DS.Finite.Bayes {BayesGOF}

Conduct Finite Bayes Inference on a DS object

Description

A function that generates the finite Bayes prior and posterior distribution, along with the Bayesian credible interval for the posterior mean.

Usage

DS.Finite.Bayes(DS.GF.obj, y.0, n.0 = NULL, 
             cred.interval = 0.9, iters = 25)

Arguments

DS.GF.obj

Object from DS.prior.

y.0

For Binomial family, number of success y_i for new study. In the Poisson family, it is the number of counts. Represents the study mean for the Normal family.

n.0

For the Binomial family, the total number of trials for the new study. In the Normal family, n.0 is the standard error of y.0. Not used for the Poisson family.

cred.interval

The desired probability for the credible interval of the posterior mean; the default is 0.90 (90%).

iters

Integer value of total number of iterations.

Value

prior.fit

Fitted values for the estimated parametric, DS, and finite Bayes prior distributions.

post.fit

Dataframe with \theta, \pi_G(\theta | y_0), and \pi_{LP}(\theta | y_0).

interval

The 100*cred.interval% Bayesian credible interval for the posterior mean.

post.vec

Vector containing the PEB posterior mean (PEB.mean), DS posterior mean (DS.mean), PEB posterior mode (PEB.mode), and the DS posterior mode (DS.mode).

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.

Efron, B., 2018. "Bayes, Oracle Bayes, and Empirical Bayes," Technical Report.

Examples

## Not run: 
### Finite Bayes: Rat with theta_71 (y_71 = 4, n_71 = 14)
data(rat)
rat.start <- gMLE.bb(rat$y, rat$n)$estimate
rat.ds <- DS.prior(rat, max.m = 4, rat.start. family = "Binomial")
rat.FB <- DS.FiniteBayes(rat.ds, y.0 = 4, n.0 = 14)
plot(rat.FB)

## End(Not run)