BayesVarSel (version 2.4.5)

pltltn: Correction for p>>n for an object of class Bvs

Description

In cases where p>>n and the true model is expected to be sparse, it is very unlikely that the Gibbs sampling will sample models in the singular subset of the model space (models with k>n). Nevertheless, depending on how large is p/n and the strenght of the signal, this part of the model space could be very influential in the final response.

Usage

pltltn(object)

Value

pltltn returns a list with the following elements:

pS

An estimation of the probability that the true model is irregular (k>n)

postprobdim

A corrected estimation of the posterior probabilities over the dimensions

inclprob

A corrected estimation of the posterior inclusion probabilities

Arguments

object

An object of class Bvs obtained with GibbsBvs

Author

Gonzalo Garcia-Donato

Maintainer: <[e-mail]>

Details

From an object created with GibbsBvs and prior probabilities specified as Scott-Berger, this function provides an estimation of the posterior probability of models with k>n which is a measure of the importance of these models. In summary, when this probability is large, the sample size is not large enough to beat such large p. Additionally, pltltn gives corrections of the posterior inclusion probabilities and posterior probabilities of dimension of the true model.

References

Berger, J.O., Garcia-Donato, G., Martínez-Beneito M.A. and Peña, V. (2016) Bayesian variable selection in high dimensional problems without assumptions on prior model probabilities. arXiv:1607.02993

See Also

See GibbsBvs for creating objects of the class Bvs.

Examples

if (FALSE) {
data(riboflavin, package="hdi")

set.seed(16091956)
#the following sentence took 37.3 minutes in a single core
#(a trick to see the evolution of the algorithm is to monitor
#the files created by the function.
#you can see the working directory running
#tempdir()
#copy this path in the clipboard. Then open another R session
#and from there (once the simulating process is running and the burnin has completed)
#write
#system("wc (path from clipboard)/AllBF")
#the number here appearing is the number of completed iterations
#
testRB<- GibbsBvs(formula=y~.,
                  data=riboflavin,
                  prior.betas="Robust",
                  init.model="null",
                  time.test=F,
                  n.iter=10000,
                  n.burnin=1000)

set.seed(16091956)
system.time(
testRB<- GibbsBvs(formula=y~.,
                  data=riboflavin,
                  prior.betas="Robust",
                  init.model="null",
                  time.test=F,
                  n.iter=10000,
                  n.burnin=1000)
)

#notice the large sparsity of the result since
#the great majority of covariates are not influential:
boxplot(testRB$inclprob)
testRB$inclprob[testRB$inclprob>.5]
#xYOAB_at xYXLE_at
#  0.9661   0.6502
#we can discharge all covariates except xYOAB_at and xYXLE_at
#the method does not reach to inform about xYXLE_at and its posterior
#probability is only slightly bigger than its prior probability

#We see that dimensions of visited models are small:
plot(testRB, option="d", xlim=c(0,100))
#so the part of the model space with singular models (k>n)
#has not been explored.
#To correct this issue we run:
corrected.testRB<- pltltn(testRB)
#Estimate of the posterior probability of the
# model space with singular models is: 0
#Meaning that it is extremely unlikely that the true model is such that k>n
#The corrected inclusion probabilities can be accessed through
#corrected.testRB but, in this case, these are essentially the same as in the
#original object (due to the unimportance of the singular part of the model space)

}