The application of a stochastic process model to geographical analysis
The use of models in geography, though widespread, has tended to lag behind their use in several other social sciences. The use of Markov chain analysis - the simplest form of stochastic process model-was not, for example, introduced to the geographic literature until the early 1960s (Brown 1963). However, during the last decade, numerous studies, both in ‘human’ and ‘physical’ geography, have adopted Markovian frameworks. Most of these studies have employ ed concepts relating to regular, finite Markov chains, though a limited number have been concerned with absorbing chains and a few with continuous and semi-continuous Markov processes. Much progress has been made, but since most applications have been con cerned with empirically based Markov chains, data deficiencies (insufficient number of observations, or inadequate time series) have limited the scope and goals of many research designs. For example, most studies have used Markov chains for descriptive purposes only and very few have used the concept as a model of geographic process. Although data deficiencies created difficulties the overriding geo graphical problem is the classification of a system of spatial states. In all approaches of our discipline, geographers have discovered that there is no unique causal ordering device for spatial series and as yet all attempts at a comprehensive definition have proved to be fruitless. Many of the more successful applications in geography have employ ed aspatial systems of states. This paper will show how both
aspatial and spatial systems of states for a regular finite Markov chain can be used in a geographic study.