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

Zhenyu Zhang, Akihiko Nishimura, Paul Bastide, Xiang Ji, Rebecca P. Payne, Philip Goulder, Philippe Lemey, Marc A. Suchard

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 quadrati-cally 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 dis-ease. This inference framework is also applicable to a broader class of covari-ance structures beyond comparative biology.

Original languageEnglish (US)
Pages (from-to)230-251
Number of pages22
JournalAnnals of Applied Statistics
Issue number1
StatePublished - 2021


  • Bayesian phylogenetics
  • Bouncy particle sampler
  • Dynamic program-ming
  • HIV evolution
  • Probit models

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty


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