Karppinen Santeri, Vihola Matti
Department of Mathematics and Statistics, University of Jyväskylä, 40014 Jyväskylä, Finland.
Stat Comput. 2021;31(3):24. doi: 10.1007/s11222-020-09975-1. Epub 2021 Mar 3.
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.
The online version contains supplementary material available at 10.1007/s11222-020-09975-1.
条件粒子滤波器（CPF）是用于一般非线性/非高斯隐马尔可夫模型的强大平滑算法。然而，CPF 在处理扩散初始分布时可能效率低下或难以应用，而扩散初始分布在统计应用中很常见。我们提出了一种简单但普遍适用的辅助变量方法，该方法可与 CPF 一起使用，以便在扩散初始分布下进行高效推断。该方法仅需要相对于初始分布可逆的可模拟马尔可夫转移，初始分布可以是不合适的。我们特别关注相对于均匀初始分布（在某个域上）可逆的随机游走类型转移，以及高斯初始分布的自回归核。我们建议在这些方法中使用在线自适应。在随机游走转移的情况下，我们的自适应使用估计的协方差和接受率自适应，并详细说明了它们的理论有效性。我们用线性高斯随机游走模型、随机波动率模型和具有时变传播率的随机流行病 compartment 模型测试了我们的方法。实验结果表明，我们的方法在几乎不需要用户指定的情况下可靠地工作，并且比将初始状态视为参数的直接粒子吉布斯算法具有更好的混合效果。
在线版本包含可在 10.1007/s11222-020-09975-1 获得的补充材料。
