arXiv 6 Apr 2026 · Statistics — Methodology
arXiv:2604.04517 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | de Jong, Piet and Shephard, Neil (1995) The simulation smoother for time series models | 0.843 | 3 | 3 | 100% |
| 2 | Durbin, James and Koopman, Siem Jan (2002) A simple and efficient simulation smoother for state space time series analysis | 0.843 | 3 | 3 | 100% |
| 3 | Omori, Yasuhiro and Chib, Siddhartha and Shephard, Neil and Nakajima… (2007) Stochastic volatility with leverage: Fast and efficient likelihood inference self | 0.737 | 3 | 2 | 100% |
| 4 | Bauwens, Luc and Veredas, David (2004) The stochastic conditional duration model: a latent variable model for the analysis of financial durations | 0.644 | 2 | 2 | 100% |
| 5 | Men, Zhongxian and Kolkiewicz, Adam W and Wirjanto, Tony S (2015) Bayesian analysis of asymmetric stochastic conditional duration model | 0.644 | 2 | 2 | 100% |
| 6 | Sylvia Frühwirth-Schnatter and Rudolf Frühwirth (2007) Auxiliary mixture sampling with applications to logistic models | 0.585 | 3 | 1 | 100% |
| 7 | Strickland, Chris M and Forbes, Catherine S and Martin, Gael M (2006) Bayesian analysis of the stochastic conditional duration model | 0.511 | 2 | 1 | 100% |
| 8 | Chib, Siddhartha and Nardari, Federico and Shephard, Neil (2002) Markov chain Monte Carlo methods for stochastic volatility models | 0.405 | 1 | 1 | 100% |
| 9 | Frühwirth-Schnatter, Sylvia and Frühwirth, Rudolf and Held, Leonhard… (2009) Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data | 0.405 | 1 | 1 | 100% |
| 10 | Kim, Sangjoon and Shephard, Neil and Chib, Siddhartha (1998) Stochastic volatility: likelihood inference and comparison with ARCH models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 13 scored citations.