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...a set of n microarrays yielding a response vector yTg = (yg1, . . . , ygn) for the gth gene. The responses will usually be log-ratios for twocolor data or log-intensities for single channel data, although other transformations are possible. The responses are assumed to be suitably normalized to remove dye-bias and other technological artifacts; see for example Huber et al (2002) or Smyth and Speed (2003). In the case of high density oligonucleotide array, the probes are assumed to have been normalized to produce an expression summary, represented here as ygi, for each gene on each array as in Li and Wong (2001) or Irizarry et al (2003). We assume that E(yg) = Xαg where X is a design matrix of full column rank and αg is a coefficient vector. We assume var(yg) = Wgσ 2 g where Wg is a known non-negative definite weight matrix. The vector yg may contain missing values and the matrix Wg may contain diagonal weights which are zero. Certain contrasts of the coefficients are assumed to be of biological interest and these are defined by βg = C T αg. We assume that it is of interest to test whether individual contrast values βgj are equal to zero. For example, with design (d) above the experimenter might want...

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...erature for microarrays, still in its infancy and with much of it unpublished, has tended to focus on frequentist data-analytic devices such as cluster analysis, bootstrapping, and linear models (see =-=Li and Wong 2000-=-; Kerr and Churchill 2000; Black and Doerge 2000; Van del Laan and Bryan 2000; Eisen, Spellman, Brown, and Botslein 1998). Parametric Bayesian modeling was featured in Newton, Kendziorski, Richmond, B...

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...< PM, but adjusted to be less than PM when MM > PM, which in general occurs for about one-third of all probes (4,6). A model for MAS 5.0 is log(PMij ± CTij) = log(qi) +eij, j = 1,, J. A recent paper =-=(7)-=- reported that variation of a speci®c probe across multiple arrays could be considerably smaller than the *To whom correspondence should be addressed. Tel: +1 410 614 5157; Fax: +1 410 955 0958; Email...

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...even identical descriptive methods have been used by a variety of researchers to evaluate measures of expression (Holder et al., 2001; Workman et al., 2002; Irizarry et al., 2003a; Naef et al., 2001; =-=Li and Wong, 2001-=-). Nor is the report comprehensive; we do not claim to have exhausted the possibilities contained even within this data and other benchmark data sets are available as well. Lemon et al. (2002), for ex...

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...m correspondence should be addressed. † Current address: Mail Code CR145, Oregon Health Sciences University, Portland, OR 79201 mutations (Fodor et al., 1993; Lockhart et al., 1996; Mei et al., 2000; =-=Li and Wong, 2001-=-). Analysis of the large amounts of data produced by these microarrays, however, requires robust computer algorithms. While heuristic approaches have been used very effectively in the past, it is usua...

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...ogs of non-positives). Various researchers have developed alternative algorithms, motivated by statistical models, that outperform the default algorithm in many applications. For example, Li and Wong =-=[16] not-=-ice a strong probe effect in both P M and P M − MM and describe it via a simple multiplicative model. By analyzing various arrayss−2 0 2 4 6 8 10 6 8 10 12 14 Nominal Log (Base 2) Concentration Lo...

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...he mean signal of these replicates were compared (Fig. 3). Previous studies have shown that gene expression measurements of low-abundance transcripts are more variable than high-abundance transcripts =-=(10,11)-=-. As indicated in Figure 3, this trend is exhibited by the Affymetrix GeneChip data and to a lesser degree by data produced by the Agilent technology. Variability of the Amersham Codelink expression d...