Traversing binary trees simply and cheaply

Over the past decades, Gaussian processes have been widely used to study trait evolution. In particular, two members of Gaussian processes, Brownian motion and the Ornstein–Uhlenbeck process, have been frequently applied for describing continuous trait evolution. Several models (OUBM, OUOU, OUBMBM, OUOUBM) have been proposed to study the impact on the optimum of a trait by other traits. Applying the Cox–Ingersoll–Ross (CIR) process on rate of evolution, which prevents rates from becoming negative, is a potentially useful extension developed here as the OUBMCIR and OUOUCIR models. Since the likelihood functions of the OUBMCIR and the OUOUCIR models are intractable, a heuristic algorithm for parameter estimation and inference under Approximate Bayesian Computation (ABC) is proposed. Simulation studies show that new models perform well. Empirical analysis using several data sets from literature also provides evidence of the validity and utility of the new models. The relevant data sets and R scripts developed for this project can be accessed through the link.1