The present paper reviews the conceptual framework and development of the Bayesian Maximum Entropy (BME) approach. BME has been considered as a significant breakthrough and contribution to applied ...stochastics by introducing an improved, knowledge-based modeling framework for spatial and spatiotemporal information. In this work, one objective is the overview of distinct BME features. By offering a foundation free of restrictive assumptions that limit comparable techniques, an ability to integrate a variety of prior knowledge bases, and rigorous accounting for both exact and uncertain data, the BME approach was coined as introducing modern spatiotemporal geostatistics. A second objective is to illustrate BME applications and adoption within numerous different scientific disciplines. We summarize examples and real-world studies that encompass the perspective of science of the total environment, including atmosphere, lithosphere, hydrosphere, and ecosphere, while also noting applications that extend beyond these fields. The broad-ranging application track suggests BME as an established, valuable tool for predictive spatial and space–time analysis and mapping. This review concludes with the present status of BME, and tentative paths for future methodological research, enhancements, and extensions.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This paper is concerned with the modeling of infectious disease spread in a composite space-time domain under conditions of uncertainty. We focus on stochastic modeling that accounts for basic ...mechanisms of disease distribution and multi-sourced in situ uncertainties. Starting from the general formulation of population migration dynamics and the specification of transmission and recovery rates, the model studies the functional formulation of the evolution of the fractions of susceptible-infected-recovered individuals. The suggested approach is capable of: a) modeling population dynamics within and across localities, b) integrating the disease representation (i.e. susceptible-infected-recovered individuals) with observation time series at different geographical locations and other sources of information (e.g. hard and soft data, empirical relationships, secondary information), and c) generating predictions of disease spread and associated parameters in real time, while considering model and observation uncertainties. Key aspects of the proposed approach are illustrated by means of simulations (i.e. synthetic studies), and a real-world application using hand-foot-mouth disease (HFMD) data from China.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
This work presents a computational formulation of the Bayesian maximum entropy (BME) approach to solve a stochastic partial differential equation (PDE) representing the advection‐reaction process ...across space and time. The solution approach provided by BME has some important features that distinguish it from most standard stochastic PDE techniques. In addition to the physical law, the BME solution can assimilate other sources of general and site‐specific knowledge, including multiple‐point nonlinear space/time statistics, hard measurements, and various forms of uncertain (soft) information. There is no need to explicitly solve the moment equations of the advection‐reaction law since BME allows the information contained in them to consolidate within the general knowledge base at the structural (prior) stage of the analysis. No restrictions are posed on the shape of the underlying probability distributions or the space/time pattern of the contaminant process. Solutions of nonlinear systems of equations are obtained in four space/time dimensions and efficient computational schemes are introduced to cope with complexity. The BME solution at the prior stage is in excellent agreement with the exact analytical solution obtained in a controlled environment for comparison purposes. The prior solution is further improved at the integration (posterior) BME stage by assimilating uncertain information at the data points as well as at the solution grid nodes themselves, thus leading to the final solution of the advection‐reaction law in the form of the probability distribution of possible concentration values at each space/time grid node. This is the most complete way of describing a stochastic solution and provides considerable flexibility concerning the choice of the concentration realization that is more representative of the physical situation. Numerical experiments demonstrated a high solution accuracy of the computational BME approach. The BME approach can benefit from the use of parallel processing (the relevant systems of equations can be processed simultaneously at each grid node and multiple integrals calculations can be accelerated significantly, etc.).
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Mapping spatial processes at a small scale is a challenge when observed data are not abundant. The article examines the residential housing market in Fort Worth, Texas, and builds price indices at ...the inter- and intra-neighborhood levels. To accomplish our objectives, we initially model price variability in the joint space-time continuum. We then use geostatistics to predict and map monthly housing prices across the area of interest over a period of 4 years. For this analysis, we introduce the Bayesian maximum entropy (BME) method into real estate research. We use BME because it rigorously integrates uncertain or secondary soft data, which are needed to build the price indices. The soft data in our analysis are property tax values, which are plentiful, publicly available, and highly correlated with transaction prices. The results demonstrate how the use of the soft data provides the ability to map house prices within a small areal unit such as a subdivision or neighborhood.
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BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
Time-resolved characterization of solar irradiance at the ground level is a critical element in solar energy analysis. Siting of nodes in a network of solar irradiance monitoring stations (MS) is a ...multi-faceted problem that directly affects the determination of the solar resource and its spatio-temporal variability. The present work proposes an objective framework to optimize the deployment of solar MS over a sub-continental region. There are two main components in the proposed methodology. The first employs cluster analysis using the affinity propagation algorithm, to select the optimal number of clusters (regions with coherent solar microclimates) upon internal coherence criteria. The second component employs stochastic prediction and validation, through the use of a Bayesian maximum entropy method, and selects the optimal MS configuration, according to geostatistical criteria, among the solutions recommended by the cluster analysis. We apply this two-pronged methodology to determine clusters and optimal locations for global horizontal irradiance monitoring across the state of California. In this proof-of-concept study, 3 disparate MS configurations are examined within the cluster partition. The subsequent geostatistical analysis indicates that all configurations rank almost equally well based on different statistical error measures. The optimal configuration can be singled out depending on desired criteria of choice.
•Large-scale cluster analysis of GHI across the state of California.•Determination of meaningful number of clusters upon cluster validity criteria.•Exploration of optimal monitoring network distribution over thee different measuring sites configuration.•Spatiotemporal prediction of solar irradiance at large spatial and sub-hour temporal scales.•Prediction with Bayesian maximum entropy enables rigorous assimilation of both hard and soft data.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Exposure analysis and mapping of spatiotemporal pollutants in relation to their health effects are important challenges facing environmental health scientists and integrated assessment modellers. In ...this work, a methodological framework is discussed to study the impact of spatiotemporal ozone (O3) exposure distributions on the health of human populations. The framework, however, is very general and can be used to study various other pollutants. The spatiotemporal analysis starts with exposure distributions producing the input to pollutokinetic (or toxicokinetic) laws which are linked to effect models which, in turn, are integrated with relationships that describe how effects are distributed across populations. Important characteristics of the environmental health framework are holisticity and stochasticity. Holisticity emphasizes the functional relationships between composite space/time O3 maps, pollutokinetic models of burden on target organs and tissues, and health effects. These relationships offer a meaningful physical interpretation of the exposure and biological processes that affect human exposure. Stochasticity involves the rigorous representation of natural uncertainties and biological variations in terms of spatiotemporal random fields. The stochastic perspective introduces a deeper epistemological understanding in the development of improved models of spatiotemporal human exposure analysis and mapping. Also, it explicitly determines the knowledge bases available and develops logically plausible rules and standards for data processing and human exposure map construction. The proposed approach allows the horizontal integration among sciences related to the human exposure problem that leads to accurate and informative spatiotemporal maps of O3 exposure and effect distributions and an integrative analysis of the whole risk case. By processing a variety of knowledge bases, the spatiotemporal analysis can bring together several sciences which are all relevant to the aspect of human exposure reality that is examined.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In recent years, there has been a fast growing interest in the space–time data processing capacity of Geographic Information Systems (GIS). In this paper we present a new GIS-based tool for advanced ...geostatistical analysis of space–time data; it combines stochastic analysis, prediction, and GIS visualization technology. The proposed toolbox is based on the Bayesian Maximum Entropy theory that formulates its approach under a mature knowledge synthesis framework. We exhibit the toolbox features and use it for particulate matter spatiotemporal mapping in Taipei, in a proof-of-concept study where the serious preferential sampling issue is present. The proposed toolbox enables tight coupling of advanced spatiotemporal analysis functions with a GIS environment, i.e. QGIS. As a result, our contribution leads to a more seamless interaction between spatiotemporal analysis tools and GIS built-in functions; and utterly enhances the functionality of GIS software as a comprehensive knowledge processing and dissemination platform.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Space-time data analysis and assimilation techniques in atmospheric sciences typically consider input from monitoring measurements. The input is often processed in a manner that acknowledges ...characteristics of the measurements (e.g., underlying patterns, fluctuation features) under conditions of uncertainty; it also leads to the derivation of secondary information that serves study-oriented goals, and provides input to space-time prediction techniques. We present a novel approach that blends a rigorous space-time prediction model (Bayesian maximum entropy, BME) with a cognitively informed visualization of high-dimensional data (spatialization). The combined BME and spatialization approach (BME-S) is used to study monthly averaged NO2 and mean annual SO4 measurements in California over the 15-year period 1988−2002. Using the original scattered measurements of these two pollutants BME generates spatiotemporal predictions on a regular grid across the state. Subsequently, the prediction network undergoes the spatialization transformation into a lower-dimensional geometric representation, aimed at revealing patterns and relationships that exist within the input data. The proposed BME-S provides a powerful spatiotemporal framework to study a variety of air pollution data sources.
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IJS, KILJ, NUK, PNG, UL, UM
This paper describes the spatiotemporal epistematics knowledge synthesis and graphical user interface (SEKS-GUI) framework and its application in medical geography problems. Based on sound ...theoretical reasoning, the interactive software library of SEKS-GUI explores heterogeneous (spatially non-homogeneous and temporally non-stationary) health attribute distributions (disease incidence, mortality, human exposure, epidemic propagation etc.); expresses the health system's dependence structure using (ordinary and generalized) spatiotemporal covariance models; synthesizes core knowledge bases, empirical evidence and multi-sourced system uncertainty; and generates a meaningful picture of the real-world system using space-time dependent probability functions and associated maps of health attributes. The implementation stages of the SEKS-GUI library are described in considerable detail using appropriate screens. The wide applicability of SEKS-GUI is demonstrated by reviewing a selection of real-world case studies. PUBLICATION ABSTRACT
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The abundance of spatial and space–time data in many research fields has led to an increasing interest in the analytics of spatial data information. This development has renewed the attention to ...predictive spatial methodologies and advancing geostatistical tools. In this context, the present work reviews a series of cross-discipline studies that utilize multiple monitoring sources, and promote applied approaches in spatial and spatiotemporal modeling to improve our understanding of uncertainty. As multi-sourced information gives birth to new aspects of uncertainty, we explore emerging patterns in dealing with uncertainty in sources across structured, unstructured, and incomplete spatial data. We also illustrate how additional forms of information, such as secondary data and physical models, can further support and benefit research in the characterization and modeling of natural attributes.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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