标题： 基于Bayesian非参数推断的$Λ$-合并：一致性和参数方法 显示英文标题

标题： Bayesian non-parametric inference for $Λ$-coalescents: consistency and a parametric method

摘要： 我们研究了带有复发性突变的$\Lambda$- 测度的$\Lambda$- 凝聚过程的贝叶斯非参数推断问题，这些过程由单位区间上的概率测度参数化。当观测值形成时间序列时，我们给出了先验的一组可验证的标准以保证后验一致性，并证明当所有观测值同时发生时，任何非平凡的先验都是不一致的。接着，我们表明对于大小为$n \in \mathbb{N}$的数据集，似然函数在那些首项$n - 2$矩相同的$\Lambda$- 测度上是常数，并集中于推断截断矩序列。我们提供了一大类可以通过可信区间的后验截断矩序列进行有限计算极值化的泛函，并提出了一种伪边缘马尔科夫-黑斯廷斯算法用于抽样后验分布。最后，我们通过模拟研究比较了精确和噪声伪边缘算法在使用和不使用延迟接受加速情况下的效率。 显示英文摘要

摘要： We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for posterior consistency when observations form a time series, and prove that any non-trivial prior is inconsistent when all observations are contemporaneous. We then show that the likelihood given a data set of size $n \in \mathbb{N}$ is constant across $\Lambda$-measures whose leading $n - 2$ moments agree, and focus on inferring truncated sequences of moments. We provide a large class of functionals which can be extremised using finite computation given a credible region of posterior truncated moment sequences, and a pseudo-marginal Metropolis-Hastings algorithm for sampling the posterior. Finally, we compare the efficiency of the exact and noisy pseudo-marginal algorithms with and without delayed acceptance acceleration using a simulation study.