Testing for significance with gene expression data from DNA microarray experiments involves simultaneous comparisons of hundreds or thousands of genes. If R denotes the number of rejections (declared significant genes) and V denotes the number of false rejections, then V/R, if R > 0, is the proportion of false rejected hypotheses. This paper proposes a model for the distribution of the number of rejections and the conditional distribution of V given R, V / R. Under the independence assumption, the distribution of R is a convolution of two binomials and the distribution of V / R has a noncentral hypergeometric distribution. Under an equicorrelated model, the distributions are more complex and are also derived. Five false discovery rate probability error measures are considered: FDR = E(V/R), pFDR = E(V/R / R > 0) (positive FDR), cFDR = E(V/R / R = r) (conditional FDR), mFDR = E(V)/E(R) (marginal FDR), and eFDR = E(V)/r (empirical FDR). The pFDR, cFDR, and mFDR are shown to be equivalent under the Bayesian framework, in which the number of true null hypotheses is modeled as a random variable. We present a parametric and a bootstrap procedure to estimate the FDRs. Monte Carlo simulations were conducted to evaluate the performance of these two methods. The bootstrap procedure appears to perform reasonably well, even when the alternative hypotheses are correlated (rho = .25). An example from a toxicogenomic microarray experiment is presented for illustration.

Background: Many researchers are concerned with the comparability and reliability of microarray gene expression data. Recent completion of the MicroArray Quality Control (MAQC) project provides a unique opportunity to assess reproducibility across multiple sites and the comparability across multiple platforms. The MAQC analysis presented for the conclusion of inter-and intra-platform comparability/ reproducibility of microarray gene expression measurements is inadequate. We evaluate the reproducibility/comparability of the MAQC data for 12901 common genes in four titration samples generated from five high-density one-color microarray platforms and the TaqMan technology. We discuss some of the problems with the use of correlation coefficient as metric to evaluate the inter-and intraplatform reproducibility and the percent of overlapping genes (POG) as a measure for evaluation of a gene selection procedure by MAQC.

Abstract. Block matching motion estimation is the heart of video coding systems. During the last two decades, hundreds of fast algorithms and VLSI architectures have been proposed. In this paper, we try to provide an extensive exploration of motion estimation with our new developments. The main concepts of fast algorithms can be classified into six categories: reduction in search positions, simplification of matching criterion, bitwidth reduction, predictive search, hierarchical search, and fast full search. Comparisons of various algorithms in terms of video quality and computational complexity are given as useful guidelines for software applications. As for hardware implementations, full search architectures derived from systolic mapping are first introduced. The systolic arrays can be divided into inter-type and intra-type with 1-D, 2-D, and tree structures. Hexagonal plots are presented for system designers to clearly evaluate the architectures in six aspects including gate count, required frequency, hardware utilization, memory bandwidth, memory bitwidth, and latency. Next, architectures supporting fast algorithms are also reviewed. Finally, we propose our algorithmic and architectural co-development. The main idea is quick checking of the entire search range with simplified matching criterion to globally eliminate impossible candidates, followed by finer selection among potential best matched candidates. The operations of the two stages are mapped to the same hardware for resource sharing. Simulation results show that our design is ten times more area-speed efficient than full search architectures while the video quality is competitively the same.

Supplementary data are available at Bioinformatics online.