Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Barber, Rina Foygel
AU - Ramdas, Aaditya
TI - The p‐filter: multilayer false discovery rate control for grouped hypotheses
JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)
PY - 2017-09-01T00:00:00///
VL - 79
IS - 4
SP - 1247
EP - 1268
KW - Multiresolution
KW - Multilayer
KW - False discovery rate
KW - Multiple testing
KW - p‐
KW - filter
KW - Multilevel
KW - Grouped hypotheses
N2 - 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 Benjamini–Hochberg 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 *p‐filter*, which
takes as input a list of *n p*‐values and *M*1 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 non‐hierarchical. The *p*‐filter generalizes two classical procedures—when *M*=1, choosing the finest partition into *n* singletons, we exactly recover the Benjamini–Hochberg 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 field‐specific prior knowledge explicitly and flexibly.
UR - https://www.ingentaconnect.com/content/bpl/rssb/2017/00000079/00000004/art00011
M3 - doi:10.1111/rssb.12218
UR - https://doi.org/10.1111/rssb.12218
ER -