BayesGOF (version 5.2)

DS.prior: Prior Diagnostics and Estimation

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 \(\pi\) around known \(g\).

g.par

Vector with estimated parameters for specified conjugate prior distribution \(g\) (i.e beta prior: \(\alpha\) and \(\beta\); normal prior: \(\mu\) and \(\tau^2\); gamma prior: \(\alpha\) and \(\beta\)).

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.

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.

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).

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

# NOT RUN {
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")
# }