Novel Bayesian Procrustes Variance-based Inferences in Geometric Morphometrics & Novel R package: BPviGM1

Abstract

Compared to abundant classical statistics-based literature, to date, very little Bayesian literature exists on Procrustes shape analysis in Geometric Morphometrics, probably because of being a relatively new branch of statistical research and because of inherent computational difficulty associated with Bayesian analysis. Moreover, we may obtain a plethora of novel inferences from Bayesian Procrustes analysis of shape parameter distributions. In this paper, we propose to regard the posterior of Procrustes shape variance as morphological variability indicators. Here we propose novel Bayesian methodologies for Procrustes shape analysis based on landmark data's isotropic variance assumption and propose a Bayesian statistical test for model validation of new species discovery using morphological variation reflected in the posterior distribution of landmark-variance of objects studied under Geometric Morphometrics. We will consider Gaussian distribution-based and heavy-tailed t distribution-based models for Procrustes analysis. To date, we are not aware of any direct R package for Bayesian Procrustes analysis for landmark-based Geometric Morphometrics. Hence, we introduce a novel, simple R package \textbf{BPviGM1} ("Bayesian Procrustes Variance-based inferences in Geometric Morphometrics 1"), which essentially contains the R code implementations of the computations for proposed models and methodologies, such as R function for Markov Chain Monte Carlo (MCMC) run for drawing samples from posterior of parameters of concern and R function for the proposed Bayesian test of model validation based on significance morphological variation. As an application, we can quantitatively show that primate male-face may be genetically viable to more shape-variation than the same for females.