Prior information in spatial analysis
Formal statistical procedures which incorporate prior, or nonsample, information can be used to enlarge the theoretical and empirical content of analytical models, and can be widely applied to adapt general statistical procedures for special investigative situations which arise in the analysis of spatial data. A class of methods which operate by modifying the parameter space of general statistical models in accordance with prior information is presented in this paper. The prior information can be obtained from theoretical or empirical sources, and the models can be given Bayesian as well as non-Bayesian interpretations. The utility of the methods is demonstrated by applying them to estimate parameters for urban-population-density functions. The resulting estimates incorporate nonsample information on total populations as well as sample information on subarea densities. The logic of the population-distribution model is also extended to take account of possible growth processes by incorporating prior information derived from earlier distributions and by incorporating the characteristics of possible growth processes.
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