Bayesian phylogenetics without sampling

Bayesian phylogenetic (evolutionary tree) inference is important for genomic epidemiology and for our understanding of evolution. Although sampling-based methods such as random-walk Markov Chain Monte Carlo have been the engine of Bayesian phylogenetics for decades, we think there are opportunities. In analogy to the way we infer trees via maximum likelihood, Bayesian phylogenetic (evolutionary tree) inference is important for genomic epidemiology and for our understanding of evolution. Trees, along with associated information, are complicated objects of inference, with intertwined discrete (tree structure) and continuous (dates, rates) structure. Random-walk Markov Chain Monte Carlo, implemented in packages such as [BEAST](http://beast.community/) (~20,000 citations) and [MrBayes](http://nbisweden.github.io/MrBayes/) (>70,000 citations), is currently the only widely-applied inference technique. We have recently [developed a rich means of parameterizing tree distributions](https://matsen.fredhutch.org/general/2018/12/05/sbn.html) with a fixed parameter set. This renders them accessible to more modern inference techniques, such as variational Bayes. We [have developed a proof-of-concept application of phylogenetic variational Bayes](https://matsen.fredhutch.org/general/2019/08/24/vbpi.html) using modern general-purpose gradient estimators. Our collaborative group also has preliminary integrations with both PyTorch and TensorFlow.