Studying Traits Relationship in Randomly Evolving Environment using non-Gaussian type Statistical Model: an Approximate Bayesian Computation Approach

• Main Authors: LAI, YEN-SHUO, 賴彥碩
• Other Authors: JHWUENG, DWUENG-CHWUAN
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/49e3k2

碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 106 === In biology, phylogenetics studies evolution history and relationship among groups of organisms. Among many methods used in phylogenetics, phylogenetic comparative method (PCM) is one of statistical method for the inference of biological evolution. PCM mainly uses a given phylogenetic tree and evolutionary assumption of trait evolution to reveal evolutionary information such a rate of evolution, a strength of the force, and optimum. Given a phylogenetic tree, assuming that the trait evolution follows a certain stochastic process, the statistical method is derived through given evolutionary conditions. In this study, we will use Brownian motion (BM), Ornstein-Uhlenbeck process (OU) and Cox-Ingersoll-Ross model(CIR) to build four non-Gaussian statistical models called OUBMBM, OUOUBM, OUBMCIR, and OUOUCIR, respectively. We then use the Approximate Bayesian Computation(ABC) approach to estimate model parameters. We conduct simulation and prose algorithm to validate our models as well as use Bayes factor to compare models using empirical datasets. Key words: Brownian motion (BM); Ornstein Uhlenbeck process(OU); Cox Ingersoll Ross model(CIR); stochastic differential equations(SDE); Approximate Bayesian Computation(ABC); Bayes Factor