rEB.Finite.Bayes: Relevance-Integrated Finite Bayes.

In LPRelevance: Relevance-Integrated Statistical Inference Engine

Relevance-Integrated Finite Bayes.

Description

Performs custom-tailored Finite Bayes inference via LASERs.

Usage

rEB.Finite.Bayes(X,z,X.target,z.target,m=c(4,6),m.EB=8, B=10, centering=TRUE,
            nsample=min(1000,length(z)), g.method='DL',LP.type='L2',  sd0=NULL,
            theta.set.prior=seq(-2.5*sd(z),2.5*sd(z),length.out=500),
            theta.set.post=seq(z.target-2.5*sd(z),z.target+2.5*sd(z),length.out=500),
            post.alpha=0.8,  plot=TRUE, ...)

Arguments

X	A n-by-d matrix of covariate values
z	A length n vector containing observations of target random variable.
X.target	A length d vector providing the set of covariates for the target case.
z.target	the target z to investigate
m	An ordered pair. First number indicates how many LP-nonparametric basis to construct for each X, second number indicates how many to construct for z.
m.EB	The truncation point reflecting the concentration of true nonparametric prior density π around known prior distribution g
B	Number of bags of bootstrap samples for Finite Bayes.
centering	Whether to perform regression-adjustment to center the data, default is TRUE.
nsample	Number of relevance samples generated for the target case.
g.method	Suggested method for finding parameter estimates \hat{μ} and \hat{τ}^2 for normal prior: "DL" uses Dersimonian and Lard technique; "SJ" uses Sidik-Jonkman; 'REML' uses restricted maximum likelihood; and "MoM" uses a method of moments technique.
LP.type	User selects either "L2" for LP-orthogonal series representation of relevance density function d or "MaxEnt" for the maximum entropy representation. Default is L2.
sd0	Fixed standard deviation for z|θ. Default is NULL, the standard error will be calculated from data.
theta.set.prior	This indicates the set of grid points to compute prior density.
theta.set.post	This indicates the set of grid points to compute posterior density.
post.alpha	The alpha level for posterior HPD interval.
plot	Whether to display plots for prior and posterior of Relevance Finite Bayes.
...	Extra parameters to pass to LASER function.

Value

A list containing the following items:

prior	Relevant Finite Bayes prior results.
$prior.fit	Prior density curve estimation.
posterior	Relevant empirical Bayes posterior results.
$post.fit	Posterior density curve estimation.
$post.mode	Posterior mode for π(θ|z,\boldsymbol{x}).
$post.mean	Posterior mean for π(θ|z,\boldsymbol{x}).
$post.mean.sd	Standard error for the posterior mean.
$HPD.interval	The HPD interval for posterior π(θ|z,\boldsymbol{x}).
g.par	Parameters for g=N(μ,τ^2).
LP.coef	Reports the LP-coefficients of the relevance function d_x(x).
sd0	Initial estimate for null standard errors.
plots	The plots for prior and posterior density.

Author(s)

Subhadeep Mukhopadhyay, Kaijun Wang

Maintainer: Kaijun Wang <[e-mail]>

References

Mukhopadhyay, S., and Wang, K (2021) "On The Problem of Relevance in Statistical Inference". <arXiv:2004.09588>

Examples

data(funnel)
X<-funnel$x
z<-funnel$z
X.target=30
z.target=4.49
rFB.out=rEB.Finite.Bayes(X,z,X.target,z.target,B=5,nsample=1000,m=c(4,8),m.EB=8,
                      theta.set.prior=seq(-4,4,length.out=500),
                      theta.set.post=seq(0,5,length.out=500),cred.interval=0.8,parallel=FALSE)
rFB.out$plots$prior
rFB.out$plots$post

LPRelevance documentation built on May 18, 2022, 9:05 a.m.