AI 中文总结
本研究将分段确定性马尔可夫过程（PDMP）采样器应用于贝叶斯变量选择，扩展其至相关先验与随机梯度场景，结合心理测量模型验证，提升了强相关参数下的采样效率。
AI 中文摘要
当模型包含大量相关参数时，贝叶斯变量选择会面临计算挑战。本研究将分段确定性马尔可夫过程（PDMP）采样器作为传统马尔可夫链蒙特卡洛（MCMC）的连续时间替代方案，用于尖-板（spike-and-slab）变量选择。在粘性PDMP采样器中，活跃参数会持续演化直至达到零值，之后可能在模型外停留随机时长再重新进入。当一个参数进入或离开模型时，其余参数会沿确定性流继续演化，这为探索具有强相关参数的后验分布提供了潜在优势机制。我们做出两项方法学贡献：其一，将现有粘性PDMP方法从独立尖-板先验扩展至相关模型先验和相关板分布；其二，研究了无偏随机梯度的应用，以在似然分解为多个因子时降低变量选择的计算成本，同时保留相同的目标分布。我们将这些扩展应用于两种心理测量模型：高斯随机截距交叉滞后面板模型和有序马尔可夫随机场。对于前者，边缘化产生固定维度的充分统计量表示，可实现高效模型评估；对于后者，模型可分解，支持对个体节点贡献进行子采样。在模拟研究中，我们将ZigZag、Bouncy Particle和Boomerang动力学与可逆跳转MCMC进行比较，考察先验相关性和随机梯度子采样对采样效率的影响。我们使用一项关于心理健康的实证研究数据说明该方法，最后讨论将PDMP采样器用于贝叶斯变量选择的优势与挑战。
英文摘要
Bayesian variable selection becomes computationally challenging when models contain many dependent parameters. We study Piecewise Deterministic Markov Process (PDMP) samplers as a continuous-time alternative to conventional Markov chain Monte Carlo for spike-and-slab variable selection. In sticky PDMP samplers, active parameters evolve continuously until they reach zero, where they may remain for a random duration before re-entering the model. While one parameter enters or leaves the model, the remaining parameters continue to evolve along the deterministic flow, offering a potentially advantageous mechanism for exploring posteriors with strongly dependent parameters. We make two methodological contributions. First, we extend existing sticky PDMP methods beyond independent spike-and-slab priors to dependent model priors and dependent slab distributions. Second, we investigate the use of unbiased stochastic gradients to reduce the computational cost of variable selection when the likelihood decomposes into many factors while retaining the same target distribution. We study these extensions to two psychometric models: a Gaussian random intercept cross-lagged panel model and an ordinal Markov random field. For the former, marginalization yields a fixed-dimensional sufficient-statistic representation that permits efficient model evaluation. For the latter, the model factorizes, which enables subsampling over person-node contributions. In simulation studies, we compare ZigZag, Bouncy Particle, and Boomerang dynamics with reversible-jump MCMC, and examine the effects of prior dependence and stochastic-gradient subsampling on sampling efficiency. We illustrate the methodology using data from an empirical study on mental well-being. Finally, we discuss the advantages and challenges when using PDMP samplers for Bayesian variable selection.
