\HeaderA{ebayes}{Empirical Bayes Statistics for Differential Expression}{ebayes}
\aliasA{eBayes}{ebayes}{eBayes}
\keyword{htest}{ebayes}
\begin{Description}\relax
Given a series of related parameter estimates and standard errors, compute moderated t-statistics, moderated F-statistic, and log-odds of differential expression by empirical Bayes shrinkage of the standard errors towards a common value.
\end{Description}
\begin{Usage}
\begin{verbatim}
ebayes(fit,proportion=0.01,stdev.coef.lim=c(0.1,4))
eBayes(fit,proportion=0.01,stdev.coef.lim=c(0.1,4))
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{fit}] an \code{MArrayLM} fitted model object produced by \code{lmFit} or \code{contrasts.fit}, or an unclassed list produced by \code{lm.series}, \code{gls.series} or \code{mrlm} containing components \code{coefficients}, \code{stdev.unscaled}, \code{sigma} and \code{df.residual}
\item[\code{proportion}] numeric value between 0 and 1, assumed proportion of genes which are differentially expressed
\item[\code{stdev.coef.lim}] numeric vector of length 2, assumed lower and upper limits for the standard deviation of log2 fold changes for differentially expressed genes
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
These functions is used to rank genes in order of evidence for differential expression.
They use an empirical Bayes method to shrink the probe-wise sample variances towards a common value and to augmenting the degrees of freedom for the individual variances (Smyth, 2004).
The functions accept as input argument \code{fit} a fitted model object from the functions \code{lmFit}, \code{lm.series}, \code{mrlm} or \code{gls.series}.
The fitted model object may have been processed by \code{contrasts.fit} before being passed to \code{eBayes} to convert the coefficients of the design matrix into an arbitrary number of contrasts which are to be tested equal to zero.
The columns of \code{fit} define a set of contrasts which are to be tested equal to zero.

The empirical Bayes moderated t-statistics test each individual contrast equal to zero.
For each probe (row), the moderated F-statistic tests whether all the contrasts are zero.
The F-statistic is an overall test computed from the set of t-statistics for that probe.
This is exactly analogous the relationship between t-tests and F-statistics in conventional anova, except that the residual mean squares and residual degrees of freedom have been moderated between probes.

The estimates \code{s2.prior} and \code{df.prior} are computed by \code{fitFDist}.
\code{s2.post} is the weighted average of \code{s2.prior} and \code{sigma\textasciicircum{}2} with weights proportional to \code{df.prior} and \code{df.residual} respectively.
The \code{lods} is sometimes known as the B-statistic.
The F-statistics \code{F} are computed by \code{classifyTestsF} with \code{fstat.only=TRUE}.

\code{eBayes} doesn't compute ordinary (unmoderated) t-statistics by default, but these can be easily extracted from 
the linear model output, see the example below.

\code{ebayes} is the earlier and leaner function.
\code{eBayes} is intended to have a more object-orientated flavor as it produces objects containing all the necessary components for downstream analysis.
\end{Details}
\begin{Value}
\code{ebayes} produces an ordinary list with the following components.
\code{eBayes} adds the following components to \code{fit} to produce an augmented object, usually of class \code{MArrayLM}.
\begin{ldescription}
\item[\code{t}] numeric vector or matrix of moderated t-statistics
\item[\code{p.value}] numeric vector of p-values corresponding to the t-statistics
\item[\code{s2.prior}] estimated prior value for \code{sigma\textasciicircum{}2}
\item[\code{df.prior}] degrees of freedom associated with \code{s2.prior}
\item[\code{s2.post}] vector giving the posterior values for \code{sigma\textasciicircum{}2}
\item[\code{lods}] numeric vector or matrix giving the log-odds of differential expression
\item[\code{var.prior}] estimated prior value for the variance of the log2-fold-change for differentially expressed gene
\item[\code{F}] numeric vector of moderated F-statistics for testing all contrasts defined by the columns of \code{fit} simultaneously equal to zero
\item[\code{F.p.value}] numeric vector giving p-values corresponding to \code{F}
\end{ldescription}
\end{Value}
\begin{Author}\relax
Gordon Smyth
\end{Author}
\begin{References}\relax
Lönnstedt, I. and Speed, T. P. (2002). Replicated microarray data. \emph{Statistica Sinica} \bold{12}, 31-46.

Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments.
\emph{Statistical Applications in Genetics and Molecular Biology}, \bold{3}, No. 1, Article 3. \url{http://www.bepress.com/sagmb/vol3/iss1/art3}
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{squeezeVar}{squeezeVar}}, \code{\LinkA{fitFDist}{fitFDist}}, \code{\LinkA{tmixture.matrix}{tmixture.matrix}}.

An overview of linear model functions in limma is given by \LinkA{06.LinearModels}{06.LinearModels}.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
#  See also lmFit examples

#  Simulate gene expression data,
#  6 microarrays and 100 genes with one gene differentially expressed
set.seed(2004); invisible(runif(100))
M <- matrix(rnorm(100*6,sd=0.3),100,6)
M[1,] <- M[1,] + 1
fit <- lmFit(M)

#  Ordinary t-statistic
par(mfrow=c(1,2))
ordinary.t <- fit$coef / fit$stdev.unscaled / fit$sigma
qqt(ordinary.t,df=fit$df.residual,main="Ordinary t")
abline(0,1)

#  Moderated t-statistic
eb <- eBayes(fit)
qqt(eb$t,df=eb$df.prior+eb$df.residual,main="Moderated t")
abline(0,1)
#  Points off the line may be differentially expressed
par(mfrow=c(1,1))
\end{ExampleCode}
\end{Examples}