Transiogram
Encyclopedia
Transiogram is the accompanying spatial correlation
measure of Markov chain random fields 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 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.
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
measure of Markov chain random fields and an important part of Markov chain geostatistics
Markov chain geostatistics
Markov chain geostatistics refer to the Markov chain models, simulation algorithms and associated spatial correlation measures based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional field for geostatistical modeling. A Markov chain random field...
. It is defined as a transition probability function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
over the distance lag. Simply, a transiogram refers to a transition probability 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
Markov chain
A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process characterized as memoryless: the next state depends only on the current state and not on the...
modeling
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
, can be further acquired through model fitting of experimental transiograms.