Bayesian spatial models with repeated measurements: with application to the herbaceous data analysis

This paper proposes a new statistical spatial model to analyze and predict the coverage percentage of the upland ground flora in the Missouri Ozark Forest Ecosystem Project (MOFEP). The flora coverage percentages are collected from clustered locations, which requires a new spatial model other than the traditional kriging method. The proposed model handles this special data structure by treating the flora coverage percentages collected from the clustered locations as repeated measurements in a Bayesian hierarchical setting. The correlation among the observations from the clustered locations are considered as well. The total vegetation coverage data in MOFEP is analyzed in this study. An Markov chain Monte Carlo algorithm based on the shrinkage slice sampler is developed for simulation from the posterior densities. The total vegetation coverage is modeled by three components, including the covariates, random spatial effect and correlated random errors. Prediction of the total vegetation coverage at unmeasured locations is developed.     

A metadata approach to statistical query processing

Concerning the task of integrating census and survey data from different sources as it is carried out by supranational statistical agencies, a formal metadata approach is investigated which supports data integration and table processing simultaneously. To this end, a metadata model is devised such that statistical query processing is accomplished by means of symbolic reasoning on machine-readable, operative metadata. As in databases, statistical queries are stated as formal expressions specifying declaratively what the intended output is; the operations necessary to retrieve appropriate available source data and to aggregate source data into the requested macrodata are derived mechanically. Using simple mathematics, this paper focuses particularly on the metadata model devised to harmonize semantically related data sources as well as the table model providing the principal data structure of the proposed system. Only an outline of the general design of a statistical information system based on the proposed metadata model is given and the state of development is summarized briefly.     

Spatial correlation matrix selection using Bayesian model averaging to characterize inter-tree competition in loblolly pine trees

Many applications of statistical methods for data that are spatially correlated require the researcher to specify the correlation structure of the data. This can be a difficult task as there are many candidate structures. Some spatial correlation structures depend on the distance between the observed data points while others rely on neighborhood structures. In this paper, Bayesian methods that systematically determine the ‘best’ correlation structure from a predefined class of structures are proposed. Bayes factors, Highest Probability Models, and Bayesian Model Averaging are employed to determine the ‘best’ correlation structure and to average across these structures to create a non-parametric alternative structure for a loblolly pine data-set with known tree coordinates. Tree diameters and heights were measured and an investigation into the spatial dependence between the trees was conducted. Results showed that the most probable model for the spatial correlation structure agreed with allometric trends for loblolly pine. A combined Matern, simultaneous autoregressive model and conditional autoregressive model best described the inter-tree competition among the loblolly pine tree data considered in this research.     

Markov Chain Monte Carlo Techniques for Studying Interoccasion and Intersubject Variability: Application to Pharmacokinetic Data

Values of pharmacokinetic parameters may seem to vary randomly between dosing occasions. An accurate explanation of the pharmacokinetic behaviour of a particular drug within a population therefore requires two major sources of variability to be accounted for, namely interoccasion variability and intersubject variability. A hierarchical model that recognizes these two sources of variation has been developed. Standard Bayesian techniques were applied to this statistical model, and a mathematical algorithm based on a Gibbs sampling strategy was derived. The accuracy of this algorithm's determination of the interoccasion and intersubject variation in pharmacokinetic parameters was evaluated from various population analyses of several sets of simulated data. A comparison of results from these analyses with those obtained from parallel maximum likelihood analyses (NONMEM) showed that, for simple problems, the outputs from the two algorithms agreed well, whereas for more complex situations the NONMEM approach may be less accurate. Statistical analyses of a multioccasion data set of pharmacokinetic measurements on the drug metoprolol (the measurements being of concentrations of drug in blood plasma from human subjects) revealed substantial interoccasion variability for all structural model parameters. For some parameters, interoccasion variability appears to be the primary source of pharmacokinetic variation.     

On robustifying some second order blind source separation methods for nonstationary time series

Blind source separation (BSS) is an important analysis tool in various signal processing applications like image, speech or medical signal analysis. The most popular BSS solutions have been developed for independent component analysis (ICA) with identically and independently distributed (iid) observation vectors. In many BSS applications the assumption on iid observations is not realistic, however, as the data are often an observed time series with temporal correlation and even nonstationarity. In this paper, some BSS methods for time series with nonstationary variances are discussed. We also suggest ways to robustify these methods and illustrate their performance in a simulation study.     

ABC Shadow algorithm: a tool for statistical analysis of spatial patterns

This paper presents an original ABC algorithm, ABC Shadow, that can be applied to sample posterior densities that are continuously differentiable. The proposed algorithm solves the main condition to be fulfilled by any ABC algorithm, in order to be useful in practice. This condition requires enough samples in the parameter space region, induced by the observed statistics. The algorithm is tuned on the posterior of a Gaussian model which is entirely known, and then, it is applied for the statistical analysis of several spatial patterns. These patterns are issued or assumed to be outcomes of point processes. The considered models are: Strauss, Candy and area-interaction.     

A Bayesian latent spatial model for mapping the cortical signature of progression to Alzheimer's disease

Prior studies have shown that atrophy in vulnerable cortical regions is associated with an increased risk of progression to clinical dementia. In this work, we utilize the longitudinal structural magnetic resonance imaging (MRI) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to investigate the relationship between the temporally changing spatial topography of cortical thickness and conversion from mild cognitive impairment to Alzheimer's disease (AD). We develop a novel Bayesian latent spatial model that employs the spatial information underlying the thickness effects across the cortical surface. The proposed method facilitates the development of imaging markers by reliably quantifying and mapping the regional vulnerability to AD progression across the cortical surface. Simulation results showed substantial gains in statistical power and estimation performance by accounting for the spatial structure of the association. Using MRI data from ADNI, we examined the topographic patterns of anatomic regions where cortical thinning is associated with an increased risk of developing AD.     

Choosing summary statistics by least angle regression for approximate Bayesian computation

Bayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.     

Double Generalized Spatial Econometric Models

The authors offer a unified method extending traditional spatial dependence with normally distributed error terms to a new class of spatial models based on the biparametric exponential family of distributions. Joint modeling of the mean and variance (or precision) parameters is proposed in this family of distributions, including spatial correlation. The proposed models are applied for analyzing Colombian land concentration, assuming that the variable of interest follows normal, gamma, and beta distributions. In all cases, the models were fitted using Bayesian methodology with the Markov Chain Monte Carlo (MCMC) algorithm for sampling from joint posterior distribution of the model parameters.     

Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach

While most regression models focus on explaining distributional aspects of one single response variable alone, interest in modern statistical applications has recently shifted towards simultaneously studying multiple response variables as well as their dependence structure. A particularly useful tool for pursuing such an analysis are copula-based regression models since they enable the separation of the marginal response distributions and the dependence structure summarised in a specific copula model. However, so far copula-based regression models have mostly been relying on two-step approaches where the marginal distributions are determined first whereas the copula structure is studied in a second step after plugging in the estimated marginal distributions. Moreover, the parameters of the copula are mostly treated as a constant not related to covariates and most regression specifications for the marginals are restricted to purely linear predictors. We therefore propose simultaneous Bayesian inference for both the marginal distributions and the copula using computationally efficient Markov chain Monte Carlo simulation techniques. In addition, we replace the commonly used linear predictor by a generic structured additive predictor comprising for example nonlinear effects of continuous covariates, spatial effects or random effects and furthermore allow to make the copula parameters covariate-dependent. To facilitate Bayesian inference, we construct proposal densities for a Metropolis–Hastings algorithm relying on quadratic approximations to the full conditionals of regression coefficients avoiding manual tuning. The performance of the resulting Bayesian estimates is evaluated in simulations comparing our approach with penalised likelihood inference, studying the choice of a specific copula model based on the deviance information criterion, and comparing a simultaneous approach with a two-step procedure. Furthermore, the flexibility of Bayesian conditional copula regression models is illustrated in two applications on childhood undernutrition and macroecology.     

A new variational Bayesian algorithm with application to human mobility pattern modeling

A new variational Bayesian (VB) algorithm, split and eliminate VB (SEVB), for modeling data via a Gaussian mixture model (GMM) is developed. This new algorithm makes use of component splitting in a way that is more appropriate for analyzing a large number of highly heterogeneous spiky spatial patterns with weak prior information than existing VB-based approaches. SEVB is a highly computationally efficient approach to Bayesian inference and like any VB-based algorithm it can perform model selection and parameter value estimation simultaneously. A significant feature of our algorithm is that the fitted number of components is not limited by the initial proposal giving increased modeling flexibility. We introduce two types of split operation in addition to proposing a new goodness-of-fit measure for evaluating mixture models. We evaluate their usefulness through empirical studies. In addition, we illustrate the utility of our new approach in an application on modeling human mobility patterns. This application involves large volumes of highly heterogeneous spiky data; it is difficult to model this type of data well using the standard VB approach as it is too restrictive and lacking in the flexibility required. Empirical results suggest that our algorithm has also improved upon the goodness-of-fit that would have been achieved using the standard VB method, and that it is also more robust to various initialization settings.     

A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models

Hierarchical spatio-temporal models allow for the consideration and estimation of many sources of variability. A general spatio-temporal model can be written as the sum of a spatio-temporal trend and a spatio-temporal random effect. When spatial locations are considered to be homogeneous with respect to some exogenous features, the groups of locations may share a common spatial domain. Differences between groups can be highlighted both in the large-scale, spatio-temporal component and in the spatio-temporal dependence structure. When these differences are not included in the model specification, model performance and spatio-temporal predictions may be weak. This paper proposes a method for evaluating and comparing models that progressively include group differences. Hierarchical modeling under a Bayesian perspective is followed, allowing flexible models and the statistical assessment of results based on posterior predictive distributions. This procedure is applied to tropospheric ozone data in the Italian Emilia–Romagna region for 2001, where 30 monitoring sites are classified according to environmental laws into two groups by their relative position with respect to traffic emissions.     

Statistical methods for noisy images with discontinuities

In this paper, we describe a new statistical method for images which contain discontinuities. The method tries to improve the quality of a 'measured' image, which is degraded by the presence of random distortions. This is achieved by using knowledge about the degradation process and a priori information about the main characteristics of the underlying ideal image. Specifically, the method uses information about the discontinuity patterns in small areas of the 'true' image. Some auxiliary labels 'explicitly' describe the location of discontinuities in the true image. A Bayesian model for the image grey levels and the discontinuity labels is built. The maximum a posteriori estimator is considered. The iterated conditional modes algorithm is used to find a (local) maximum of the posterior distribution. The proposed method has been successfully applied to both artificial and real magnetic resonance images. A comparison of the results with those obtained from three other known methods also has been performed. Finally, the connection between Bayesian 'explicity and 'implicit' models is studied. In implicit modelling, there is no use of any set of labels explicitly describing the location of discontinuities. For these models, we derive some constraints of the function by which the presence of the discontinuities is taken into account.     

Reference priors for linear models with general covariance structures

We develop a new class of reference priors for linear models with general covariance structures. A general Markov chain Monte Carlo algorithm is also proposed for implementing the computation. We present several examples to demonstrate the results: Bayesian penalized spline smoothing, a Bayesian approach to bivariate smoothing for a spatial model, and prior specification for structural equation models.     

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

The Log-Gaussian Cox process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly stochastic property, that is, it is a hierarchical combination of a Poisson process at the first level and a Gaussian process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data.     

Blind source separation filters-based-fault detection and isolation in a three tank system

Fault detection and Isolation takes a strategic position in modern industrial processes for which various approaches are proposed. These approaches are usually developed and based on a consistency test between an observed state of the process provided by sensors and an expected behaviour provided by a mathematical model of the system. These methods require a reliable model of the system to be monitored which is a complex task. Alternatively, we propose in this paper to use blind source separation filters (BSSFs) in order to detect and isolate faults in a three tank pilot plant. This technique is very beneficial as it uses blind identification without an explicit mathematical model of the system. The independent component analysis (ICA), relying on the assumption of the statistical independence of the extracted sources, is used as a tool for each BSSF to extract signals of the process under consideration. The experimental results show the effectiveness and robustness of this approach in detecting and isolating faults that are on sensors in the system.     

A joint modeling approach for spatial earthquake risk variations

Modeling spatial patterns and processes to assess the spatial variations of data over a study region is an important issue in many fields. In this paper, we focus on investigating the spatial variations of earthquake risks after a main shock. Although earthquake risks have been extensively studied in the literatures, to our knowledge, there does not exist a suitable spatial model for assessing the problem. Therefore, we propose a joint modeling approach based on spatial hierarchical Bayesian models and spatial conditional autoregressive models to describe the spatial variations in earthquake risks over the study region during two periods. A family of stochastic algorithms based on a Markov chain Monte Carlo technique is then performed for posterior computations. The probabilistic issue for the changes of earthquake risks after a main shock is also discussed. Finally, the proposed method is applied to the earthquake records for Taiwan before and after the Chi-Chi earthquake.     

Variable-Selection-Based Epidemic Disease Diagnosis

Epidemic surveillance in a community involves monitoring infection trend, triggering alarms before outbreaks, and identifying sources and paths of disease transmission. Algorithms for outbreak detection that are derived from industrial statistical process control (SPC) and scan statistics have been reported in the literature, but there are relatively few methods reported for identifying transmission paths. In this work, we propose an expanded spatial-temporal (EST) model for identifying infection sources. Three dimensional information, subject, location, and time, are expanded into a two-dimensional space by dividing the time horizon into segments and multiplying each segment by the locations. Based on the EST model, we further propose a variable-selection algorithm to identify potential location/time combinations as sources of infection, and thus achieve diagnosis. Numerical simulations show that the proposed scheme is effective in locating infection sources.     

Bayesian local influence analysis of skew-normal spatial dynamic panel data models

The existing studies on spatial dynamic panel data model (SDPDM) mainly focus on the normality assumption of response variables and random effects. This assumption may be inappropriate in some applications. This paper proposes a new SDPDM by assuming that response variables and random effects follow the multivariate skew-normal distribution. A Markov chain Monte Carlo algorithm is developed to evaluate Bayesian estimates of unknown parameters and random effects in skew-normal SDPDM by combining the Gibbs sampler and the Metropolis–Hastings algorithm. A Bayesian local influence analysis method is developed to simultaneously assess the effect of minor perturbations to the data, priors and sampling distributions. Simulation studies are conducted to investigate the finite-sample performance of the proposed methodologies. An example is illustrated by the proposed methodologies.     

SPACE–TIME MODELLING OF SYDNEY HARBOUR WINDS

This paper develops a space‐time statistical model for local forecasting of surface‐level wind fields in a coastal region with complex topography. The statistical model makes use of output from deterministic numerical weather prediction models which are able to produce forecasts of surface wind fields on a spatial grid. When predicting surface winds at observing stations , errors can arise due to sub‐grid scale processes not adequately captured by the numerical weather prediction model , and the statistical model attempts to correct for these influences. In particular , it uses information from observing stations within the study region as well as topographic information to account for local bias. Bayesian methods for inference are used in the model , with computations carried out using Markov chain Monte Carlo algorithms. Empirical performance of the model is described , illustrating that a structured Bayesian approach to complicated space‐time models of the type considered in this paper can be readily implemented and can lead to improvements in forecasting over traditional methods.