通过离散对偶过程进行近似滤波
Approximate filtering via discrete dual processes
AI总结：
本文研究了扩散与离散状态空间马尔可夫链的对偶性，提出在Cox-Ingersoll-Ross和Wright-Fisher扩散驱动的隐马尔可夫模型中应用近似滤波策略，并与精确策略和粒子滤波基准进行比较。
摘要：
我们考虑对一个作为扩散过程演化的动态参数进行滤波的任务，给定在离散时刻从与扩散边际律共轭的似然中收集的数据，且存在一个离散状态空间上的通用对偶过程。最近的研究表明，相对于一个类死亡过程的对偶性意味着滤波分布是有限混合，使得通过在观测数量上具有多项式复杂度的递归算法进行精确滤波和平滑变得可行。在此，我们针对扩散与离散状态空间上的正则跳跃连续时间马尔可夫链之间的对偶情况提供了通用结果，这通常导致滤波分布由以对偶过程状态空间为索引的可数混合给出。我们研究了在由 Cox-Ingersoll-Ross 和 Wright-Fisher 扩散驱动的两个隐马尔可夫模型上几种近似策略的性能，这些模型允许生灭类型的对偶，并将它们与基于死亡类型对偶的可用精确策略以及作为通用基准的扩散状态空间上的自举粒子滤波进行了比较。
英文摘要：
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case of duality between the diffusion and a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox-Ingersoll-Ross and Wright-Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
