Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.14279/8652
Title: Response to ‘Comments on “Combining Spatial Transition Probabilities for Stochastic Simulation of Categorical Fields” with Communications on Some Issues Related to Markov Chain Geostatistics
Authors: Cao, Guofeng 
Kyriakidis, Phaedon 
Goodchild, Michael F. 
Major Field of Science: Engineering and Technology
Field Category: Environmental Engineering
Keywords: Categorical data;Transition probability;Geostatistics;Conditional independence;Markov random field
Issue Date: 27-Sep-2012
Source: International Journal of Geographical Information Science, 2012, vol. 26, no. 10, pp. 1741-1750
Volume: 26
Issue: 10
Start page: 1741
End page: 1750
Abstract: 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.
URI: https://hdl.handle.net/20.500.14279/8652
ISSN: 13623087
DOI: 10.1080/13658816.2012.717630
Rights: © Informa UK Limited, an Informa Group Company
Type: Article
Affiliation : University of Illinois at Urbana-Champaign 
University of California 
University of Aegean 
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