The Statistical Analysis of Spatial Pattern, 1975 Ettore Majorana International Science Series, Vol. 15

In a contribution (Bartlett, 1971 a) to the Symposium on Statistical Ecology at Yale in 1969, I noted in my introductory remarks that that paper was not intended to be in any way a review of statistical techniques for analysing spatial patterns. My contribution to a conference at Sheffield in 1973 aimed, at least in part, to supply such a review and forms the basis of this monograph; but in these prefatory remarks I must still make clear what I decided to discuss, and what I have omitted. Broadly speaking, the coverage is that included in seminars and lectures I have given on this theme since 1969. We may divide problems of spatial pattern (in contrast with complete random chaos) into (i) detecting departures from randomness, Oi) analysing such departures when detected, for example, in relation to some stochastic model and (iii) special problems which require separate consideration; for example, sophisticated problems of pattern recognition in specific fields, such as the computer reading of handwriting or recognition of chromosomes.

I Survey of underlying theory.- 1 Continuous, point and line processes.- 1.1 Continuous processes X(r). Autocorrelation and spectral theory.- 1.2 Point processes N(r). Some specific models and their distributional theory.- 1.2.1 Spectral theory.- 1.2.2 Contagion and inhibitory models.- 1.3 Line processes.- 2 Nearest-neighbour systems on a lattice.- 2.1 Lattice processes Xi. Continuous variables. Conditional and simultaneous systems.- 2.1.1 Markov fields in continuous space.- 2.2 Binary and other discrete variables.- 2.2.1 The auto-logistic model.- 2.2.2 Sub-critical ‘temperatures’.- 2.3 General specification of conditional lattice systems.- 2.3.1 Spatial-temporal processes for other auto-schemes.- II Examples of statistical analyses.- 3 Analyses of continuous and point processes.- 3.1 Continuous processes X(r). Pielou’s example.- 3.2 Point processes. A simulated clustering model. X2 analyses. Mead’s randomization test.- 3.2.1 Spectral analysis.- 3.2.2 Nearest-neighbour distances between gulls’ nests.- 3.3 Line processes.- 4 Analyses of processes on a lattice.- 4.1 Lattice processes Xi. Continuous variables. Examples using simultaneous and conditional models.- 4.2 Discrete variables. Simple X2 analyses. Further analyses and examples.- Appendix Tables AI and AII.- References.