DPbetabinom {DPpackage} | R Documentation |
This function generates a posterior density sample for a semiparametric version of the Beta-Binomial model using a Dirichlet process prior for the mixing distribution.
DPbetabinom(y,ngrid,prior,mcmc,state,status, data=sys.frame(sys.parent()),work.dir=NULL)
y |
a matrix giving the binomial data. The first column must include the number of sucess and the second column the number of trials. |
ngrid |
number of grid points where the predictive density estimate is evaluated. |
prior |
a list giving the prior information. The list includes the following
parameter: a0 and b0 giving the hyperparameters for
prior distribution of the precision parameter of the Dirichlet process
prior, alpha giving the value of the precision parameter (it
must be specified if a0 is missing, see details
below), and a1 and b1 giving the parameters of the
beta centering distribution. |
mcmc |
a list giving the MCMC parameters. The list must include
the following integers: nburn giving the number of burn-in
scans, nskip giving the thinning interval, nsave giving
the total number of scans to be saved, and ndisplay giving
the number of saved scans to be displayed on screen (the function reports
on the screen when every ndisplay iterations have been carried
out). |
state |
a list giving the current value of the parameters. This list is used if the current analysis is the continuation of a previous analysis. |
status |
a logical variable indicating whether this run is new (TRUE ) or the
continuation of a previous analysis (FALSE ). In the latter case
the current value of the parameters must be specified in the
object state . |
data |
data frame. |
work.dir |
working directory. |
This generic function fits a semiparametric version of the Beta-Binomial model (Liu, 1996):
yi | ni, pi ~ Binom(ni,pi), i=1,...,n
pi | G ~ G
G | alpha, G0 ~ DP(alpha G0)
where, the baseline distribution is the beta distribution,
G0 = Beta(a1,b1)
To complete the model specification, the following hyperprior can be assumed for the total mass parameter:
alpha | a0, b0 ~ Gamma(a0,b0)
Notice that the baseline distribution, G0, is a conjugate prior in this model specification. Therefore, standard algorihtms for conjugate DP models are used (see, e.g., Escobar and West, 1995; MacEachern, 1998).
An object of class DPbetabinom
representing the DP Beta-Binomial model fit.
Generic functions such as print
, summary
, and plot
have methods to
show the results of the fit. The results include the baseline parameters, alpha
, and the
number of clusters.
The MCMC samples of the parameters in the model are stored in the object
thetasave
. The object is included in the
list save.state
and are matrices which can be analyzed directly by functions
provided by the coda package. The subject-specific binomial probabilities are stored
in the object randsave
.
The list state
in the output object contains the current value of the parameters
necessary to restart the analysis. If you want to specify different starting values
to run multiple chains set status=TRUE
and create the list state based on
this starting values. In this case the list state
must include the following objects:
ncluster |
an integer giving the number of clusters. |
p |
a vector of dimension (no. observations+1) giving the current value of the binomial probabilities. |
ss |
an interger vector defining to which of the ncluster clusters each observation belongs. |
alpha |
giving the value of the precision parameter. |
Alejandro Jara <ajarav@udec.cl>
Fernando Quintana <quintana@mat.puc.cl>
Escobar, M.D. and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90: 577-588.
Liu, J.S. (1996). Nonparametric Hierarchical Bayes via Sequential Imputations. The Annals of Statistics, 24: 911-930.
MacEachern, S.N. (1998) Computational Methods for Mixture of Dirichlet Process Models, in Practical Nonparametric and Semiparametric Bayesian Statistics, eds: D. Dey, P. Muller, D. Sinha, New York: Springer-Verlag, pp. 1-22.
## Not run: # Data data(rolling) y <- cbind(rolling$y1,rolling$y2) # Prior information prior<-list(alpha=1, a1=1, b1=1) # Initial state state <- NULL # MCMC parameters mcmc <- list(nburn=5000, nsave=10000, nskip=3, ndisplay=100) # Fitting the model fit <- DPbetabinom(y=y,ngrid=100, prior=prior, mcmc=mcmc, state=state, status=TRUE) fit summary(fit) # density estimate plot(fit,output="density") # parameters plot(fit,output="param") ## End(Not run)