best_binomial_bandit_sim {bandit}

best_binomial_bandit_sim

Description

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

Usage

best_binomial_bandit_sim(x, n, alpha = 1, beta = 1, ndraws = 5000)

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.

ndraws

number of random draws from the posterior

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 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(10,20,30,33)
n=c(100,102,120,130)
best_binomial_bandit_sim(x,n, ndraws=1000)
round(best_binomial_bandit(x,n),3)

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

best_binomial_bandit_sim(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)