{"title":"Bayesian variable selection for matrix autoregressive models","authors":"Alessandro Celani, Paolo Pagnottoni, Galin Jones","doi":"10.1007/s11222-024-10402-y","DOIUrl":null,"url":null,"abstract":"<p>A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators.</p>","PeriodicalId":22058,"journal":{"name":"Statistics and Computing","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics and Computing","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11222-024-10402-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators.
针对高维矩阵自回归模型中的变量选择提出了一种贝叶斯方法，该方法反映并利用了数据的原始矩阵结构，以（a）降低维度和（b）提高多维关系结构的可解释性。该模型推导出一种简洁的形式，便于估算过程，并提出了两种估算计算方法：马尔科夫链蒙特卡罗算法和可扩展的贝叶斯 EM 算法。后者基于用于快速后验模式识别的尖峰和板块框架，能够在大尺度上对矩阵值时间序列进行贝叶斯数据分析。通过模拟实例和对国家经济指标面板的应用，研究了所提模型的理论特性、比较性能和计算效率。
期刊介绍：
Statistics and Computing is a bi-monthly refereed journal which publishes papers covering the range of the interface between the statistical and computing sciences.
In particular, it addresses the use of statistical concepts in computing science, for example in machine learning, computer vision and data analytics, as well as the use of computers in data modelling, prediction and analysis. Specific topics which are covered include: techniques for evaluating analytically intractable problems such as bootstrap resampling, Markov chain Monte Carlo, sequential Monte Carlo, approximate Bayesian computation, search and optimization methods, stochastic simulation and Monte Carlo, graphics, computer environments, statistical approaches to software errors, information retrieval, machine learning, statistics of databases and database technology, huge data sets and big data analytics, computer algebra, graphical models, image processing, tomography, inverse problems and uncertainty quantification.
In addition, the journal contains original research reports, authoritative review papers, discussed papers, and occasional special issues on particular topics or carrying proceedings of relevant conferences. Statistics and Computing also publishes book review and software review sections.
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