EBpostdens {SpatialEpi}

Produce plots of empirical 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

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

Arguments

Y

observed disease counts

E

expected disease counts

alpha

x

beta

x

Xrow

x

lower

x

upper

x

main

x

Value

A plot containing the gamma posterior distribution

Author(s)

Jon Wakefield

Examples

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")