论文标题
有效的贝叶斯估计和使用半疗法的马尔可夫模型中切割后验
Efficient Bayesian estimation and use of cut posterior in semiparametric hidden Markov models
论文作者
论文摘要
我们考虑具有有限状态空间和非参数排放分布的隐藏马尔可夫模型中的估计问题。展示了过渡矩阵的有效估计器，并推导了半参数伯恩斯坦 - 冯·米斯的结果。之后，我们提出了一种使用切割后部的模块化方法，以共同估计过渡矩阵和发射密度。我们在这种方法的收缩率上得出了一般定理。然后，我们展示如何应用该结果来获得我们环境中排放密度的收缩率结果；一个关键的中间步骤是倒置不平等，将边际密度与$ l^1 $之间的距离之间的距离$ l^1 $。最后，显示了平滑概率的收缩结果，这避免了样品分裂的常见方法。提供了仿真，既证明了理论及其实施的便利性。
We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is deduced. Following from this, we propose a modular approach using the cut posterior to jointly estimate the transition matrix and the emission densities. We derive a general theorem on contraction rates for this approach. We then show how this result may be applied to obtain a contraction rate result for the emission densities in our setting; a key intermediate step is an inversion inequality relating $L^1$ distance between the marginal densities to $L^1$ distance between the emissions. Finally, a contraction result for the smoothing probabilities is shown, which avoids the common approach of sample splitting. Simulations are provided which demonstrate both the theory and the ease of its implementation.
