Model selection for a class of stochastic processes or random fields with bounded range

Methods are developed for finding an optimal model for a non-Gaussian stationary stochastic process or homogeneous random field under limited information. The available information consists of: (i) one or more finite length samples of the process or field; and (ii) knowledge that the process or field takes values in a bounded interval of the real line whose ends may or may not be known. The methods are developed and applied to the special case of non-Gaussian processes or fields belonging to the class of beta translation processes. Beta translation processes provide a flexible model for representing physical phenomena taking values in a bounded range, and are therefore useful for many applications. Numerical examples are presented to illustrate the utility of beta translation processes and the proposed methods for model selection.