3,689 research outputs found
Empirical Bayes methods for controlling the false discovery rate with dependent data
False discovery rate (FDR) has been widely used as an error measure in large
scale multiple testing problems, but most research in the area has been focused
on procedures for controlling the FDR based on independent test statistics or
the properties of such procedures for test statistics with certain types of
stochastic dependence. Based on an approach proposed in Tang and Zhang (2005),
we further develop in this paper empirical Bayes methods for controlling the
FDR with dependent data. We implement our methodology in a time series model
and report the results of a simulation study to demonstrate the advantages of
the empirical Bayes approach.Comment: Published at http://dx.doi.org/10.1214/074921707000000111 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Wavelet Galerkin method for fractional elliptic differential equations
Under the guidance of the general theory developed for classical partial
differential equations (PDEs), we investigate the Riesz bases of wavelets in
the spaces where fractional PDEs usually work, and their applications in
numerically solving fractional elliptic differential equations (FEDEs). The
technique issues are solved and the detailed algorithm descriptions are
provided. Compared with the ordinary Galerkin methods, the wavelet Galerkin
method we propose for FEDEs has the striking benefit of efficiency, since the
condition numbers of the corresponding stiffness matrixes are small and
uniformly bounded; and the Toeplitz structure of the matrix still can be used
to reduce cost. Numerical results and comparison with the ordinary Galerkin
methods are presented to demonstrate the advantages of the wavelet Galerkin
method we provide.Comment: 20 pages, 0 figure
- …