Some considerations on significance analysis for deformation detection via frequentist and Bayesian tests

Abstract

The Bayesian approach to significance testing, that makes use of prior information, has been studied in the last years, particularly to allow the detection of deformations which are small with respect to measurement errors from repeated surveys. Some investigations showed up to now that, under particular conditions concerning both the parameters of the prior distribution and the structure of the control network, Bayesian tests give stronger results than tests based on the frequentist approach, with regard to the detectability of deformations. In the present paper, after illustrating the essential developments and the most relevant results of previous works, new analytical developments and numerical simulations are carried out, to illustrate some critical aspects and advantages of the frequentist and Bayesian methods. It is shown, starting from simple examples involving only Gaussian and truncated Gaussian distributions and from a simplified formulation of the prior deformation model, that the testing procedures based on the frequentist approach, which do not introduce any a priori information, are in many cases of practical interest insensitive to internal consistencies of the displacements (e.g., to the fact that they have a common direction). It is also illustrated that the introduction of prior information, even in a non Bayesian context, more easily allows the detection of little displacements. Besides it is noted that in some cases Bayesian tests detect displacements in the presence of observed non-coherent movements, even if prior probability densities describing coherent movements are introduced.