An Ising-Type Model for Spatio-Temporal Interactions
2005, v.11, Issue 3, 535-552
A model which possesses both spatial and time dependence is the Markov chain Markov field [X. Guyon, Random Fields on a Network, Springer-Verlag, New York, 1995]. Here inference about the parameter for spatio-temporal interaction of a special case of a Markov chain Markov field model is considered. A statistic which is minimal sufficient for the spatio-temporal interaction parameter and its asymptotic distribution are derived. A condition for stationarity of the sufficient statistic process and the stationary distribution are given. Likelihood based inference methods such as estimation, hypothesis testing and monitoring are briefly examined.
Keywords: asymptotic distribution,interaction,Markov chain Markovfield,perfect simulation,stationarity,sufficient statistic