The theory of search from a statistical viewpoint

Summary The statistical approach to search is a subject which interfaces with many other fields. This work continues a series of papers which studies these relationship with special emphasis on geometric problems in non-sequential search. A targetT is sought using a series of testsX ₁,X ₂.... From each test there is an observationY _i=f(X _i , θ), where θ is an unknown parameter andT=T(θ). Spacing theories and the theories of Voronoi regions can be used to represent the solutions to Bayes and entropy-based formulations to the search problem by partitioning the search field intoconsistent regions where the target is known to lie, given the observations. Other examples are from integration where the target is a function. Covering theory is studied and the last section gives a brief comparison with a sequential approach. Read before the Spanish Statistical Society at a meeting organized by the Universidad de Almería on Friday, April 29, 1994