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.

中文翻译：

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用于不完整生死记录贝叶斯推断的整数网格桥采样器

生死过程的桥路空间与单纯形和整数网格的乘积空间的排他并集之间建立了一一对应的关系。推导出具有固定向上跳跃次数的整数网格桥的精确计数公式。然后在这种受限的桥路空间上构建一个统一的采样器。这导致蒙特卡洛方案，整数网格桥采样器，IGBS，来评估生死过程的转移概率。即使是罕见事件的近乎零概率现在也可以用受控的相对误差进行评估。基于 IGBS 的不完整出生-死亡观察的贝叶斯推断在演示示例和分析记录真实流行病事件的严重不完整数据集时很容易执行。使用基本自举过滤器（一种基本的顺序重要性重采样算法）进行比较。令人困扰的过滤失败在新方案中没有找到位置。