Produce the probabilities of exceeding a threshold given a posterior gamma distribution.

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Description

This function produces the posterior probabilities of exceeding a threshold given a gamma distributions with parameters (alpha+Y, (alpha+E*mu)/mu) where mu = exp(x beta). This model arises from Y being Poisson with mean theta times E where theta is the relative risk and E are the expected numbers. The prior on theta is gamma with parameters alpha and beta. The parameters alpha and beta may be estimated using empirical Bayes.

Usage

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EBpostthresh(Y, E, alpha, beta, Xrow = NULL, rrthresh)

Arguments

Y

observed disease counts

E

expected disease counts

alpha
beta
Xrow
rrthresh

Value

Posterior probabilities of exceedence are returned.

Author(s)

Jon Wakefield

See Also

eBayes

Examples

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data(scotland)
Y <- scotland$data$cases
E <- scotland$data$expected
ebresults <- eBayes(Y,E)
# Find probabilities of exceedence of 3
thresh3 <- EBpostthresh(Y, E, alpha=ebresults$alpha, beta=ebresults$beta,
rrthresh=3)
mapvariable(thresh3, scotland$spatial.polygon)

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