We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured uorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates of gene expression changes are derived within a simple hierarchical model that accounts for measurement error and uctuations in absolute gene expression levels. Signi cant gene expression changes are identi ed by deriving the posterior odds of change within a similar model. The methods are tested via simulation and are applied to a panel of Escherichia coli microarrays.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.This article examines some problems of significance testing for one-sided hypotheses of the form Ho: 0 6 0?6 versus H1: 0 > 0o, where 0 is the parameter of interest. In the usual setting, let x be the observed data and let T(X) be a test statistic such that the family of distributions of T(X) is stochastically increasing in 0. Define C, as {X: T(X) -T(x) 2 O}. The p value is p(x) = suposo0 Pr(X E Cx I 0). In the presence of a nuisance parameter o, there may not exist a nontrivial Cx with a p value independent of q7. We consider tests based on generalized extreme regions of the form C(0, q) = {X: T(X; x, 0, q) 2 T(x; x, 0, Cf)}, and conditions on T(X; x, 0, q) are given such that the p value p(x) = sup0,,, Pr(X E Cj(0, C)) is free of the nuisance parameter q, where T is stochastically increasing in 0. We provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions, a problem for which the fixed-level testing approach has not produced a nontrivial solution except in a special case. We also provide an exact solution to the Behrens-Fisher problem. The p value for the Behrens-Fisher problem turns out to be numerically (but not logically) the same as Jeffreys's Bayesian solution and the Behrens-Fisher fiducial solution. Our approach of testing on the basis of p values is especially useful in multiparameter problems where nontrivial tests with a fixed level of significance are difficult or impossible to obtain.

Nonsense-mediated mRNA decay (NMD) is a eukaryotic mechanism of RNA surveillance that selectively eliminates aberrant transcripts coding for potentially deleterious proteins. NMD also functions in the normal repertoire of gene expression. In Saccharomyces cerevisiae, hundreds of endogenous RNA Polymerase II transcripts achieve steady-state levels that depend on NMD. For some, the decay rate is directly influenced by NMD (direct targets). For others, abundance is NMD-sensitive but without any effect on the decay rate (indirect targets). To distinguish between direct and indirect targets, total RNA from wild-type (Nmd+) and mutant (Nmd−) strains was probed with high-density arrays across a 1-h time window following transcription inhibition. Statistical models were developed to describe the kinetics of RNA decay. 45% ± 5% of RNAs targeted by NMD were predicted to be direct targets with altered decay rates in Nmd− strains. Parallel experiments using conventional methods were conducted to empirically test predictions from the global experiment. The results show that the global assay reliably distinguished direct versus indirect targets. Different types of targets were investigated, including transcripts containing adjacent, disabled open reading frames, upstream open reading frames, and those prone to out-of-frame initiation of translation. Known targeting mechanisms fail to account for all of the direct targets of NMD, suggesting that additional targeting mechanisms remain to be elucidated. 30% of the protein-coding targets of NMD fell into two broadly defined functional themes: those affecting chromosome structure and behavior and those affecting cell surface dynamics. Overall, the results provide a preview for how expression profiles in multi-cellular eukaryotes might be impacted by NMD. Furthermore, the methods for analyzing decay rates on a global scale offer a blueprint for new ways to study mRNA decay pathways in any organism where cultured cell lines are available.

No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.A flexible method is introduced to model the structure of a covariance matrix C and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix A, the matrix exponential transformation, C = exp (A), is a positive definite matrix. Because there is no constraint on the possible values of the upper triangular elements on A, any possible structure of interest can be imposed on them. The method presented here is not intended to replace the existing special models available for a covariance matrix, but rather to provide a broad range of further structures that supplements existing methodology. Maximum likelihood estimation procedures are used to estimate the parameters, and the large-sample asymptotic properties are obtained. A simulation study and two real-life examples are given to illustrate the method introduced. KEY WORDS: Covariance matrix; Golden-Thompson inequality; Matrix exponential transformation; Maximum likelihood estimation; Volterra integral equation. Tom Y. M. Chiu is Statistician, SPSS, Inc., Chicago, IL 60611. Tom Leonard is Associate Professor and Kam-Wah Tsui is Professor, Department of Statistics, University of Wisconsin, Madison, WI 53706. The authors are grateful to , two anonymous referees, and an associate editor for many helpful suggestions. Thanks are also due to Sook-Fwe Yap for computing advice and to Karen Pridham and the University of Wisconsin School of Nursing for providing the medical data set. The initial stages of this research were supported under the Army Research Office (ARO) Contract DAAG29-80-C-0041. of C. Because As = T[log(D)]5T' for any nonnegative integer s, substituting for As in (1) readily confirms that C = TDT'. Hence the matrix logarithmic transformation takes only logs of the eigenvalues of C, while leaving the eigenvectors unchanged. Several properties of the transformations (1) and (2) are now described when C is p x p positive definite matrix. a. Invariance under rotations: Let W denote any p x p orthonormal matrix. Then (2) implies that log(WCW') = WAW' = W[log C]W'. (3) b. The generalized variance: The determinant ICI satisfies log | C = tr(A),where tr(*) denotes the trace of a matrix. c. The inverse C-1 satisfies C' = exp{-A}.(5) d. It is not generally true that if Ct is some t x t positive definite submatrix of C consisting of t rows of C and the corresponding t columns, then