BayesGOF (version 4.0)

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. "Bayesian Modeling via Goodness-of-Fit," Technical report, https://arxiv.org/abs/1802.00474 .

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")
# }