{"title":"High dimensional Bernstein-von Mises: simple examples.","authors":"Iain M Johnstone","doi":"10.1214/10-IMSCOLL607","DOIUrl":"10.1214/10-IMSCOLL607","url":null,"abstract":"<p><p>In Gaussian sequence models with Gaussian priors, we develop some simple examples to illustrate three perspectives on matching of posterior and frequentist probabilities when the dimension p increases with sample size n: (i) convergence of joint posterior distributions, (ii) behavior of a non-linear functional: squared error loss, and (iii) estimation of linear functionals. The three settings are progressively less demanding in terms of conditions needed for validity of the Bernstein-von Mises theorem.</p>","PeriodicalId":88897,"journal":{"name":"Institute of Mathematical Statistics collections","volume":"6 ","pages":"87-98"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2990974/pdf/nihms-199314.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29498390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on bounds for VC dimensions.","authors":"Aad van der Vaart, Jon A Wellner","doi":"10.1214/09-IMSCOLL508","DOIUrl":"10.1214/09-IMSCOLL508","url":null,"abstract":"<p><p>We provide bounds for the VC dimension of class of sets formed by unions, intersections, and products of VC classes of sets 𝒞(1),…,𝒞(m.</p>","PeriodicalId":88897,"journal":{"name":"Institute of Mathematical Statistics collections","volume":"5 ","pages":"103-107"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2924594/pdf/nihms177738.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29203664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model selection and sensitivity analysis for sequence pattern models.","authors":"Mayetri Gupta","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>In this article we propose a maximal a posteriori (MAP) criterion for model selection in the motif discovery problem and investigate conditions under which the MAP asymptotically gives a correct prediction of model size. We also investigate robustness of the MAP to prior specification and provide guidelines for choosing prior hyper-parameters for motif models based on sensitivity considerations.</p>","PeriodicalId":88897,"journal":{"name":"Institute of Mathematical Statistics collections","volume":"1 ","pages":"390-407"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2887058/pdf/nihms120964.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29067838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model selection and sensitivity analysis for sequence pattern models.","authors":"Mayetri Gupta","doi":"10.1214/193940307000000301","DOIUrl":"https://doi.org/10.1214/193940307000000301","url":null,"abstract":"In this article we propose a maximal a posteriori (MAP) criterion for model selection in the motif discovery problem and investigate conditions under which the MAP asymptotically gives a correct prediction of model size. We also investigate robustness of the MAP to prior specification and provide guidelines for choosing prior hyper-parameters for motif models based on sensitivity considerations.","PeriodicalId":88897,"journal":{"name":"Institute of Mathematical Statistics collections","volume":"59 1","pages":"390-407"},"PeriodicalIF":0.0,"publicationDate":"2008-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76091915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}