Sampling a probability distribution with known likelihood is a fundamental
task in computational science and engineering. Aiming at multimodality, we
propose a new sampling method that takes advantage of both birth-death process
and exploration component. The main idea of this method is \textit{look before
you leap}. We keep two sets of samplers, one at warmer temperature and one at
original temperature. The former one serves as pioneer in exploring new modes
and passing useful information to the other, while the latter one samples the
target distribution after receiving the information. We derive a mean-field
limit and show how the exploration process determines sampling efficiency.
Moreover, we prove exponential asymptotic convergence under mild assumption.
Finally, we test on experiments from previous literature and compared our
methodology to previous ones.

提出一种新的基于出生死亡过程和探索组件的采样方法，该方法巧妙地利用温度较高的样本集来探索新模式并传递信息，以提高采样效率，并在之前的文献实验中进行了比较和测试。

使用 Birth-Death 过程和探索组件加速 Langevin 采样

Accelerate Langevin Sampling with Birth-Death process and Exploration  Component

Binary trait data record the presence or absence of distinguishing traits in
individuals. We treat the problem of estimating ancestral trees with time depth
from binary trait data. Simple analysis of such data is problematic. Each
homology class of traits has a unique birth event on the tree, and the birth
event of a trait visible at the leaves is biased towards the leaves. We propose
a model-based analysis of such data, and present an MCMC algorithm that can
sample from the resulting posterior distribution. Our model is based on using a
birth-death process for the evolution of the elements of sets of traits. Our
analysis correctly accounts for the removal of singleton traits, which are
commonly discarded in real data sets. We illustrate Bayesian inference for two
binary-trait data sets which arise in historical linguistics. The Bayesian
approach allows for the incorporation of information from ancestral languages.
The marginal prior distribution of the root time is uniform. We present a
thorough analysis of the robustness of our results to model mispecification,
through analysis of predictive distributions for external data, and fitting
data simulated under alternative observation models. The reconstructed ages of
tree nodes are relatively robust, whilst posterior probabilities for topology
are not reliable.

通过 Bayesian 方法，提出一种基于出现历史性状的二元数据，从中估计具有时间深度的祖先树的模型分析，该方法基于出现历史性状的重要类别 (homology classes)，并使用基于一种出生死亡过程 (birth-death process) 的模型来构建。