| NPBayes {NPBayes} | R Documentation |
This function will compute the nonparametric Bayes estimator of survival/distribution function from censored data with square error loss. The prior is a Dirichlet process.
The data can be uncensored, right censored, left censored or interval censored, but must be nonnegative. We assume F(0)=0.
A left censored observation, t, is handled as an interval censored one
with lefts = 0; rights = t.
NPBayes(B, theta, u, uncen=numeric(0), rightcen=numeric(0),
lefts=numeric(0), rights=numeric(0))
B |
a positive number. The parameter for the Dirichlet process prior. The weight of prior information. If B is very small, then the resulting prior is "non-informative". |
theta |
a positive number. Another parameter for Dirichlet process prior. The measure/parameter is α [t, infty ) = B exp( - theta t) . |
u |
a non-negative number, where the Bayes estimator 1- hat F(u) is to be computed. |
uncen |
optional vector holding the uncensored observations. |
rightcen |
optional vector holding the right censored observations. |
lefts |
optional vectors holding the left end-points of interval censored observations. |
rights |
optional vectors holding the right end-points of interval censored observations. Their length must agree. |
If uncen, rightcen, lefts and rights
are all missing, the estimator will be just the prior,
1-hat F(u) = exp(-theta u) .
The observations must all be non-negative.
Due to rounding error and loss of significant digits in subtraction, the result can be untrustworthy when there are many interval censored data.
a single value that is the nonparametric Bayes estimator 1- hat F(u) .
Mai Zhou.
Susarla and Van Ryzin (1976) Nonparametric Bayesian estimation of survival curves from incomplete observations. J. Amer. Statist. Assoc. 71, 897-902.
Zhou, M. (2000). Nonparametric Bayes estimator of survival functions for doubly/interval censored data. Tech Report, Univ. of Kentucky.
See also Zhou, M. (2004). Statistica Sinica.
uncensored <- c(1,5,9) rightcensored <- c(4,7) NPBayes(B=12, theta=0.2, u=3.2, uncen=uncensored, rightcen=rightcensored) leftpt <- 0 rightpt <- 3 NPBayes(B=12, theta=0.2, u=3.2, uncen=uncensored, rightcen=rightcensored, lefts = leftpt, rights = rightpt)