Phylogenetic comparative methods are a set of statistical methods that model the evolutionary history of species, especially in the context where one has data on certain traits of related extant species that have evolved over a phylogenetic tree in accordance to an underlying stochastic process. This thesis presents a Hessian-based closed-form asymptotic confidence region that covers a wide family of Gaussian continuous-trait evolution models; the result has been implemented in an R package. Also, some analyses have been done on the simpler Brownian Motion and Ornstein-Uhlenbeck process cases; and this leads to novel exact confidence regions for the Brownian Motion’s parameters and a closed-form ’partial’ unbiased estimator for the Ornstein-Uhlenbeck process’ varaince-covariance matrix when other parameters are given. The thesis contains two papers. Paper I is an applied work that uses discrete-trait speciation and extinction model to investigate early spread of COVID-19; it shows that it is possible to detect statistical signals of inter-continental spread of the virus from a very noisy world-wide phylogeny. Paper II is a more mathematical work that derived the closed-form formulae for the Hessian matrix of a wide family of Gaussian-process-based multivariate continuous-trait PCM models; accompanying with the Paper I have developed an R package called glinvci, publicly available on The Comprehensive R Archive Network (CRAN), that can compute Hessian-based confidence regions for these models while at the same time allowing users to have missing data and multiple evolutionary regimes. / <p><strong>Funding:</strong> Vetenskapsrådet [Grant 2017-04951] and STIMA.</p><p>2024-04-05: Series have been corrected in the e-version</p><p></p>
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-201907 |
| Date | January 2024 |
| Creators | Kiang, Woodrow Hao Chi |
| Publisher | Linköpings universitet, Statistik och maskininlärning, Linköpings universitet, Filosofiska fakulteten, Linköping |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, comprehensive summary, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | FiF-avhandling - Filosofiska fakulteten – Linköpings universitet, 1401-4637 ; 134 |
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