Simulation-based inference via telescoping ratio estimation for trawl processes
利用逐级比率估计对 trawl 过程进行基于模拟的推断AI 解读 ↓
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利用逐级比率估计对 trawl 过程进行基于模拟的推断
- 研究问题
- 对于可模拟但难以估计、具有偏态、非高斯尾部和长记忆等特征的时间过程，如何提高后验推断效率并改善区间校准？
- 方法与思路
- 作者按参数维度顺序分解并学习后验密度，用 Chebyshev 多项式近似生成独立后验样本，再加入诊断与事后校准方法。
- 材料陈述的贡献
- 摘要称，该框架节省训练样本并支持摊销推断；校准后可复用于不同长度的新序列，并以能源需求中的 trawl 过程展示效果。
- 阅读关注点
- 应核对逐级比率与后验分解的实现、多项式近似误差、覆盖率诊断，以及跨序列长度复用所依赖的校准条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未提供覆盖率数值、训练成本和误差保证，不能确认任意序列上的校准有效性。
原文摘要
The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics. While such models are often easy to simulate from, parameter estimation remains challenging. Simulation-based inference (SBI) offers a promising way forward, but existing methods typically require large training datasets or complex architectures and frequently yield confidence (credible) regions that fail to attain their nominal values, raising doubts on the reliability of estimates for the very features that motivate the use of these models. To address these challenges, we propose a fast and accurate, sample-efficient SBI framework for amortized posterior inference applicable to intractable stochastic processes. The proposed approach relies on two main steps: first, we learn the posterior density by decomposing it sequentially across parameter dimensions. Then, we use Chebyshev polynomial approximations to efficiently generate independent posterior samples, enabling accurate inference even when Markov chain Monte Carlo methods mix poorly. We further develop novel diagnostic tools for SBI in this context, as well as post-hoc calibration techniques; the latter not only lead to performance improvements of the learned inferential tool, but also to the ability to reuse it directly with new time series of varying lengths, thus amortizing the training cost. We demonstrate the method's effectiveness on trawl processes, a class of flexible infinitely divisible models that generalize univariate Gaussian processes, applied to energy demand data.