{"title":"具有复杂后验的贝叶斯模型推断:指数影响的贝叶斯正交","authors":"Pengfei Wei","doi":"10.1016/j.ymssp.2025.113333","DOIUrl":null,"url":null,"abstract":"<div><div>Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.</div></div>","PeriodicalId":51124,"journal":{"name":"Mechanical Systems and Signal Processing","volume":"239 ","pages":"Article 113333"},"PeriodicalIF":8.9000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bayesian model inference with complex posteriors: Exponential-impact-informed Bayesian Quadrature\",\"authors\":\"Pengfei Wei\",\"doi\":\"10.1016/j.ymssp.2025.113333\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.</div></div>\",\"PeriodicalId\":51124,\"journal\":{\"name\":\"Mechanical Systems and Signal Processing\",\"volume\":\"239 \",\"pages\":\"Article 113333\"},\"PeriodicalIF\":8.9000,\"publicationDate\":\"2025-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanical Systems and Signal Processing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0888327025010349\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanical Systems and Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888327025010349","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Bayesian model inference with complex posteriors: Exponential-impact-informed Bayesian Quadrature
Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.
期刊介绍:
Journal Name: Mechanical Systems and Signal Processing (MSSP)
Interdisciplinary Focus:
Mechanical, Aerospace, and Civil Engineering
Purpose:Reporting scientific advancements of the highest quality
Arising from new techniques in sensing, instrumentation, signal processing, modelling, and control of dynamic systems