152,556 research outputs found
Multiple testing via for large-scale imaging data
The multiple testing procedure plays an important role in detecting the
presence of spatial signals for large-scale imaging data. Typically, the
spatial signals are sparse but clustered. This paper provides empirical
evidence that for a range of commonly used control levels, the conventional
procedure can lack the ability to detect statistical
significance, even if the -values under the true null hypotheses are
independent and uniformly distributed; more generally, ignoring the neighboring
information of spatially structured data will tend to diminish the detection
effectiveness of the procedure. This paper first
introduces a scalar quantity to characterize the extent to which the "lack of
identification phenomenon" () of the
procedure occurs. Second, we propose a new multiple comparison procedure,
called , to accommodate the spatial information of
neighboring -values, via a local aggregation of -values. Theoretical
properties of the procedure are investigated under weak
dependence of -values. It is shown that the
procedure alleviates the of the
procedure, thus substantially facilitating the selection of more stringent
control levels. Simulation evaluations indicate that the procedure improves the detection sensitivity of the procedure with little loss in detection specificity. The computational
simplicity and detection effectiveness of the procedure
are illustrated through a real brain fMRI dataset.Comment: Published in at http://dx.doi.org/10.1214/10-AOS848 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
FDR and victims of family violence: Ensuring a safe process and outcomes
Family dispute resolution (FDR) is a positive first-stop process for family law matters, particularly those relating to disputes about children. FDR provides the parties with flexibility within a positive, structured and facilitated framework for what are often difficult and emotional negotiations. However, there are a range of issues that arise for victims of family violence in FDR that can make it a dangerous and unsafe process for them unless appropriate precautions are taken. This article discusses the nature of FDR and identifies the many positive aspects of it for women participants. The article then considers the nature and dynamic of family violence in order to contextualise the discussion that follows regarding concerns for the safety of participants in the FDR process. Finally, it offers some suggestions about how Australia could approach FDR differently to make it safer for victims of family violence
False discovery and false nondiscovery rates in single-step multiple testing procedures
Results on the false discovery rate (FDR) and the false nondiscovery rate
(FNR) are developed for single-step multiple testing procedures. In addition to
verifying desirable properties of FDR and FNR as measures of error rates, these
results extend previously known results, providing further insights,
particularly under dependence, into the notions of FDR and FNR and related
measures. First, considering fixed configurations of true and false null
hypotheses, inequalities are obtained to explain how an FDR- or FNR-controlling
single-step procedure, such as a Bonferroni or \u{S}id\'{a}k procedure, can
potentially be improved. Two families of procedures are then constructed, one
that modifies the FDR-controlling and the other that modifies the
FNR-controlling \u{S}id\'{a}k procedure. These are proved to control FDR or FNR
under independence less conservatively than the corresponding families that
modify the FDR- or FNR-controlling Bonferroni procedure. Results of numerical
investigations of the performance of the modified \u{S}id\'{a}k FDR procedure
over its competitors are presented. Second, considering a mixture model where
different configurations of true and false null hypotheses are assumed to have
certain probabilities, results are also derived that extend some of Storey's
work to the dependence case.Comment: Published at http://dx.doi.org/10.1214/009053605000000778 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Controlling the False Discovery Rate in Astrophysical Data Analysis
The False Discovery Rate (FDR) is a new statistical procedure to control the
number of mistakes made when performing multiple hypothesis tests, i.e. when
comparing many data against a given model hypothesis. The key advantage of FDR
is that it allows one to a priori control the average fraction of false
rejections made (when comparing to the null hypothesis) over the total number
of rejections performed. We compare FDR to the standard procedure of rejecting
all tests that do not match the null hypothesis above some arbitrarily chosen
confidence limit, e.g. 2 sigma, or at the 95% confidence level. When using FDR,
we find a similar rate of correct detections, but with significantly fewer
false detections. Moreover, the FDR procedure is quick and easy to compute and
can be trivially adapted to work with correlated data. The purpose of this
paper is to introduce the FDR procedure to the astrophysics community. We
illustrate the power of FDR through several astronomical examples, including
the detection of features against a smooth one-dimensional function, e.g.
seeing the ``baryon wiggles'' in a power spectrum of matter fluctuations, and
source pixel detection in imaging data. In this era of large datasets and high
precision measurements, FDR provides the means to adaptively control a
scientifically meaningful quantity -- the number of false discoveries made when
conducting multiple hypothesis tests.Comment: 15 pages, 9 figures. Submitted to A
Nonlinear response and fluctuation dissipation relations
A unified derivation of the off equilibrium fluctuation dissipation relations
(FDR) is given for Ising and continous spins to arbitrary order, within the
framework of Markovian stochastic dynamics. Knowledge of the FDR allows to
develop zero field algorithms for the efficient numerical computation of the
response functions. Two applications are presented. In the first one, the
problem of probing for the existence of a growing cooperative length scale is
considered in those cases, like in glassy systems, where the linear FDR is of
no use. The effectiveness of an appropriate second order FDR is illustrated in
the test case of the Edwards-Anderson spin glass in one and two dimensions. In
the second one, the important problem of the definition of an off equilibrium
effective temperature through the nonlinear FDR is considered. It is shown
that, in the case of coarsening systems, the effective temperature derived from
the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure
Generalized fluctuation-dissipation relation and effective temperature in off-equilibrium colloids
The fluctuation-dissipation relation (FDR), a fundamental result of
equilibrium statistical physics, ceases to be valid when a system is taken out
of the equilibrium. A generalization of FDR has been theoretically proposed for
out-of-equilibrium systems: the kinetic temperature entering FDR is substituted
by a time-scale dependent effective temperature. We combine the measurements of
the correlation function of the rotational dynamics of colloidal particles
obtained via dynamic light scattering with those of the birefringence response
to study the generalized FDR in an off-equilibrium clay suspension undergoing
aging. We i) find that FDR is strongly violated in the early stage of the aging
process and is gradually recovered as the aging time increases and, ii), we
determine the aging time evolution of the effective temperature, giving support
to the proposed generalization scheme.Comment: 4 pages, 3 figure
- …