The Boolean model is a random closed set process consisting of a Poisson point process (producing germs) coupled with an independent random shape process (grains). Origins of grains are translated to germs to produce an arrangement of overlapping (or interpenetrating) shapes. An accurate discrete approximation to the continuous linear Boolean model o?ers computationally e±cient likelihood procedures including maximum likelihood estimation and likelihood ratio tests. The discrete approximation allows covering probabilities to be calculated using recursive formulas, which approach continuous densities as the sampling rate increases. Inference for higher dimensional Boolean models is handled by linear transects. Two two-dimensional estimation examples demonstrate the e±cacy of this method.
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