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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]

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]