86,250 research outputs found
Multiple Testing for Exploratory Research
Motivated by the practice of exploratory research, we formulate an approach
to multiple testing that reverses the conventional roles of the user and the
multiple testing procedure. Traditionally, the user chooses the error
criterion, and the procedure the resulting rejected set. Instead, we propose to
let the user choose the rejected set freely, and to let the multiple testing
procedure return a confidence statement on the number of false rejections
incurred. In our approach, such confidence statements are simultaneous for all
choices of the rejected set, so that post hoc selection of the rejected set
does not compromise their validity. The proposed reversal of roles requires
nothing more than a review of the familiar closed testing procedure, but with a
focus on the non-consonant rejections that this procedure makes. We suggest
several shortcuts to avoid the computational problems associated with closed
testing.Comment: Published in at http://dx.doi.org/10.1214/11-STS356 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multiple testing procedures under confounding
While multiple testing procedures have been the focus of much statistical
research, an important facet of the problem is how to deal with possible
confounding. Procedures have been developed by authors in genetics and
statistics. In this chapter, we relate these proposals. We propose two new
multiple testing approaches within this framework. The first combines
sensitivity analysis methods with false discovery rate estimation procedures.
The second involves construction of shrinkage estimators that utilize the
mixture model for multiple testing. The procedures are illustrated with
applications to a gene expression profiling experiment in prostate cancer.Comment: Published in at http://dx.doi.org/10.1214/193940307000000176 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Peak Detection as Multiple Testing
This paper considers the problem of detecting equal-shaped non-overlapping
unimodal peaks in the presence of Gaussian ergodic stationary noise, where the
number, location and heights of the peaks are unknown. A multiple testing
approach is proposed in which, after kernel smoothing, the presence of a peak
is tested at each observed local maximum. The procedure provides strong control
of the family wise error rate and the false discovery rate asymptotically as
both the signal-to-noise ratio (SNR) and the search space get large, where the
search space may grow exponentially as a function of SNR. Simulations assuming
a Gaussian peak shape and a Gaussian autocorrelation function show that desired
error levels are achieved for relatively low SNR and are robust to partial peak
overlap. Simulations also show that detection power is maximized when the
smoothing bandwidth is close to the bandwidth of the signal peaks, akin to the
well-known matched filter theorem in signal processing. The procedure is
illustrated in an analysis of electrical recordings of neuronal cell activity.Comment: 37 pages, 8 figure
Multiple testing with persistent homology
Multiple hypothesis testing requires a control procedure. Simply increasing
simulations or permutations to meet a Bonferroni-style threshold is
prohibitively expensive. In this paper we propose a null model based approach
to testing for acyclicity, coupled with a Family-Wise Error Rate (FWER) control
method that does not suffer from these computational costs. We adapt an False
Discovery Rate (FDR) control approach to the topological setting, and show it
to be compatible both with our null model approach and with previous approaches
to hypothesis testing in persistent homology. By extending a limit theorem for
persistent homology on samples from point processes, we provide theoretical
validation for our FWER and FDR control methods
Multiple testing, uncertainty and realistic pictures
We study statistical detection of grayscale objects in noisy images. The
object of interest is of unknown shape and has an unknown intensity, that can
be varying over the object and can be negative. No boundary shape constraints
are imposed on the object, only a weak bulk condition for the object's interior
is required. We propose an algorithm that can be used to detect grayscale
objects of unknown shapes in the presence of nonparametric noise of unknown
level. Our algorithm is based on a nonparametric multiple testing procedure. We
establish the limit of applicability of our method via an explicit,
closed-form, non-asymptotic and nonparametric consistency bound. This bound is
valid for a wide class of nonparametric noise distributions. We achieve this by
proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report
2011-004. Link to the abstract at EURANDOM Repository:
http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at
EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd
- …