Novel Bayesian Procrustes Variance-based Analysisin Geometric Morphometrics (Part 1)

Procrustes shape analysis is an essential sub-discipline under Geometric Morphometrics. Compared to classical statistics-based literature, very little Bayesian literature exists for any sub-discipline of Geometric Morphometrics. This paper takes a novel Bayesian approach for considerable advantages of Bayesian over classical. This paper presents a novel Bayesian Procrustes shape analysis methodology for shape parameter distributions (part 1: 2D landmark data & isotropic variance assumption of landmark data). Here we consider the posterior of Procrustes shape variance as morphological variability indicators, which is on par with various laws of mathematical population genetics like Hardy-Weinberg law (Stern, 1943; Masel, 2012). The proposed Bayesian approach does not require any PCA (Principal component analysis) type approximations. This paper also proposes novel Bayesian statistical tests for model validation of new species discovery using morphological variation reflected in the posterior distribution of landmark-variance objects studied under Geometric Morphometrics. We applied our proposed Bayesian Procrustes Analysis on “apes” data of O’Higgins and Dryden (1993). We compared the posterior variance of the shape of females vs. males for each of the Gorillas, chimpanzees, and orangutans. The statistical conclusion favors the novel hypothesis on face shape: “ male primate manifests more fluctuation in face shape than females ,” which suggests further research in the future. All the computations and R code done in this paper are organized into a novel, simple R package BPviGM1 (”Bayesian Procrustes Variance-based inferences in Geometric Morphometrics 1”) kept in Github, which essentially contains the R code implementations of the computations for proposed models and methodologies.