Unified Mixture Sampler for State-Space Models: Application to Stochastic Conditional Duration Models

2026-04-06

AI Summary

This study addresses the challenge of efficient Bayesian inference in nonlinear state-space models with unknown shape parameters—such as those involving Weibull or Gamma distributions—where the “exp-exp” likelihood kernel impedes tractable computation. To overcome this, the authors propose a Unified Mixture Sampler (UMS) that leverages the ten-component Gaussian mixture approximation of Omori et al. (2007), augmented with a deterministic recentering-and-scaling algorithm to dynamically update mixture components during MCMC iterations. A lightweight Metropolis–Hastings correction ensures validity without compromising efficiency. UMS eliminates the need for distribution-specific approximations and, for the first time, enables generic, accurate, and computationally efficient Bayesian inference across Logit, Poisson, and various stochastic conditional duration (SCD) models. Compared to conventional slice sampling, UMS substantially reduces posterior sample autocorrelation while maintaining high inferential accuracy.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• state-space models
• stochastic conditional duration
• exp-exp likelihood
• shape parameters
• MCMC sampling

Innovation

• Unified Mixture Sampler
• State-Space Models
• Exp-Exp Likelihood
• MCMC Efficiency
• Adaptive Mixture Approximation