DPMdencens之学解

DPMdencens示例

DPMdencens {DPpackage} R Documentation Bayesian density estimation for

interval-censored data using a DPM of

normals

Description

This function generates a posterior density sample for a Dirichlet process mixture of normals model for interval-censored data区间删失数据 .

Usage

DPMdencens(left,right,ngrid=100,grid=NULL,prior,mcmc,state,status) Arguments

left a vector or matrix giving the lower limit for each response variable. Note that

the responses are defined on the entire real line and that unknown limits

should be indicated by NA.

right a vector or matrix giving the upper limit for each response variable. Note that

the responses are defined on the entire real line and that unknown limits

should be indicated by NA.

ngrid number of grid points where the density estimate is evaluated. The default

value is 100.

grid matrix of dimension ngrid*nvar of grid points where the density estimate is

evaluated. The default value is NULL and the grid is chosen according to the range of the interval limits.

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), nu2 andpsiinv2 giving the hyperparameters of the inverted Wishart prior distribution for the scale matrix, Psi1, of the inverted Wishart part of the baseline distribution, tau1 and tau2 giving the hyperparameters for the gamma prior distribution of the scale parameter k0 of the normal part of the

DPMdencens示例

baseline distribution,m2 and s2 giving the mean and the covariance of the normal prior for the mean, m1, of the normal component of the baseline

distribution, respectively, nu1 andpsiinv1 (it must be specified if nu2 is

missing, see details below) giving the hyperparameters of the inverted

Wishart part of the baseline distribution and, m1giving the mean of the normal part of the baseline distribution (it must be specified if m2 is missing, see

details below) and, k0 giving the scale parameter of the normal part of the baseline distribution (it must be specified if tau1 is missing, see details

below).

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.

Details

This generic function fits a Dirichlet process mixture of normal model for density estimation (Escobar and West, 1995) based on interval-censored data:

yij in [lij,uij),i=1,…,n, j=1,…,m,

yi | mui, Sigmai ~ N(mui,Sigmai), i=1,…,n,

(mui,Sigmai) | G ~ G,

G | alpha, G0 ~ DP(alpha G0),

where, yi=(yi1,…,yim), and the baseline distribution is the conjugate normal-inverted-Wishart distribution,

G0 = N(mu| m1, (1/k0) Sigma) IW (Sigma | nu1, psi1)

To complete the model specification, independent hyperpriors are assumed (optional),

DPMdencens示例

alpha | a0, b0 ~ Gamma(a0,b0)

m1 | m2, s2 ~ N(m2,s2)

k0 | tau1, tau2 ~ Gamma(tau1/2,tau2/2)

psi1 | nu2, psi2 ~ IW(nu2,psi2)

Note that the inverted-Wishart prior is parametrized such that if A ~ IWq(nu, psi) then E(A)= psiinv/(nu-q-1).

To let part of the baseline distribution fixed at a particular value, set the corresponding hyperparameters of the prior distributions to NULL in the hyperprior specification of the model.

Although the baseline distribution, G0, is a conjugate prior in this model specification, an algorithm based on auxiliary parameters is adopted. Specifically, the algorithm 8 with m=1 of Neal (2000) is considered in the DPMdencens function.

Finally, note that this function can be used to fit the DPM of normals model for ordinal data proposed by Kottas, Mueller and Quintana (2005). In this case, the arbitrary cut-off points must be specified in left and right.

Samples from the predictive distribution contained in the (last columns) of the object randsave (please see below) can be used to obtain an estimate of the cell probabilities.

Value

An object of class DPMdencens representing the DP mixture of normals 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 function DPrandom can be used to extract the posterior mean of the subject-specific means and covariance matrices.

DPMdencens示例

The MCMC samples of the parameters and the errors in the model are stored in the object thetasave and randsave, respectively. Both objects are included in the listsave.state and are matrices which can be analyzed directly by functions provided by the coda package.

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.

muclus a matrix of dimension (nobservations+100)*(nvariables) giving the means

of the clusters (only the first ncluster are considered to start the chain). sigmaclus a matrix of dimension

(nobservations+100)*( (nvariables)*((nvariables)+1)/2) giving the lower matrix of the covariance matrix of the clusters (only the firstncluster are considered to start the chain).

ss

alpha

m1

k0

psi1

y an interger vector defining to which of the ncluster clusters each observation belongs. giving the value of the precision parameter. giving the mean of the normal components of the baseline distribution. giving the scale parameter of the normal part of the baseline distribution. giving the scale matrix of the inverted-Wishart part of the baseline distribution. giving the matrix of imputed data points.

Author(s)

Alejandro Jara

References

Escobar, M.D. and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90: 577-588.

DPMdencens示例

Kottas, A., Mueller, P., Quintana, F. (2005). Nonparametric Bayesian modeling for multivariate ordinal data. Journal of Computational and Graphical Statistics, 14: 610-625.

Neal, R. M. (2000). Markov Chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9: 249-265.

See Also DPrandom, DPdensity

Examples

## Not run:

####################################

# Bivariate example:

# Censored data is artificially

# created

####################################

data(airquality)

缺失数据为NA

attach(airquality)

将数据中变量能直接读取

ozone <- Ozone**(1/3)

开立方根

radiation <- Solar.R

重新赋名

y <- na.omit(cbind(radiation,ozone))

删除带有na的行,并给出行号

# create censored-data

xxlim <- seq(0,300,50)

yylim <- seq(1.5,5.5,1)

生成两个数列

left <- matrix(0,nrow=nrow(y),ncol=2)

right <- matrix(0,nrow=nrow(y),ncol=2)

生成与变量y同行,列为2的全0阵

for(i in 1:nrow(y))

{

left[i,1] <- NA

right[i,1] <- NA