{"title":"Bayesian Analysis of Change Point Problems Using Conditionally Specified Priors","authors":"G. Shahtahmassebi, José María Sarabia","doi":"10.1007/s40745-023-00484-2","DOIUrl":null,"url":null,"abstract":"<div><p>In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this paper, we consider a class of conjugate prior distributions obtained from conditional specification methodology for solving this problem. We illustrate the application of such distributions in Bayesian change point detection analysis with Poisson processes. We obtain the posterior distribution of model parameters using general bivariate distribution with gamma conditionals. Simulation from the posterior are readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.</p></div>","PeriodicalId":36280,"journal":{"name":"Annals of Data Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40745-023-00484-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Data Science","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40745-023-00484-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Decision Sciences","Score":null,"Total":0}
引用次数: 0
Abstract
In data analysis, change point problems correspond to abrupt changes in stochastic mechanisms generating data. The detection of change points is a relevant problem in the analysis and prediction of time series. In this paper, we consider a class of conjugate prior distributions obtained from conditional specification methodology for solving this problem. We illustrate the application of such distributions in Bayesian change point detection analysis with Poisson processes. We obtain the posterior distribution of model parameters using general bivariate distribution with gamma conditionals. Simulation from the posterior are readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.
期刊介绍：
Annals of Data Science (ADS) publishes cutting-edge research findings, experimental results and case studies of data science. Although Data Science is regarded as an interdisciplinary field of using mathematics, statistics, databases, data mining, high-performance computing, knowledge management and virtualization to discover knowledge from Big Data, it should have its own scientific contents, such as axioms, laws and rules, which are fundamentally important for experts in different fields to explore their own interests from Big Data. ADS encourages contributors to address such challenging problems at this exchange platform. At present, how to discover knowledge from heterogeneous data under Big Data environment needs to be addressed. ADS is a series of volumes edited by either the editorial office or guest editors. Guest editors will be responsible for call-for-papers and the review process for high-quality contributions in their volumes.
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