Data used to estimate the burden of diseases (BOD) are usually sparse, noisy, and heterogeneous. These data are collected from surveys, registries, and systematic reviews that have different areal units, are conducted at different times, and are reported for different age groups. In this study, we developed a Bayesian geo‐statistical model to combine aggregated sparse, noisy BOD data from different sources with misaligned areal units. Our model incorporates the correlation of space, time, and age to estimate health indicators for areas with no data or a small number of observations. The model also considers the heterogeneity of data sources and the measurement errors of input data in the final estimates and uncertainty intervals. We appli

This paper develops a Bayesian nonparametric model for skewed spatial data with nonstationary dependence structure. A transformed Gaussian model is proposed for the atoms of the kernel stick-breaking process by transforming the margins of a Gaussian process to flexible marginal distributions. This study proves that the correlation structure of the underlying spatial process is nonstationary. Results from both simulated and real datasets demonstrate that the proposed model possesses better spatial prediction performance and offers computational advantages compared to the Bayesian nonparametric model with the Gaussian base measure.

This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a separate scalar parameter. Explicit expressions for the cumulative distribution function, the density function and the moments were derived. The stochastic representation of the distribution facilitates implementing Bayesian estimation via the Markov chain Monte Carlo methods. Some real-life data as well as simulated data are analyzed to illustrate the flexibility of the distribution for modeling asymmetric bimodality.

In some statistical issues, several continuous spatial outcomes are simultaneously measured at each sampling location. In such circumstances, it is common to model the data through a multivariate Gaussian model. As the normality assumption is often untenable, this paper proposes a multivariate skewed spatial model which, by virtue of its capacity for capturing skewness, is potentially more flexible than symmetric ones. Specifically, a multivariate version of the Gaussian-log Gaussian convolution process is developed. The resulting covariance for the multivariate process is in general nonseparable. We also discuss the other properties of the induced covariance function. Furthermore, Markov chain Monte Carlo methods are used to m

This paper develops a new class of spatio-temporal process models that can simultaneously capture skewness and non-stationarity. The proposed approach which is based on using the closed skew-normal distribution in the low-rank representation of stochastic processes, has several favorable properties. In particular, it greatly reduces the dimension of the spatio-temporal latent variables and induces flexible correlation structures. Bayesian analysis of the model is implemented through a Gibbs MCMC algorithm which incorporates a version of the Kalman filtering algorithm. All fully conditional posterior distributions have closed forms which show another advantageous property of the proposed model. We demonstrate the efficiency of our model thro

In spatial statistics, it is usual to consider a Gaussian process for spatial latent variables. As the data often exhibit non-normality, we introduce a novel skew process, named hereafter Gaussian-log Gaussian convolution (GLGC) to construct latent spatial models which provide great flexibility in capturing skewness. Some properties including closed-form expressions for the moments and the skewness of the GLGC process are derived. Particularly, we show that the mean square continuity and differentiability of the GLGC process are established by those of the Gaussian and log-Gaussian processes considered in its structure. Moreover, the usefulness of the proposed approach is demonstrated through the analysis of spatial data, including mixed or

In the present research, the effects of surface rock fragments and soil clay content on surface runoff and soil loss was investigated under the laboratory conditions. The aim of the test was to increase the general understanding of how soil clay content and surface rock fragments affect the soil erosion process. A rainfall simulator was added to an erosion plot and these apparatuses were used to investigate the effects of varying soil clay content (SCC) and soil rock fragments (SRF) on soil erosion by measuring runoff volume and sediment yield at regular time intervals during the simulation. The results indicated that the main effects of soil clay content and surface rock fragments were all significant at the 0.95 level (p<0.05) for the run

In spatial generalized linear mixed models (SGLMMs), statistical inference encounters problems, since random effects in the model imply high-dimensional integrals to calculate the marginal likelihood function. In this article, we temporarily treat parameters as random variables and express the marginal likelihood function as a posterior expectation. Hence, the marginal likelihood function is approximated using the obtained samples from the posterior density of the latent variables and parameters given the data. However, in this setting, misspecification of prior distribution of correlation function parameter and problems associated with convergence of Markov chain Monte Carlo (MCMC) methods could have an unpleasant influence on the likeliho

This paper introduces a multivariate skew Gaussian process and uses it to extend the family of multivariate spatial generalized linear mixed models to include skew Gaussian random effects. In this setting, the param-eter estimation encounters problems because the likelihood function involves high dimensional integrations which are computationally intensive. For estimating parameters of the complicated model structure, this article proposes an algorithm which is a combination of boosting with a variant of stochastic approximation. This algorithm which known as stochastic approximation boosting (SAB) algorithm, uses the Markov chain Monte Carlo method based on slice sampling to obtain simulations from full conditional distribution of random e

In spatial statistics, models are often constructed based on some common, but possible restrictive assumptions for the underlying spatial process, including Gaussianity as well as stationarity and isotropy. However, these assumptions are frequently violated in applied problems. In order to simultaneously handle skewness and non-homogeneity (i.e., non-stationarity and anisotropy), we develop the fixed rank kriging model through the use of skew-normal distribution for its non-spatial latent variables. Our approach to spatial modeling is easy to implement and also provides a great flexibility in adjusting to skewed and large datasets with heterogeneous correlation structures. We adopt a Bayesian framework for our analysis, and d

Most of the existing Bayesian nonparametric models for spatial areal data assume that the neighborhood structures are known, however in practice this assumption may not hold. In this paper, we develop an area-specific stick breaking process for distributions of random effects with the spatially-dependent weights arising from the block averaging of underlying continuous surfaces. We show that this prior, which does not depend on specifying neighboring schemes, is noticeably flexible in effectively capturing heterogeneity in spatial dependency across areas. We illustrate the methodology with a dataset involving expenditure credit of 31 provinces of Iran.

This paper proposes a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a decomposable graph so that the pattern of zero off-diagonal elements in the precision matrix corresponds to the missing edges of the given graph. We present conditions that guarantee the propriety of the posterior distributions under the standard noninformative priors for mean vector and precision matrix, and a proper prior for skewness parameter. The identifiability of the parameters is investigated by a simulation study. Finally, we apply our methodology to two data sets.