# Baseball

# Model 1

model
{
for (i in 1:N) {
     y[i] ~ dbin( p[i], n[i] ) ;
     p[i] ~ dbeta( alpha, beta ) ;
}

#alpha ~ dgamma( 0.11, 0.11) ;
#beta ~ dgamma(1.0, 0.33 ) ;
alpha ~ dgamma(0.0001, 0.0001) ;
beta ~ dgamma(0.0001, 0.0001) ;

betamean <- alpha /( alpha + beta) ;
}

data
list( y = c( 1,0,1,1,1,0,1,0), n = c(5,4,3,5,3,4,4,2), N = 8)

inits
list( alpha = 1, beta = 1, p = c(.5, .5, .5, .5, .5, .5, .5, .5) )

list(alpha = 100, beta = 10, p = c(.9, .9, .9, .9, .9, .9, .9, .9) )

list(alpha = 10, beta = 100, p = c(.1, .1, .1, .1, .1, .1, .1, .1))


# Model 2

model
{
for (i in 1:N) {
   y[i] ~ dbin(p[i], n[i] ) ;
   logit(p[i])  <- v[i] ;
   v[i] ~ dnorm( mu, tausq) ;
}

mu ~ dnorm(0, 0.0001) ;
tausq ~ dgamma( 1, 1) ;

logitinvmu <- exp(mu) / ( 1 + exp(mu) ) ;

}

list( mu = 0, tausq = 1)

list( mu = 5, tausq = 100)

list( mu = -5, tausq = 0.01)