Order restricted inference in chronobiology

Abstract

This paper is motivated by applications in oscillatory systems where researchers are typically interested in discovering components of those systems that display rhythmic temporal patterns. The contributions of this paper are twofold. First, a methodology is developed based on a circular signal plus error model that is defined using order restrictions. This mathematical formulation of rhythmicity is simple, easily interpretable and very flexible, with the latter property derived from the nonparametric formulation of the signal. Second, we address various commonly encountered problems in the analysis of oscillatory systems data. Specifically, we propose a methodology for (a) detecting rhythmic signals in an oscillatory system and (b) estimating the unknown sampling time that occurs when tissues are obtained from subjects whose time of death is unknown. The proposed methodology is computationally efficient, outperforms the existing methods, and is broadly applicable to address a wide range of questions related to oscillatory systems.

Statistical methodology and software to analyse oscillatory signals with applications to biology

“…Since the order dened by C is not a closed convex cone, the derivation of Y is non-trivial (Robertson et al (1988)). In Larriba et al (2020), a computationally ecient IR-based algorithm is designed to derive Y . Point estimators for t U and t L can be immediately derived from that algorithm as the point estimation of the indexes U and L.…”

“…Altough TSP has not an exact solution, there are several heuristic procedures, many of them implemented in R, which provide accurate approximate solutions to this problem (Hahsler and Hornik (2007)). Moreover, relative eciency rates of agreement (RRE), between a circular order and a data set, and concordance (C RE), between two circular orders are dened in Larriba et al (2020) to validate the procedure.…”

“…Finalmente, Larriba et al (2020) presenta el marco teórico general, basado en metodología ORI, para el análisis de datos en cronobiología, y puede considerarse la contribución más importante de la tesis. En concreto, se establece la denición rigurosa de señal circular, utilizando restricciones de orden tanto en el espacio Euclídeo como en el espacio circular y se propone un modelo estadístico de señal circular más ruido para el análisis de señales rítmicas.…”

“…Larriba et al (2020) is the most relevant contribution of this thesis. Going an step further, it states a general statistical framework, based on ORI methodology, to formulate, interpret and solve crucial rhythmicity related issues in chronobiology.…”

“…Even more, CYCLOPS reordered expressions might be identied as non-rhythmic ones which may lead biologists to wrong conclusions. Full detailed results are given in the Result Section ofLarriba et al (2020). The R-based software developed to perform the analyses in this paper is available upon request since a full R-package including, among others the ORI-based methodology described here, is being developed by the authors.…”