DS.prior: Prior Diagnostics and Estimation

In BayesGOF: Bayesian Modeling via Frequentist Goodness-of-Fit

Description

A function that generates the uncertainty diagnostic function (U-function) and estimates DS(G,m) prior model.

Usage

DS.prior(input, max.m = 8, g.par, 
         family = c("Normal","Binomial", "Poisson"), 
         LP.type = c("L2", "MaxEnt"), 
         smooth.crit = "BIC", iters = 200, B = 1000,
		 max.theta = NULL)

Arguments

input	For "Binomial", a dataframe that contains the k pairs of successes y and the corresponding total number of trials n. For "Normal", a dataframe that has the k means y_i in the first column and their respective standard errors s_i in the second. For the "Poisson", a vector of that includes the untabled count data.
max.m	The truncation point m reflects the concentration of true unknown π around known g.
g.par	Vector with estimated parameters for specified conjugate prior distribution g (i.e beta prior: α and β; normal prior: μ and τ^2; gamma prior: α and β).
family	The distribution of y_i. Currently accommodates three families: Normal, Binomial, and Poisson.
LP.type	User selects either "L2" for LP-orthogonal series representation of U-function or "MaxEnt" for the maximum entropy representation. Default is L2.
smooth.crit	User selects either "BIC" or "AIC" as criteria to both determine optimal m and smooth final LP parameters; default is "BIC".
iters	Integer value that gives the maximum number of iterations allowed for convergence; default is 200.
B	Integer value for number of grid points used for distribution output; default is 1000.
max.theta	For "Poisson", user can provide a maximum theta value for prior; default is the maximum count value in input.

Details

Function can take m=0 and will return the Bayes estimate with given starting parameters. Returns an object of class DS.GF.obj; this object can be used with plot command to plot the U-function (Ufunc), Deviance Plots (mDev), and DS-G comparison (DS_G).

Value

LP.par	m smoothed LP-Fourier coefficients, where m is determined by maximum deviance.
g.par	Parameters for g.
LP.max.uns	Vector of all LP-Fourier coefficients prior to smoothing, where the length is the same as max.m.
LP.max.smt	Vector of all smoothed LP-Fourier coefficients, where the length is the same as max.m.
prior.fit	Fitted values for the estimated prior.
UF.data	Dataframe that contains values required for plotting the U-function.
dev.df	Dataframe that contains deviance values for values of m up to max.m.
m.val	The value of m (less than or equal to the maximum m from user) that has the maximum deviance and represents the appropriate number of LP-Fourier coefficients.
sm.crit	Smoothing criteria; either "BIC" or "AIC".
fam	The user-selected family.
LP.type	User-selected representation of U-function.
obs.data	Observed data provided by user for input.

Author(s)

Doug Fletcher, Subhadeep Mukhopadhyay

References

Mukhopadhyay, S. and Fletcher, D., 2018. "Generalized Empirical Bayes via Frequentist Goodness of Fit," Nature Scientific Reports, 8(1), p.9983, https://www.nature.com/articles/s41598-018-28130-5.

Mukhopadhyay, S., 2017. "Large-Scale Mode Identification and Data-Driven Sciences," Electronic Journal of Statistics, 11(1), pp.215-240.

Examples

data(rat)
rat.start <- gMLE.bb(rat$y, rat$n)$estimate
rat.ds <- DS.prior(rat, max.m = 4, rat.start, family = "Binomial")
rat.ds
plot(rat.ds, plot.type = "Ufunc")
plot(rat.ds, plot.type = "DSg")
plot(rat.ds, plot.type = "mDev")

BayesGOF documentation built on May 2, 2019, 8:57 a.m.