Markov chain geostatistics uses
Markov chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
spatial models,
simulation algorithms and associated spatial
correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
measures (e.g.,
transiogram) based on the Markov chain random field theory, which extends a single
Markov chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
into a multi-dimensional random field for
geostatistical modeling. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability
matrices are difficult to estimate from sparse
sample
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of s ...
data and are impractical in representing the complex spatial
heterogeneity of states, the
transiogram, which is defined as a
transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.
References
# Li, W. 2007. Markov chain random fields for estimation of categorical variables. Math. Geol., 39(3): 321–335.
# Li, W. et al. 2015. Bayesian Markov chain random field cosimulation for improving land cover classification accuracy. Math. Geosci., 47(2): 123–148.
# Li, W., and C. Zhang. 2019. Markov chain random fields in the perspective of spatial Bayesian networks and optimal neighborhoods for simulation of categorical fields. Computational Geosciences, 23(5): 1087-1106.
# http://gisweb.grove.ad.uconn.edu/weidong/Markov_chain_spatial_statistics.htm
Geostatistics
Interpolation
Markov models