Produce plots of emprical Bayes posterior densities when the data Y are Poisson with expected number E and relative risk theta, with the latter having a gamma distribution with known values alpha and beta, which are estimated using empirical Bayes.

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Description

This function produces plots of empirical Bayes posterior densities which are gamma distributions with parameters (alpha+Y, (alpha+E*mu)/mu) where mu = exp(x beta). The SMRs are drawn on for comparison.

Usage

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EBpostdens(Y, E, alpha, beta, Xrow = NULL, lower = NULL, upper = NULL, main = "")

Arguments

Y

observed disease counts

E

expected disease counts

alpha
beta
Xrow
lower
upper
main

Value

A plot containing the gamma posterior distribution

Author(s)

Jon Wakefield

See Also

EBpostthresh, eBayes

Examples

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data(scotland)
Y <- scotland$data$cases
E <- scotland$data$expected
ebresults <- eBayes(Y,E)
EBpostdens(Y[1], E[1], ebresults$alpha, ebresults$beta, lower=0, upper=15,
main="Area 1")

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