论文标题
用于不完整的出生死亡记录的贝叶斯推断的整数网格桥采样器
An integer grid bridge sampler for the Bayesian inference of incomplete birth-death records
论文作者
论文摘要
在出生死亡过程的桥梁路径空间与单纯形和整数网格的产品空间的独家联合之间建立了一对一的对应关系。公式是为具有固定数量向上跳跃的整数网格桥的确切计数而得出的。然后构建了在这种受限的桥梁路径空间上的均匀采样器。这导致了蒙特卡洛方案，即整数网格桥采样器IGB，以评估出生死亡过程的过渡概率。现在，即使是罕见事件的接近零概率也可以通过受控的相对误差进行评估。基于IGB的贝叶斯对不完整的出生死亡观测值的推断很容易在演示示例和分析严重不完整的数据集的分析中记录真实流行病事件。比较使用基本的Bootstrap滤波器，这是一种基本的顺序重要性重采样算法。令人困扰的过滤故障在新方案中没有发现任何位置。
A one-to-one correspondence is established between the bridge path space of birth-death processes and the exclusive union of the product spaces of simplexes and integer grids. Formulae are derived for the exact counting of the integer grid bridges with fixed number of upward jumps. Then a uniform sampler over such restricted bridge path space is constructed. This leads to a Monte Carlo scheme, the integer grid bridge sampler, IGBS, to evaluate the transition probabilities of birth-death processes. Even the near zero probability of rare event could now be evaluated with controlled relative error. The IGBS based Bayesian inference for the incomplete birth-death observations is readily performed in demonstrating examples and in the analysis of a severely incomplete data set recording a real epidemic event. Comparison is performed with the basic bootstrap filter, an elementary sequential importance resampling algorithm. The haunting filtering failure has found no position in the new scheme.
