best_binomial_bandit {bandit}

best_binomial_bandit

Description

Compute the Bayesian probabilities for each arm being the best binomial bandit.

Usage

best_binomial_bandit(x, n, alpha=1, beta=1)

Arguments

x

as in prop.test, a vector of the number of successes

n

as in prop.test, a vector of the number of trials

alpha

shape parameter alpha for the prior beta distribution.

beta

shape parameter beta for the prior beta distribution.

Value

a vector of probabilities for each arm being the best binomial bandit; this can be used for future randomized allocation

Author(s)

Thomas Lotze <[e-mail]> and Markus Loecher

References

Steven L. Scott, A modern Bayesian look at the multi-armed bandit, Appl. Stochastic Models Bus. Ind. 2010; 26:639-658. (http://www.economics.uci.edu/~ivan/asmb.874.pdf)

See Also

prop.test

Examples

x=c(10,20,30,50)
n=c(100,102,120,130)
arm_probabilities = best_binomial_bandit(x,n)
print(arm_probabilities)
paste("The best arm is likely ", which.max(arm_probabilities), ", with ",
	round(100*max(arm_probabilities), 2), " percent probability of being the best.", sep="")

best_binomial_bandit(c(2,20),c(100,1000))

best_binomial_bandit(c(2,20),c(100,1000), alpha = 2, beta = 5)

#quick look at the various shapes of the beta distribution as we change the shape params:
AlphaBeta = cbind(alpha=c(0.5,5,1,2,2),beta=c(0.5,1,3,2,5))
M = nrow(AlphaBeta)
y= matrix(0,100,ncol=M)
x = seq(0,1,length=100)
for (i in 1:M) y[,i] = dbeta(x,AlphaBeta[i,1],AlphaBeta[i,2])
matplot(x,y,type="l", ylim = c(0,3.5), lty=1, lwd=2)
param_strings = paste("a=", AlphaBeta[,"alpha"], ", b=", AlphaBeta[,"beta"], sep="")
legend("top", legend = param_strings, col=1:M, lty=1)