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\name{threshBayes}
\alias{threshBayes}
\title{Threshold model using Bayesian MCMC}
\usage{
threshBayes(tree, X, types=NULL, ngen=10000, control=list(), ...)
}
\arguments{
\item{tree}{an object of class \code{"phylo"}.}
\item{X}{a numeric matrix containing values for a numerically coded discrete character and a continuous character; or two discrete characters. The row names of \code{X} should be species names. Discrete characters need to be provided as numeric values of \code{0} or \code{1} and only binary traits are permitted.}
\item{types}{a vector of length \code{ncol(X)} containing the data types for each column of \code{X}, for instance \code{c("discrete","continuous")}.}
\item{ngen}{a integer indicating the number of generations for the MCMC.}
\item{control}{a list of control parameters for the MCMC. Control parameters include: \code{sample}, the sampling interval for the MCMC; \code{propvar}, a vector containing (in this order) proposal variances for the two rates (if the type is \code{"discrete"} this will be ignored), the two ancestral states, and the correlation; \code{propliab}, a single proposal variance for the liabilities; \code{pr.mean}, a vector for the mean of the prior probability distributions for each parameter, in the same order as \code{propvar}; \code{pr.liab}, currently ignored; \code{pr.var}, a vector with variances for the prior densities for each parameter, in the same order as \code{pr.mean} - note that for the rates we use an exponential distribution so the first two means are currently ignored; and \code{pr.vliab} currently ignored.}
\item{...}{other optional arguments.}
}
\description{
This function uses Bayesian MCMC to fit the quantitative genetics threshold model (Felsenstein 2012) to data for two discrete characters or one discrete and one continuous character.
}
\value{
This function returns an object of class \code{"threshBayes"} consisting of a list with at least the following two elements: \code{par} a matrix containing the posterior sample for the model parameters (evolutionary rates, ancestral states, and correlation); \code{liab} a matrix containing the posterior sample of the liabilities. For continuous characters, the liabilities are treated as known and so the posterior samples are just the observed values.
}
\details{
The \code{plot} method for the object class \code{"threshBayes"} can be used to plot a posterior density of the correlation coefficient, \emph{r}.
Discrete characters must be binary, coded as \code{0} and \code{1}.
}
\references{
Felsenstein, J. (2012) A comparative method for both discrete and continuous characters using the threshold model. \emph{American Naturalist}, \bold{179}, 145-156.
Revell, L. J. (2012) phytools: An R package for phylogenetic comparative biology (and other things). \emph{Methods Ecol. Evol.}, \bold{3}, 217-223.
Revell, L. J. (2014) Ancestral character estimation under the threshold model from quantitative genetics. \emph{Evolution}, bold{68}, 743-759.
}
\author{Liam Revell \email{liam.revell@umb.edu}}
\seealso{
\code{\link{anc.Bayes}}, \code{\link{bmPlot}}, \code{\link{evol.rate.mcmc}}
}
\keyword{phylogenetics}
\keyword{comparative method}
\keyword{bayesian}
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