论文标题
有条件的弗莱明 - 维奥特和道森 - 瓦特纳布扩散的平滑分布
Smoothing distributions for conditional Fleming-Viot and Dawson-Watanabe diffusions
论文作者
论文摘要
我们研究了Fleming-Viot和Dawson-Watanabe类型的两个度量值扩散的未观察状态的分布，这是基于过去，现在和未来收集的基础种群的观察。如果被视为非参数隐藏的马尔可夫模型，则等于找到这些过程的平滑分布，我们表明的可以分别以递归形式将其显式描述为Dirichlet和Gamma随机测量法则的有限混合物。我们表征了这些混合物的时间相关权重，考虑了数据收集时间之间的潜在时间间隔，并充分描述了假设离散或非原子分布对驱动突变的基础过程的含义。特别是，我们表明，通过非原子突变后代分布，推理自动上行混合物组件，这些混合物成分（作为原子）在不同的收集时间上共享的类型。还确定了来自数据条件下的人口的进一步样本的预测分布，并证明是广义polya urns的混合物，有条件地是在道森 - 瓦塔纳布案中的潜在变量上。
We study the distribution of the unobserved states of two measure-valued diffusions of Fleming-Viot and Dawson-Watanabe type, conditional on observations from the underlying populations collected at past, present and future times. If seen as nonparametric hidden Markov models, this amounts to finding the smoothing distributions of these processes, which we show can be explicitly described in recursive form as finite mixtures of laws of Dirichlet and gamma random measures respectively. We characterize the time-dependent weights of these mixtures, accounting for potentially different time intervals between data collection times, and fully describe the implications of assuming a discrete or a nonatomic distribution for the underlying process that drives mutations. In particular, we show that with a nonatomic mutation offspring distribution, the inference automatically upweights mixture components that carry, as atoms, observed types shared at different collection times. The predictive distributions for further samples from the population conditional on the data are also identified and shown to be mixtures of generalized Polya urns, conditionally on a latent variable in the Dawson-Watanabe case.
