rEB.proc: Relevance-Integrated Empirical Bayes Inference

In LPRelevance: Relevance-Integrated Statistical Inference Engine

Relevance-Integrated Empirical Bayes Inference

Description

Performs custom-tailored empirical Bayes inference via LASERs.

Usage

rEB.proc(X, z, X.target, z.target, m = c(4, 6), nbag = NULL, centering = TRUE,
	lp.reg.method = "lm", coef.smooth = "BIC", nsample = min(length(z),2000),
	theta.set.prior = NULL, theta.set.post = NULL, LP.type = "L2",
	g.method = "DL", sd0 = NULL, m.EB = 8, parallel = FALSE,
	avg.method = "mean", post.curve = "HPD", post.alpha = 0.8,
	color = "red", ...)

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.
nbag	Number of bags of parametric bootstrapped samples to use, set to NULL to disable.
centering	Whether to perform regression-adjustment to center the data, default is TRUE.
lp.reg.method	Method for estimating the relevance function and its conditional LP-Fourier coefficients. We currently support thee options: lm (inbuilt with subset selection), glmnet, and knn.
coef.smooth	Specifies the method to use for LP coefficient smoothing (AIC or BIC). Uses BIC by default.
nsample	Number of relevance samples generated for the target case.
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.
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.
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.
sd0	Fixed standard deviation for z|θ. Default is NULL, the standard error will be calculated from data.
m.EB	The truncation point reflecting the concentration of true nonparametric prior density π around known prior distribution g
parallel	Use parallel computing for obtaining the relevance samples, mainly used for very huge nsample, default if FALSE.
avg.method	For parametric bootstrapping, this specifies how the results from different bags are aggregated. ("mean" or "median".)
post.curve	For plotting, this specifies what to show on posterior curve. "HPD" provides HPD interval, "band" gives confidence band.
post.alpha	Confidence level to use when plotting posterior confidence band, or the alpha level for HPD interval.
color	The color of the plots.
...	Extra parameters to pass to other functions. Currently only supports the arguments for knn().

Value

A list containing the following items:

result	Contains relevant empirical Bayes prior and posterior results.
sd0	Initial estimate for null standard errors.
prior	Relevant empirical Bayes prior results.
$g.par	Parameters for g=N(μ,τ^2).
$g.method	Method used for finding the parameter estimates \hat{μ} and \hat{τ}^2 for g.
$LP.coef	Reports the LP-coefficients of the relevance function d_x(x).
posterior	Relevant empirical Bayes posterior results.
$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, when using parametric bootstrap.
$HPD.interval	The HPD interval for posterior π(θ|z,\boldsymbol{x}).
$post.alpha	same as input post.alpha.
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=60
z.target=4.49
rEB.out<-rEB.proc(X,z,X.target,z.target,m=c(4,8),
	theta.set.prior=seq(-2,2,length.out=200),
	theta.set.post=seq(-2,5,length.out=200),
	centering=TRUE,m.EB=6,nsample=1000)
rEB.out$plots$rEB.post
rEB.out$plots$rEB.prior

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