Large-scale inference of correlation among mixed-type biological traits with phylogenetic multivariate probit models

Inferring concerted changes among biological traits along an evolutionary history remains important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, task also requires sufficient flexibility and computational efficiency to incorporate multiple continuous discrete as data size increases. To accomplish this, we jointly model mixed-type by assuming latent parameters binary outcome dimensions at tips of unknown tree informed molecular sequences. This gives rise a phylogenetic multivariate probit model. With large sample sizes, posterior computation under this is problematic, it repeated sampling high-dimensional truncated normal distribution. Current best practices employ multiple-try rejection that suffers slow-mixing cost scales quadratically in size. We develop new inference approach exploits: (1) bouncy particle sampler (BPS) based on piecewise deterministic Markov processes simultaneously all dimensions, (2) novel dynamic programming reduces likelihood gradient evaluations BPS linear In application with 535 HIV viruses 24 necessitates 12,840-dimensional normal, our method makes possible estimate across-trait detect factors affect pathogen’s capacity cause disease. framework applicable broader class covariance structures beyond comparative biology.