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A Conditional-Probability Approach to the Development of Spatial Pattern

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  • J Odland

    (Department of Geography, Indiana University, Bloomington, Indiana 47401, USA)

Abstract

A stochastic model for the development of spatial patterns is introduced and used to investigate the process of housing deterioration in an American city. Space is treated as a sequence of discrete locations and a spatial-lag structure is incorporated in the model by defining multivalued random variables whose values indicate conditions at a central location and at a series of spatial lags. The possible combinations of these values define the states of a Markov process, and a description of this process can be obtained by estimating probabilities for the transitions from state to state. Qualitative inferences about the effects of a process on existing spatial patterns are obtained by comparing an initial distribution, for the multivalued random variables, with the limiting distribution implied by the process description. Application of the model involves selection of an appropriate random variable as well as estimation of a set of transition probabilities. Results for Indianapolis in 1977 indicate that the probability of housing deterioration is strongly associated with the presence of deteriorated structures in nearby locations.

Suggested Citation

  • J Odland, 1979. "A Conditional-Probability Approach to the Development of Spatial Pattern," Environment and Planning A, , vol. 11(3), pages 313-326, March.
    • Handle: RePEc:sae:envira:v:11:y:1979:i:3:p:313-326
    DOI: 10.1068/a110313
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    References listed on IDEAS

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    1. Bell, E. J. & Hinojosa, R. C., 1977. "Markov analysis of land use change: Continuous time and stationary processes," Socio-Economic Planning Sciences, Elsevier, vol. 11(1), pages 13-17.
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    Cited by:

    1. Elizabeth Delmelle & Jean-Claude Thill & Chunhua Wang, 2016. "Spatial dynamics of urban neighborhood quality of life," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 56(3), pages 687-705, May.

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