Bayes-optimal spending function — sfabz • FABInference

Compute Bayes optimal spending function

sfabz(theta, psi, alpha = 0.05)

Arguments

theta	value of theta being tested
psi	a list of parameters for the spending function, including mu, the prior expectation of E[y] tau2, the prior variance of E[y] sigma2 the variance of y
alpha	level of test

theta

value of theta being tested

psi

a list of parameters for the spending function, including

mu, the prior expectation of E[y]
tau2, the prior variance of E[y]
sigma2 the variance of y

alpha

level of test

Value

a scalar value giving the optimal tail-area probability

Details

This function computes the value of s that minimizes the acceptance probability of a biased level-alpha test for a normal population with known variance, under a specified prior predictive distribution.

Author

Peter Hoff

Examples

thetas<-seq(-1,1,length=100)  
s<-NULL 
for(theta in thetas){ s<-c(s,sfabz(theta,list(mu=0,tau2=1,sigma2=1)) ) }  
plot(thetas,s,type="l")