the region, spatial interpolation is applied to predict the value of a random field at an unobserved location from observations of its value at nearby locations. Kriging interpolation is a kind of interpolation method based on geostatistics. Kriging method is the best geostatistical linear-unbiased estimator that yields a zero mean residual error and minimizes the error variance. We interpolate the electric field levels at non-sampled points using the ordinary kriging method. We can estimate the value of an unknown point
Geostatistical analysis of disease data: a case study of tuberculosis incidence in Iran
Published in Journal of Applied Statistics, 2018
S. Reza H. Shojaei, Yadollah Waghei, Mohsen Mohammadzadeh
In the past decades several methods are developed to predict the value of a variable based on the observations in a new location, such as inverse distance weighted, spatial regression, kriging and Poisson kriging. The kriging method is a statistical technique that includes the spatial correlation structure in data analysis. The Ordinary Kriging (OK) is also provided before Poisson Kriging (PK) method for spatial prediction widely used in different fields like meteorology and geology. This article describes how to estimate the disease incidence rates using two methods for annually SPTB data collected from all counties of Iran. Several studies have focused on TB epidemiology in different parts of Iran (see, e.g. [4,15]). We compare the accuracy of the two methods and also examine the spatial patterns using provided maps.