Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient flexibility and computational efficiency to incorporate multiple continuous and discrete traits as data size increases. To accomplish this, we jointly model mixed-type traits by assuming latent parameters for binary outcome dimensions at the tips of an unknown tree informed by molecular sequences. This gives rise to a phylogenetic multivariate probit model. With large sample sizes, posterior computation under this model is problematic, as it requires repeated sampling from a high-dimensional truncated normal distribution. Current best practices employ multiple-try rejection sampling that suffers from slow-mixing and a computational cost that scales quadratically in sample size. We develop a new inference approach that exploits: (1) the bouncy particle sampler (BPS) based on piecewise deterministic Markov processes to simultaneously sample all truncated normal dimensions, and (2) novel dynamic programming that reduces the cost of likelihood and gradient evaluations for BPS to linear in sample size. In an application with 535 HIV viruses and 24 traits that necessitates sampling from a 12,840-dimensional truncated normal, our method makes it possible to estimate the across-trait correlation and detect factors that affect the pathogen’s capacity to cause disease. This inference framework is also applicable to a broader class of covariance structures beyond comparative biology.
We thank Oliver Pybus for useful discussions on an earlier version of the data set analyzed here. The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 725422—ReservoirDOCS). The Artic Network receives funding from the Wellcome Trust through project 206298/Z/17/Z. PB acknowledges support by the Research Foundation—Flanders (“Fonds voor Wetenschappelijk Onderzoek—Vlaanderen,” 12Q5619N and V434319N). MAS acknowledges support through NSF grant DMS 1264153 and NIH grants R01 AI107034 and U19 AI135995. PL acknowledges support by the Research Foundation—Flanders (“Fonds voor Wetenschappelijk Onderzoek—Vlaanderen,” G066215N, G0D5117N and G0B9317N).
"Large-scale inference of correlation among mixed-type biological traits with phylogenetic multivariate probit models." Ann. Appl. Stat. 15 (1) 230 - 251, March 2021. https://doi.org/10.1214/20-AOAS1394