\name{gammaFitEM}
\alias{gammaFitEM}

\title{ Estimate the methylation status by fitting a Gamma mixture model using EM algorithm }

\description{
Estimate the methylation status by fitting a two component Gamma mixture model using EM algorithm based on the all M-values of a particular sample 
}
\usage{
gammaFitEM(M, initialFit = NULL, fix.k = NULL, weighted = TRUE, maxIteration = 50, tol = 1e-04, plotMode = FALSE, truncate=FALSE, verbose = FALSE)
}

\arguments{
  \item{M}{ a vector of M-values covering the whole genome }
  \item{initialFit}{ the initial estimation of the gamma parameters returned by .initialGammaEstimation function }
  \item{fix.k}{ the k parameter of  the gamma function which is fixed during estimation }
  \item{weighted}{ determine whether to down-weight the long tails of two component densities beyond their modes }
  \item{maxIteration}{ maximum iterations allowed before converging }
  \item{tol}{ the difference threshold used to determine convergence }
  \item{plotMode}{ determine whether plot the histogram and density plot estimation }
  \item{truncate}{ determine whether to truncate the tails beyond the modes during parameter estimation}
  \item{verbose}{ determine whether plot intermediate messages during iterations }
}
\details{

The assumption of this function is that the M-value distribution is composed of the mixture of two shifted gamma distributions, which are defined as:
dgamma(x-s[1], shape=k[1], scale=theta[1]) and dgamma(s[2]-x, shape=k[2], scale=theta[2]). Here s represents the shift.

}
\value{

The return is a list with "gammaFit" class attribute, which includes the following items:
 \item{logLikelihood}{the log-likelihood of the fitting model}
 \item{k}{parameter k of gamma distribution}
 \item{theta}{parameter theta of gamma distribution}
 \item{shift}{parameter shift of gamma distribution}
 \item{proportion}{the proportion of two components (gamma distributions)}
 \item{mode}{the mode positions of the gamma distributions}
 \item{probability}{the estimated methylation status posterior probability of each CpG site}
}

\author{ Pan Du }

\seealso{
  \code{\link{methylationCall}} and \code{\link{plotGammaFit}}
}

\examples{

data(example.lumiMethy)
M <- exprs(example.lumiMethy)
fittedGamma <- gammaFitEM(M[,1], initialFit=NULL, maxIteration=50, tol=0.0001, plotMode=TRUE, verbose=FALSE)

}

\keyword{methods}