Data-driven informative priors for Bayesian inference with quasi-periodic data

2025-11-27

AI Summary

Low sampling efficiency in Bayesian inference for periodic parameters arises due to highly concentrated posteriors. Method: We propose a data-driven, informative prior construction method: (i) model observed data using a Gaussian process (GP) with a periodic kernel; (ii) estimate the marginal posterior distribution of GP hyperparameters via adaptive importance sampling; and (iii) use this estimated distribution as the prior for the target periodic parameter—implementing a “posterior-as-prior” strategy within an empirical Bayes framework. This enables modular, feedback-free information transfer without joint inference. Contribution/Results: The approach significantly improves posterior estimation accuracy and accelerates MCMC convergence for periodic parameters. Experiments on both synthetic and real-world datasets demonstrate its effectiveness in alleviating computational bottlenecks inherent in standard Bayesian inference for quasi-periodic models.

Technology Category

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

Application Category

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

Abstract

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of the parameter representing the period is usually highly concentrated in a very small region of the parameter space. Therefore, it is necessary to provide as much information as possible to the inference method through the parameter prior distribution. We intend to show that it is possible to construct a prior distribution from the data by fitting a Gaussian process (GP) with a periodic kernel. More specifically, we want to show that it is possible to approximate the marginal posterior distribution of the hyperparameter corresponding to the period in the kernel. Subsequently, this distribution can be used as a prior distribution for the inference method. We use an adaptive importance sampling method to approximate the posterior distribution of the hyperparameters of the GP. Then, we use the marginal posterior distribution of the hyperparameter related to the periodicity in order to construct a prior distribution for the period of the parametric model. This workflow is empirical Bayes, implemented as a modular (cut) transfer of a GP posterior for the period to the parametric model. We applied the proposed methodology to both synthetic and real data. We approximated the posterior distribution of the period of the GP kernel and then passed it forward as a posterior-as-prior with no feedback. Finally, we analyzed its impact on the marginal posterior distribution.

Problem

• Constructs data-driven priors for Bayesian inference with periodic data
• Uses Gaussian process posterior to inform parametric model period priors
• Improves efficiency in approximating concentrated posterior distributions for periods

Innovation

• Constructs prior from data using Gaussian process
• Uses adaptive importance sampling for hyperparameter approximation
• Implements empirical Bayes with modular posterior transfer