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Transiogram is the accompanying spatial correlation measure of simplified Markov chain random field (MCRF) models based on the conditional independence assumption and an important part of Markov chain geostatistics. It is defined as a transition probability function over the distance lag. Simply, a transiogram refers to a transition probability-lag diagram. Transiograms include auto-transiograms and cross-transiograms. The former represent the spatial auto-correlation of a single category, and the latter represent the spatial interclass relationships among different categories. Experimental transiograms can be directly estimated from sparse sample data. Transiogram models, which provide transition probabilities at any lags for Markov chain modeling, can be further acquired through model fitting of experimental transiograms. In general, the transiogram is a spatial correlation measure following the style of variogram, and it includes a set of concepts and a set of methods for obtaining transition probability values from sample data and provide transition probabilities values for simplified MCRF models.


  • Li, W. (2007) "Transiograms for characterizing spatial variability of soil classes". Soil Science Society of America Journal 71(3): 881-893
  • Li W, Zhang C (2010) "Linear interpolation and joint model fitting of experimental transiograms for Markov chain simulation of categorical spatial variables". Int J Geogr Info Sci 24: 821–839.