% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.mleFBByOptim.Rd,v 1.3 2015/03/21 23:40:34 takayama Exp $
\name{hgm.z.mleFBByOptim}
%%Todo, write documents for hgm.z.mleDemo, hgm.ssFB
%\alias{hgm.ncso3}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{
MLE of Fisher-Bingham distribution by optim and HGM.
}
\description{
It makes the maximal likelihood estimate (MLE) for the Fisher-Bingham
distribution on S^d.
}
\usage{
hgm.z.mleFBByOptim(d=0,ss=NULL,data=NULL,start=NULL,lb=NULL,up=NULL,bigValue=10000)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{d}{The dimension of the sphere}
\item{ss}{Sufficient statistics}
\item{data}{
The argument data is a set of data on the d-dimensional sphere.
Its format is an n by (d+1) matrix where n is the number of data.
When data is given, ss must be NULL
and ss is calculated from data by hgm.ssFB(data).
}
\item{start}{
Starting point for the function optim. The default value is a random
vector.
}
\item{lb}{
An array of length sslen = (d+1)*(d+2)/2 + (d+1), each of which
is the lower bound of the parameter. The default value is -100.
}
\item{ub}{
An array of length sslen = (d+1)*(d+2)/2 + (d+1), each of which
is the upper bound of the parameter. The default value is 100.
}
\item{bigValue}{
It is used as a value wall to avoid that the evaluation point is out of
the search domain defined by lb and ub.
}
}
\details{
It solves the MLE for the Fisher-Bingham distribution.
The normalizing constant is evaluated by hgm_ko_ncfb (external program,
which should in the path).
The function
% \code{\link[RCurl]{postForm}}
\code{\link{optim}}
is used for the optimization.
The output is used as a starting point for the holonomic gradient method.
See nk_fb_gen_c.rr of \url{http://www.math.kobe-u.ac.jp/Asir}.
This function generates temporary work files whose names start with tmp.
\code{data <- read.table(fileName,sep=",")} can be used to read CSV data
from a file.
}
\value{
The output format is that of the function optim().
}
\references{
T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere,
Computational Statistics (2013)
\url{http://dx.doi.org/10.1007/s00180-013-0456-z}
}
\author{
T.Koyama, H.Nakayama, K.Nishiyama, N.Takayama.
}
\note{
%% ~~further notes~~
}
%% ~Make other sections like Warning with \section{Warning }{....} ~
\seealso{
\code{\link{optim}}
}
\examples{
## =====================================================
## Example 1. Asteroid data in [N3OST2]
## =====================================================
\dontrun{
d <- 2
ss <- c(0.3119,0.0292,0.0707,
0.3605,0.0462,
0.3276,
0.0063,0.0054,0.0762)
start <- c(0.1,0.1,1,1,1,-1,-1,-1,-1)
hgm.z.mleFBByOptim(d=d,ss=ss,start=start)
}
}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{ Holonomic gradient method }
\keyword{ HGM }
\keyword{ Fisher-Bingham distribution on S^d}
\keyword{ MLE }