% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/MCMCbinaryChange.R
\name{MCMCbinaryChange}
\alias{MCMCbinaryChange}
\title{Markov Chain Monte Carlo for a Binary Multiple Changepoint Model}
\usage{
MCMCbinaryChange(
  data,
  m = 1,
  c0 = 1,
  d0 = 1,
  a = NULL,
  b = NULL,
  burnin = 10000,
  mcmc = 10000,
  thin = 1,
  verbose = 0,
  seed = NA,
  phi.start = NA,
  P.start = NA,
  marginal.likelihood = c("none", "Chib95"),
  ...
)
}
\arguments{
\item{data}{The data.}

\item{m}{The number of changepoints.}

\item{c0}{\eqn{c_0} is the shape1 parameter for Beta prior on
\eqn{\phi} (the mean).}

\item{d0}{\eqn{d_0} is the shape2 parameter for Beta prior on
\eqn{\phi} (the mean).}

\item{a}{\eqn{a} is the shape1 beta prior for transition
probabilities.  By default, the expected duration is computed and
corresponding a and b values are assigned. The expected duration
is the sample period divided by the number of states.}

\item{b}{\eqn{b} is the shape2 beta prior for transition
probabilities.  By default, the expected duration is computed and
corresponding a and b values are assigned. The expected duration
is the sample period divided by the number of states.}

\item{burnin}{The number of burn-in iterations for the sampler.}

\item{mcmc}{The number of MCMC iterations after burn-in.}

\item{thin}{The thinning interval used in the simulation.  The
number of MCMC iterations must be divisible by this value.}

\item{verbose}{A switch which determines whether or not the
progress of the sampler is printed to the screen.  If
\code{verbose} is greater than 0, the iteration number and the
posterior density samples are printed to the screen every
\code{verbose}th iteration.}

\item{seed}{The seed for the random number generator.  If NA,
current R system seed is used.}

\item{phi.start}{The starting values for the mean. The default
value of NA will use draws from the Uniform distribution.}

\item{P.start}{The starting values for the transition matrix. A
user should provide a square matrix with dimension equal to the
number of states. By default, draws from the \code{Beta(0.9,
0.1)} are used to construct a proper transition matrix for each
raw except the last raw.}

\item{marginal.likelihood}{How should the marginal likelihood be
calculated?  Options are: \code{none} in which case the marginal
likelihood will not be calculated, and \code{Chib95} in which
case the method of Chib (1995) is used.}

\item{...}{further arguments to be passed}
}
\value{
An mcmc object that contains the posterior sample.  This
  object can be summarized by functions provided by the coda
  package.  The object contains an attribute \code{prob.state}
  storage matrix that contains the probability of \eqn{state_i} for
  each period, and the log-marginal likelihood of the model
  (\code{logmarglike}).
}
\description{
This function generates a sample from the posterior distribution of
a binary model with multiple changepoints. The function uses the
Markov chain Monte Carlo method of Chib (1998).  The user supplies
data and priors, and a sample from the posterior distribution is
returned as an mcmc object, which can be subsequently analyzed with
functions provided in the coda package.
}
\details{
\code{MCMCbinaryChange} simulates from the posterior distribution
of a binary model with multiple changepoints.

The model takes the following form: \deqn{Y_t \sim
\mathcal{B}ernoulli(\phi_i),\;\; i = 1, \ldots, k} Where \eqn{k}
is the number of states.

We assume Beta priors for \eqn{\phi_{i}} and for transition
probabilities: \deqn{\phi_i \sim \mathcal{B}eta(c_0, d_0)} And:
\deqn{p_{mm} \sim \mathcal{B}eta{a}{b},\;\; m = 1, \ldots, k} Where
\eqn{M} is the number of states.
}
\examples{

    \dontrun{
    set.seed(19173)
    true.phi<- c(0.5, 0.8, 0.4)

    ## two breaks at c(80, 180)
    y1 <- rbinom(80, 1,  true.phi[1])
    y2 <- rbinom(100, 1, true.phi[2])
    y3 <- rbinom(120, 1, true.phi[3])
    y  <- as.ts(c(y1, y2, y3))

    model0 <- MCMCbinaryChange(y, m=0, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model1 <- MCMCbinaryChange(y, m=1, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model2 <- MCMCbinaryChange(y, m=2, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model3 <- MCMCbinaryChange(y, m=3, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model4 <- MCMCbinaryChange(y, m=4, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")
    model5 <- MCMCbinaryChange(y, m=5, c0=2, d0=2, mcmc=100, burnin=100, verbose=50,
    	      marginal.likelihood = "Chib95")

    print(BayesFactor(model0, model1, model2, model3, model4, model5))

    ## plot two plots in one screen
    par(mfrow=c(attr(model2, "m") + 1, 1), mai=c(0.4, 0.6, 0.3, 0.05))
    plotState(model2, legend.control = c(1, 0.6))
    plotChangepoint(model2, verbose = TRUE, ylab="Density", start=1, overlay=TRUE)

    }

}
\references{
Jong Hee Park. 2011. ``Changepoint Analysis of Binary
  and Ordinal Probit Models: An Application to Bank Rate Policy
  Under the Interwar Gold Standard."
  \emph{Political Analysis}. 19: 188-204.
  <doi:10.1093/pan/mpr007>

Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park. 2011.
``MCMCpack: Markov Chain Monte Carlo in R.'', \emph{Journal of
Statistical Software}.  42(9): 1-21.
\doi{10.18637/jss.v042.i09}.

Siddhartha Chib. 1995. ``Marginal Likelihood from the Gibbs
Output.''  \emph{Journal of the American Statistical
Association}. 90: 1313-1321. <doi: 10.1080/01621459.1995.10476635>
}
\seealso{
\code{\link{MCMCpoissonChange}},\code{\link{plotState}},
  \code{\link{plotChangepoint}}
}
\keyword{models}