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Li and Zhang (2012b, Comments on ‘Combining spatial transition probabilities for stochastic simulation of categorical fields’ with communications on some issues related to Markov chain geostatics) raised a series of comments on our recent paper (Cao, G., Kyriakidis, P.C., and Goodchild, M.F., 2011. Combining spatial transition probabilities for stochastic simulation of categorical fields. International Journal of Geographical Information Science, 25 (11), 1773–1791), which include a notation error in the model equation provided for the Markov chain random field (MCRF) or spatial Markov chain model (SMC), originally proposed by Li (2007b, Markov chain random fields for estimation of categorical variables. Mathematical Geology, 39 (3), 321–335), and followed by Allard et al. (2011, An efficient maximum entropy approach for categorical variable prediction. European Journal of Soil Science, 62, 381–393) about the misinterpretation of MCRF (or SMC) as a simplified form of the Bayesian maximum entropy (BME)-based approach, the so-called Markovian-type categorical prediction (MCP) (Allard, D., D'Or, D., and Froideveaux, R., 2009. Estimating and simulating spatial categorical data using an efficient maximum entropy approach. Avignon: Unite Biostatisque et Processus Spatiaux Institute National de la Recherche Agronomique. Technical Report No. 37; Allard, D., D'Or, D., and Froideveaux, R., 2011. An efficient maximum entropy approach for categorical variable prediction. European Journal of Soil Science, 62, 381–393). Li and Zhang (2012b, Comments on ‘Combining spatial transition probabilities for stochastic simulation of categorial fields’ with communication on some issues related to Markov chain geostatistics. International Journal of Geographical Information Science) also raised concerns regarding several statements Cao et al. (2011, Combining spatial transition probabilities for stochastic simulation of categorical fields. International Journal of Geographical Information Science, 25 (11), 1773–1791) had made, which mainly include connections between permanence of ratios and conditional independence, connections between MCRF and Bayesian networks and transiograms as spatial continuity measures. In this response, all of the comments and concerns will be addressed, while also communicating with Li and other colleagues on general topics in Markov chain geostatistics. [ABSTRACT FROM AUTHOR]

In this article, the prediction problem of categorical spatial data, that is, the estimation of class occurrence probability for (target) locations with unknown class labels given observed class labels at sample (source) locations, is analyzed in the framework of generalized linear mixed models, where intermediate, latent (unobservable) spatially correlated Gaussian variables (random effects) are assumed for the observable non-Gaussian responses to account for spatial dependence information. Within such a framework, a spatial multinomial logistic mixed model is proposed specifically to model categorical spatial data. Analogous to the dual form of kriging family, the proposed model is represented as a multinomial logistic function of spatial covariances between target and source locations. The associated inference problems, such as estimation of parameters and choice of the spatial covariance function for latent variables, and the connection of the proposed model with other methods, such as the indicator variants of the kriging family (indicator kriging and indicator cokriging) and Bayesian maximum entropy, are discussed in detail. The advantages and properties of the proposed method are illustrated via synthetic and real case studies. [ABSTRACT FROM AUTHOR]

Categorical spatial data, such as land use classes and socioeconomic statistics data, are important data sources in geographical information science (GIS). The investigation of spatial patterns implied in these data can benefit many aspects of GIS research, such as classification of spatial data, spatial data mining, and spatial uncertainty modeling. However, the discrete nature of categorical data limits the application of traditional kriging methods widely used in Gaussian random fields. In this article, we present a new probabilistic method for modeling the posterior probability of class occurrence at any target location in space-given known class labels at source data locations within a neighborhood around that prediction location. In the proposed method, transition probabilities rather than indicator covariances or variograms are used as measures of spatial structure and the conditional or posterior (multi-point) probability is approximated by a weighted combination of preposterior (two-point) transition probabilities, while accounting for spatial interdependencies often ignored by existing approaches. In addition, the connections of the proposed method with probabilistic graphical models (Bayesian networks) and weights of evidence method are also discussed. The advantages of this new proposed approach are analyzed and highlighted through a case study involving the generation of spatial patterns via sequential indicator simulation. [ABSTRACT FROM AUTHOR]

A new-generation of night-time lights (NTL) image products, the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) monthly composites, have been produced and released by the National Oceanic and Atmospheric Administration's National Centers for Environmental Information. Compared with the last generation NTL image products, the Defense Meteorological Satellite Program's Operational Linescan System stable light composites, the new NTL image products have finer spatial resolution with compatible radiance values across different month/year images. However, the current defects in VIIRS DNB monthly composites show ephemeral lights, relatively high radiance in winter months, and missing data over the high-latitude regions of the northern hemisphere in summer months. This study presents a method to improve the accuracy of the new NTL image products by statistically modelling the time series VIIRS NTL images and uses the improved imagery to estimate socio-economic factors. In this method, we first estimate radiance for each pixel with 'no data' in May, June, July, and August images and then exponentially smooth the monthly time series images to produce a 2014 annual VIIRS DNB image for the contiguous USA. Sum radiance derived from the smoothed annual image shows stronger correlations with gross domestic product at the state level and smaller standard errors of the estimate at the metropolitan and county levels compared with that extracted from the annual image produced by simply averaging the original monthly DNB composites. Such results infer that exponential smoothing effectively improves the quality of the VIIRS DNB images for annual economic estimation. [ABSTRACT FROM AUTHOR]

With the proposition of the Digital Earth (DE) concept, Virtual Geographic Information System (VGIS) has started to play the role of a Digital Earth prototype system. Many core problems involved in VGIS, such as out-of-core management and interactive rendering of very large scale terrain and image data, have been well studied in the past decades. However, the jitter problem, a common problem in VGIS that often causes annoying visual artefacts and deteriorates the output image quality, draws little attention. In this paper, after an intensive analysis of the jitter problem, a comprehensive framework is proposed to address such a problem while accounting for the characteristics of different data types in VGIS, such as terrain or ocean mesh data, vector data and 3-D model data. Specifically, this framework provides an improved dynamic local coordinate system (DLCS) method for terrain or ocean mesh data. For vector data, the framework provides a simple and effective multiple local coordinate systems (MLCS) method. The framework provides a MLCS method for 3-D model data making full use of the existing local coordinate system of the model. The advantages of the proposed methods over current approaches are analysed and highlighted through case studies involving large GIS datasets. [ABSTRACT FROM AUTHOR]

We develop a multivariate regression model when responses or predictors are on nonlinear manifolds, rather than on Euclidean spaces. The nonlinear constraint makes the problem challenging and needs to be studied carefully. By performing principal component analysis (PCA) on tangent space of manifold, we use principal directions instead in the model. Then, the ordinary regression tools can be utilized. We apply the framework to both shape data (ozone hole contours) and functional data (spectrums of absorbance of meat in Tecator dataset). Specifically, we adopt the square-root velocity function representation and parametrization-invariant metric. Experimental results have shown that we can not only perform powerful regression analysis on the non-Euclidean data but also achieve high prediction accuracy by the constructed model. [ABSTRACT FROM AUTHOR]

Tracking spatial and temporal trends of events (e.g. disease outbreaks and natural disasters) is important for situation awareness and timely response. Social media, with increasing popularity, provide an effective way to collect event-related data from massive populations and thus a significant opportunity to dynamically monitor events as they emerge and evolve. While existing research has demonstrated the value of social media as sensors in event detection, estimating potential time spans and influenced areas of an event from social media remains challenging. Challenges include the unstable volumes of available data, the spatial heterogeneity of event activities and social media data, and the data sparsity. This paper describes a systematic approach to detecting potential spatiotemporal patterns of events by resolving these challenges through several interrelated strategies: using kernel density estimation for smoothed social media intensity surfaces; utilizing event-unrelated social media posts to help map relative event prevalence; and normalizing event indicators based on historical fluctuation. This approach generates event indicator maps and significance maps explaining spatiotemporal variations of event prevalence to identify space-time regions with potentially abnormal event activities. The approach has been applied to detect influenza activity patterns in the conterminous US usingTwitterdata. A set of experiments demonstrated that our approach produces high-resolution influenza activity maps that could be explained by available ground truth data. [ABSTRACT FROM PUBLISHER]