\name{stability.sim}
\alias{stability.sim}

\title{Stability analysis of the mutagenetic trees mixture model}
\description{
The function includes stability analysis on different levels of the mutagenetic trees mixture
model: GPS values, encoded probability distribution, tree topologies.
Each analysis contains the values of different similarity measures
with their corresponding p-values.
}
\usage{
stability.sim(no.trees = 3, no.events = 9, prob = c(0.2, 0.8),
no.draws = 300, no.rands = 100, no.sim = 1)
}
\arguments{
\item{no.trees}{An \code{integer} larger than 2 giving the number of tree components
of the mixture models considered in the stability analysis. The
default value is 3.}
\item{no.events}{An \code{integer} larger than 0 giving the number of genetic events of the mixture models
considered in the stability analysis.}
\item{prob}{A \code{numeric} vector of length 2 specifying the
boundaries for the edge weights of the randomly generated trees. The
first component of the vector (the lower boundary) must be smaller
than the second component (the upper boundary). The default value is (0.2, 0.8).}
\item{no.draws}{An \code{integer} larger than 0 giving the size of the
data sample drawn from the random models used for learning the
mixture models. The default value is 300.}
\item{no.rands}{An \code{integer} larger than 0 specifying the number
of random models used for calculating the p-values. The default value is 100.}
\item{no.sim}{An \code{integer} larger than 0 specifying the number of
iterations used for the waiting time simulations (a part of the GPS
calculation). The default value is 1.}
}
\details{
The stability analysis is performed by first drawing a true mixture
model uniformly at random from the model space, and drawing a data
sample from it. Afterwards, a mutagenetic trees model is fitted to the
drawn sample. The quality of the features derived from the model is
then assessed by comparing its quality with the quality of the
corresponding features of a sufficient number of random mixture models
sampled uniformly from the model space. A p-value is obtained as a
percentage of cases in which the true model is closer to a random
model tnah to the fitted model.
}
\value{
\item{comp1 }{Results from the stability analysis of the GPS values
derived from a fitted mixture model.
A \code{matrix} with 4 columns and \code{no.sim} rows. The first two columns give the similarity
values and their corresponding p-values when the Euclidian distance
is used as a similarity measure for comparing the respective GPS
vectors. The last two columns depict the same results, but with the
rank correlation distance used as a similarity measure.
}
\item{comp2 }{Results from the stability analysis of the probability
distributions induced by a fitted mixture model. A \code{matrix} with 6
columns and \code{no.sim} rows. Each two columns give the values of the comparissons between
the true and the fitted probability distributions and their
corresponding p-values, when using the cosine distance, the L1 distance, and the
Kullback-Leibler divergence as similarity measures.}
\item{comp3 }{Results from the stability analysis of the topologies
of the tree components of a fitted mixture model. A \code{matrix} with 2
columns and \code{no.sim} rows that give the value of the comparisson of the topologies
between the true and the corresponding fitted model and their
p-values. The similarity measure underlying the number of different
edges was used.}
\item{comp4 }{Similar to \code{comp3}. However, the similarity measure for
comparing the tree topologies besides the number of distinct edges
includes the L1 distances of the level vectors of events. See
\item{comp5 }{A \code{matrix} where the columns correspond to the
true GPS vector from each simulation iteration. The matrix has
\code{no.sim} columns and \code{no.draws} rows.}
\item{comp6 }{Same as \code{comp5}, but the matrix contains the
fitted GPS values from each simulation iteration.}
\item{comp7 }{A \code{list} where each component corresponds to the
true models generated in each simulation iteration. the length of
the list is \code{no.sim}.}
\item{comp8 }{Same as \code{comp7}, but the list contains the fitted models.}
}

\references{Learning multiple evolutionary pathways from cross-sectional
data, N. Beerenwinkel et al.; Estimating cancer survival and clinical outcome based on
genetic tumor progression scores, J. Rahnenf\"urer et al.}

\note{
The stability simulation examples are time consuming. They are commented out because of the time restrictions of the check of the package.
For trying out the code please copy it and uncomment it.
}

\author{Jasmina Bogojeska}

\seealso{