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Journal of the American Statistical Association Volume 99, 2004 - Issue 468
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Primary Article

False Discovery Control for Random Fields

M Perone Pacifico Marco Perone Pacifico is Ricercatore, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy . Christopher Genovese is Associate Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Isabella Verdinelli is Professor, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy and Professor in Residence, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Larry Wasserman is Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Perone Pacifico's research supported by Progetto Giovani Ricercatori “La Sapienza” and Cofinanziamento MIUR. Genovese's research was supported by National Science Foundation (NSF) grants SES 9866147, ITR 0121671. Verdinelli's research supported by Progetto di Ateneo “La Sapienza” and Cofinanziamento MIUR. Wasserman's research was supported by National Institutes of Health grants R01-CA54852-07 and MH57881 and NSF grants DMS-98-03433, ITR-0121671, and DMS-01-04016. The authors would like to thank EliMerriam for his help in producing Figure 7. The authors also thank an associate editor and four referees for their very thorough reviews.
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C Genovese Marco Perone Pacifico is Ricercatore, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy . Christopher Genovese is Associate Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Isabella Verdinelli is Professor, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy and Professor in Residence, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Larry Wasserman is Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Perone Pacifico's research supported by Progetto Giovani Ricercatori “La Sapienza” and Cofinanziamento MIUR. Genovese's research was supported by National Science Foundation (NSF) grants SES 9866147, ITR 0121671. Verdinelli's research supported by Progetto di Ateneo “La Sapienza” and Cofinanziamento MIUR. Wasserman's research was supported by National Institutes of Health grants R01-CA54852-07 and MH57881 and NSF grants DMS-98-03433, ITR-0121671, and DMS-01-04016. The authors would like to thank EliMerriam for his help in producing Figure 7. The authors also thank an associate editor and four referees for their very thorough reviews.
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I Verdinelli Marco Perone Pacifico is Ricercatore, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy . Christopher Genovese is Associate Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Isabella Verdinelli is Professor, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy and Professor in Residence, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Larry Wasserman is Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Perone Pacifico's research supported by Progetto Giovani Ricercatori “La Sapienza” and Cofinanziamento MIUR. Genovese's research was supported by National Science Foundation (NSF) grants SES 9866147, ITR 0121671. Verdinelli's research supported by Progetto di Ateneo “La Sapienza” and Cofinanziamento MIUR. Wasserman's research was supported by National Institutes of Health grants R01-CA54852-07 and MH57881 and NSF grants DMS-98-03433, ITR-0121671, and DMS-01-04016. The authors would like to thank EliMerriam for his help in producing Figure 7. The authors also thank an associate editor and four referees for their very thorough reviews.
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L Wasserman Marco Perone Pacifico is Ricercatore, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy . Christopher Genovese is Associate Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Isabella Verdinelli is Professor, Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza,” Roma 00185, Italy and Professor in Residence, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Larry Wasserman is Professor, Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213 . Perone Pacifico's research supported by Progetto Giovani Ricercatori “La Sapienza” and Cofinanziamento MIUR. Genovese's research was supported by National Science Foundation (NSF) grants SES 9866147, ITR 0121671. Verdinelli's research supported by Progetto di Ateneo “La Sapienza” and Cofinanziamento MIUR. Wasserman's research was supported by National Institutes of Health grants R01-CA54852-07 and MH57881 and NSF grants DMS-98-03433, ITR-0121671, and DMS-01-04016. The authors would like to thank EliMerriam for his help in producing Figure 7. The authors also thank an associate editor and four referees for their very thorough reviews.
Pages 1002-1014 | Published online: 31 Dec 2011
 
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Abstract

This article extends false discovery rates to random fields, for which there are uncountably many hypothesis tests. We develop a method for finding regions in the field's domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur. The method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold. From the confidence envelopes, we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion. An essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true-null locations. We demonstrate our method with applications to scan statistics and functional neuroimaging.

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