  The combinatorial sequential Monte Carlo (CSMC) has been demonstrated to be
an efficient complementary method to the standard Markov chain Monte Carlo
(MCMC) for Bayesian phylogenetic tree inference using biological sequences. It
is appealing to combine the CSMC and MCMC in the framework of the particle
Gibbs (PG) sampler to jointly estimate the phylogenetic trees and evolutionary
parameters. However, the Markov chain of the particle Gibbs may mix poorly if
the underlying SMC suffers from the path degeneracy issue. Some remedies,
including the particle Gibbs with ancestor sampling and the interacting
particle MCMC, have been proposed to improve the PG. But they either cannot be
applied to or remain inefficient for the combinatorial tree space. We introduce
a novel CSMC method by proposing a more efficient proposal distribution. It
also can be combined into the particle Gibbs sampler framework to infer
parameters in the evolutionary model. The new algorithm can be easily
parallelized by allocating samples over different computing cores. We validate
that the developed CSMC can sample trees more efficiently in various particle
Gibbs samplers via numerical experiments. Our implementation is available at
https://github.com/liangliangwangsfu/phyloPMCMC
