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.

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")

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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