\HeaderA{find.a0}{Computation of the Fudge Factor}{find.a0}
\keyword{htest}{find.a0}
\begin{Description}\relax
Provides the required information for obtaining the optimal choice of the fudge factor
in the Empirical Bayes Analysis of Microarrays that uses the modified t statistics.
\end{Description}
\begin{Usage}
\begin{verbatim}
   find.a0(data,cl,B=100,balanced=FALSE,mat.samp=NULL,delta=0.9,alpha=(0:9)/10,
       include.0=TRUE,p0=NA,plot.legend=TRUE,na.rm=FALSE,rand=TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{data}] the data set that should be analyzed. Every row of this data set must
correspond to a gene, and each column to a biological sample.
\item[\code{cl}] a vector containing the class labels of the samples. In the two class unpaired case,
the label of a sample is either 0 (e.g., control group) or 1 (e.g., case group). 
In the two class paired case, the labels are the integers between 1 and \eqn{n/2}{}
(e.g., after treatment group) and between -1 and \eqn{-n/2}{} (e.g., before treatment
group), where \eqn{n}{} is the length of \code{cl} and \eqn{k}{} is paired with \eqn{-k}{}.
For one group data, the label for each sample should be 1.
\item[\code{B}] number of permutations used in the calculation of the null density.
\item[\code{balanced}] if \code{TRUE}, only balanced permutations will be used. Default is
\code{FALSE}.
\item[\code{mat.samp}] a permutation matrix. If specified, this matrix will be used, even if
\code{rand} and \code{B} are specified.
\item[\code{delta}] a gene will be called differentially expressed, if its posterior
probability of being differentially expressed is large than or equal to
\code{delta}.
\item[\code{alpha}] a vector of possible values for the fudge factor \eqn{a_0}{a0} in terms
of quantiles of the standard deviations of the genes.
\item[\code{include.0}] if \code{TRUE} (default), \eqn{a_0=0}{a0=0} will also be a possible
choice for the fudge factor.
\item[\code{p0}] the prior probability that a gene is differentially expressed. If not
specified, it will automatically be computed.
\item[\code{plot.legend}] if \code{TRUE} (default), a legend will be added to the plot of the
expression scores vs.\ their logit-transformed posterior probability.
\item[\code{na.rm}] if \code{FALSE} (default), the expression score of genes with one or more
missing values will be set to \code{NA}. If \code{TRUE}, the missing values
will be replaced by the genewise mean of the non-missing values.
\item[\code{rand}] if specified, the random number generator will be put in a reproducible
state.
\end{ldescription}
\end{Arguments}
\begin{Value}
a list of the numbers of genes called differentially expressed by the EBAM analysis
for several choices of \eqn{a_0}{a0}, and the plot of the expression scores vs.\ their
corresponding logit-transformed posterior probability of being significant.
\begin{ldescription}
\item[\code{sig.a0}] vector containing the number of differentially expressed genes for the
specified set of values for \eqn{a_0}{a0}.
\item[\code{a0}] the optimal choice of the fudge factor using the criterion of Efron et al. (2001)
that the \eqn{a_0}{a0} should be used which leads to the most differentially
expressed genes.
\end{ldescription}
\end{Value}
\begin{Note}\relax
The results of \code{find.a0} must be assigned to an object for the further analysis
with \code{ebam}.
\end{Note}
\begin{Author}\relax
Holger Schwender, \email{holger.schw@gmx.de}
\end{Author}
\begin{References}\relax
Efron, B., Tibshirani, R., Storey, J.D., and Tusher, V. (2001). Empirical Bayes
Analysis of a Microarray Experiment, \emph{JASA}, 96, 1151-1160.

Storey, J.D., and Tibshirani, R. (2003). Statistical significance for genome-wide
experiments, \emph{Technical Report}, Department of Statistics, Stanford University.

Schwender, H. (2003). Assessing the false discovery rate in a statistical analysis of
gene expression data, Chapter 7, \emph{Diploma thesis}, Department of Statistics,
University of Dortmund, \url{http://de.geocities.com/holgerschw/thesis.pdf}.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{ebam}{ebam}}  \code{\LinkA{ebam.wilc}{ebam.wilc}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}## Not run: 
    library(multtest)
    # Load the data of Golub et al. (1999). data(golub) contains
    # a 3051x38 gene expression matrix called golub, a vector of
    # length called golub.cl that consists of the 38 class labels,
    # and a matrix called golub.gnames whose third column contains
    # the gene names.
    data(golub)
    
    # Now the optimal value for the fudge factor a0 is computed,
    # where possible values of the a0 are 0 and the 0, 0.05 and
    # 0.1 quantile of the standard deviations of the genes. 
    # Setting rand=123 makes the results reproducible.
    
    find.out<-find.a0(golub,golub.cl,alpha=c(0,0.05,0.1),rand=123)
## End(Not run)\end{ExampleCode}
\end{Examples}