J. Japan Statist. Soc., Vol. 36 (No. 2), pp. 121-147, 2006

Bayesian Estimation of Soft-Core Potential Models for Spatial Point Patterns

Masahilo Okabe and Masaharu Tanemura

Abstract. For a spatial pattern of points interacting with a repulsive potential in a given finite region of the plane, Bayesian estimation of parametric interaction potential functions between individuals (the Soft-Core models) is proposed. The computations are performed by the use of MCMC (Markov Chain Monte Carlo) methods. We consider two prior distributions with the jumping distributions within Markov chain simulations. Simulated marginal posterior densities of model parameters are fitted to the generalized gamma distribution. We compare marginal posterior modes with the maximum likelihood estimates of the model parameters. The validity of our procedure is graphically demonstrated by the L-statistics. As illustrations, the application to several real data is presented.

Key words and phrases: Bayesian estimation, L-statistics, MCMC methods, repulsive interaction, Soft-Core models.

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