best_binomial_bandit_sim {bandit} R Documentation

## 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.

`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)
```

[Package bandit version 0.5.0 Index]