Correlated Functional Models with Derivative Information for Modeling Microfading Spectrometry Data on Rock Art Paintings

Rock art paintings present high sensitivity to light, and an exhaustive evaluation of the potential color degradation effects is essential for further conservation and preservation actions on these rock art systems. Microfading spectrometry (MFS) is a technique that provides time series of stochastic observations that represent color fading over time at the measured points on the surface under study. In this work, a reliable and robust modeling framework for a short and greatly fluctuating observation dataset collected over the surfaces of rock art paintings located on the walls of Cova Remigia in Ares del Maestrat, Castellon, Spain, is presented. The model is based on a spatially correlated spline-based time series model that takes into account prior information in the form of model derivatives to guarantee monotonicity and long-term saturation for predictions of new color fading estimates at unobserved locations on the surface. The correlation among the (spatially located) time series is modeled by defining Gaussian process (GP) priors over the spline coefficients across time series. The goal is to obtain a complete spatio-temporal mapping of color fading estimates for the study area, which results in very important and useful information that will potentially serve to create better policies and guidelines for heritage preservation and sustainable rock art cultural tourism.