We propose a unified mixture sampler (UMS) that provides a universal estimation framework for nonlinear state-space models with "exp-exp" likelihood kernels. Unlike existing methods that require deriving new mixture approximations for each specific distribution, our approach dynamically adapts the standard ten-component mixture from Omori et al. (2007) through a deterministic re-centering and rescaling algorithm. Applying this to the stochastic conditional duration (SCD) model, we demonstrate that the proposed sampler can efficiently handle unknown shape parameters - such as those in Weibull or Gamma distributions - by updating mixture components near-instantaneously during MCMC iterations. The UMS not only simplifies implementation but also ensures exact inference via a lightweight Metropolis-Hastings step. Numerical examples show that our method substantially outperforms the conventional slice sampling approach, significantly reducing autocorrelation in MCMC samples while maintaining high computational efficiency. This unified framework encompasses a wide range of applications, including logit, Poisson, and various SCD model specifications, providing a highly efficient alternative to model-specific samplers.

翻译：我们提出了一种统一混合采样器（UMS），它为具有“exp-exp”似然核的非线性状态空间模型提供了一个通用估计框架。与现有方法需要针对每个特定分布推导新的混合近似不同，我们的方法通过确定性重新定心和重新缩放算法，动态调整Omori等人（2007）的标准十分量混合。将该方法应用于随机条件持续时间（SCD）模型，我们证明所提出的采样器能够高效处理未知形状参数——例如威布尔分布或伽马分布中的参数——通过在马尔可夫链蒙特卡洛（MCMC）迭代过程中近乎瞬时地更新混合分量。UMS不仅简化了实现，还通过轻量级Metropolis-Hastings步骤确保了精确推断。数值示例表明，我们的方法显著优于传统的切片采样方法，在保持高计算效率的同时大幅降低了MCMC样本的自相关性。这一统一框架涵盖了广泛的应用，包括logit、泊松以及各种SCD模型规范，为模型特定采样器提供了一种高效替代方案。