Showing papers on "Markov random field published in 1979"

Limiting results for arrays of binary random variables on rectangular lattices under sparseness conditions

Abstract: In this article we give limiting results for arrays {Xij (m, n) (i, j) Dmn } of binary random variables distributed as particular types of Markov random fields over m x n rectangular lattices Dmn. Under some sparseness conditions which restrict the number of X ij (m, n)'s which are equal to one we show that the random variables (l = 1, ···, r) converge to independent Poisson random variables for 0 < d1 < d2 < · ·· < dr when m→∞ nd∞. The particular types of Markov random fields considered here provide clustering (or repulsion) alternatives to randomness and involve several parameters. The limiting results are used to consider statistical inference for these parameters. Finally, a simulation study is presented which examines the adequacy of the Poisson approximation and the inference techniques when the lattice dimensions are only moderately large.

A random field model for quantitation and prediction of biological patterns

Abstract: A Markov random field model is proposed to quantitate and predict the formation of biological patterns. A tissue is viewed in two dimensions as an equally spaced lattice, the sites of which correspond to the centres of the cells. Each cell can be in either of two states: 0 or 1. In the case of a one cell-type tissue, the states represent different characteristics of the cell, e.g. healthy versus malignant. By estimating local interactions, we are able to quantitate the mechanisms inducing pattern formation and even predict the likelihood of specific patterns. Three examples are discussed: (1) alignment of enamel cells in the rat incisor, (2) quantitation of invasive capacity of one cell-type with oespect to another, and (3) sorting-out of two cell-types.