rft1d: Smooth one-dimensional random field upcrossing probabilities in Python

Abstract

Through topological expectations regarding smooth, thresholded n-dimensional Gaussian continua, random field theory (RFT) describes probabilities associated with both the field-wide maximum and threshold-surviving upcrossing geometry. A key application of RFT is a correction for multiple comparisons which affords field-level hypothesis testing for both univariate and multivariate fields. For unbroken isotropic fields just one parameter in addition to the mean and variance is required: the ratio of a field’s size to its smoothness. Ironically the simplest manifestation of RFT (1D unbroken fields) has rarely surfaced in the literature, even during its foundational development in the late 1970s. This Python package implements 1D RFT primarily for exploring and validating RFT expectations, but also describes how it can be applied to yield statistical inferences regarding sets of experimental 1D fields.