{"title":"A unified approach to model-based signal processing using Bayesian marginal inference","authors":"A. Quinn","doi":"10.1109/SSAP.1992.246857","DOIUrl":null,"url":null,"abstract":"The author adopts a strong Bayesian philosophy and derives the marginal inference for the nonlinear parameters in a general deterministic signal model, having integrated over the linear terms. The marginal inference is shown to embody Ockham's razor in an objective manner via the Ockham parameter inference. From this, a new definition of hypothesis complexity, is proposed. The marginal inference provides a means of testing the status of an alternative-free hypothesis, thereby unifying the detection and estimation tasks. Robust estimates may then be inferred below the thresholds for maximum likelihood estimation. The analysis is extended to a multi-hypothesis environment, using the example of a periodic model of unknown order. The fundamental frequency is estimated in a unified procedure which can either (i) simultaneously estimate the model order, or (ii) marginalize analytically over the model order. Both techniques confer improved inferential consistency and a much reduced numerical load when compared with the popular evidence-based technique, which is also described.<<ETX>>","PeriodicalId":309407,"journal":{"name":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","volume":"114 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992] IEEE Sixth SP Workshop on Statistical Signal and Array Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SSAP.1992.246857","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The author adopts a strong Bayesian philosophy and derives the marginal inference for the nonlinear parameters in a general deterministic signal model, having integrated over the linear terms. The marginal inference is shown to embody Ockham's razor in an objective manner via the Ockham parameter inference. From this, a new definition of hypothesis complexity, is proposed. The marginal inference provides a means of testing the status of an alternative-free hypothesis, thereby unifying the detection and estimation tasks. Robust estimates may then be inferred below the thresholds for maximum likelihood estimation. The analysis is extended to a multi-hypothesis environment, using the example of a periodic model of unknown order. The fundamental frequency is estimated in a unified procedure which can either (i) simultaneously estimate the model order, or (ii) marginalize analytically over the model order. Both techniques confer improved inferential consistency and a much reduced numerical load when compared with the popular evidence-based technique, which is also described.<>