@article {Barber:2017:1369-7412:1247,title = "The pfilter: multilayer false discovery rate control for grouped hypotheses",
journal = "Journal of the Royal Statistical Society: Series B (Statistical Methodology)",
parent_itemid = "infobike://bpl/rssb",
publishercode ="bp",
year = "2017",
volume = "79",
number = "4",
publication date ="2017-09-01T00:00:00",
pages = "1247-1268",
itemtype = "ARTICLE",
issn = "1369-7412",
eissn = "1467-9868",
url = "http://www.ingentaconnect.com/content/bpl/rssb/2017/00000079/00000004/art00011",
doi = "doi:10.1111/rssb.12218",
keyword = "Multiresolution, Multilayer, False discovery rate, Multiple testing, pāfilter, Multilevel, Grouped hypotheses"
author = "Barber, Rina Foygel and Ramdas, Aaditya",
abstract = "In many practical applications of multiple testing, there are natural ways to partition the hypotheses into groups by using the structural, spatial or temporal relatedness of the hypotheses, and this prior knowledge is not used in the classical BenjaminiHochberg procedure
for controlling the false discovery rate (FDR). When one can define (possibly several) such partitions, it may be desirable to control the group FDR simultaneously for all partitions (as special cases, the finest partition divides the n hypotheses into n
groups of one hypothesis each, and this corresponds to controlling the usual notion of FDR, whereas the coarsest partition puts all n hypotheses into a single group, and this corresponds to testing the global null hypothesis). We introduce the pfilter, which
takes as input a list of n pvalues and M1 partitions of hypotheses, and produces as output a list of n or fewer discoveries such that the group FDR is provably simultaneously controlled for all partitions. Importantly, since the partitions are arbitrary,
our procedure can also handle multiple partitions which are nonhierarchical. The pfilter generalizes two classical procedureswhen M=1, choosing the finest partition into n singletons, we exactly recover the BenjaminiHochberg procedure, whereas,
choosing instead the coarsest partition with a single group of size n, we exactly recover the Simes test for the global null hypothesis. We verify our findings with simulations that show how this technique can not only lead to the aforementioned multilayer FDR control but also lead
to improved precision of rejected hypotheses. We present some illustrative results from an application to a neuroscience problem with functional magnetic resonance imaging data, where hypotheses are explicitly grouped according to predefined regions of interest in the brain, thus allowing
the scientist to employ fieldspecific prior knowledge explicitly and flexibly.",
}