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.

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 可能效率低下或难以应用于分散初始分布，这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，它可以与 CPF 一起使用，以便对扩散初始分布进行有效推理。该方法只需要相对于初始分布可逆的可模拟马尔可夫转换，这可能是不正确的。我们特别关注对于均匀初始分布（在某些域上）是可逆的随机游走类型转换，以及用于高斯初始分布的自回归核。我们建议在方法中使用在线改编。在随机游走转换的情况下，我们的适应使用估计的协方差和接受率适应，我们详细说明了它们的理论有效性。我们使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隔间模型测试了我们的方法。实验结果表明，我们的方法在几乎没有用户规范的情况下可靠地工作，并且可以比将初始状态视为参数的直接粒子吉布斯算法更好地混合。以及具有时变传播率的随机流行病隔间模型。实验结果表明，我们的方法在几乎没有用户规范的情况下可靠地工作，并且可以比将初始状态视为参数的直接粒子吉布斯算法更好地混合。以及具有时变传播率的随机流行病隔间模型。实验结果表明，我们的方法在几乎没有用户规范的情况下可靠地工作，并且可以比将初始状态视为参数的直接粒子吉布斯算法更好地混合。