Unified mixture sampler for state–space models: Application to stochastic conditional duration models

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 a 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 and Poisson models, as well as various SCD model specifications, providing a highly efficient alternative to model-specific samplers.