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# Multinomial Distribution. 2008 U.S. Presidential Election

########################################################################

model

{

for(i in 1:51)

{

M[i] <- 500 # Sample size for the poll is assume to be 500 each.

N[i] <- 5000 # Sample size from the predictive dist

y[i, 1] <- M[i]*M.pct[i]/100

y[i, 2] <- M[i]*O.pct[i]/100

y[i, 3] <- M[i]*(100-M.pct[i]-O.pct[i])/100

y[i, 1:3] ~ dmulti( theta[i,1:3], M[i]) # likelihood

theta[i, 1:3] ~ ddirch(alpha[1:3]) # prior

y.pred[i, 1:3] ~ dmulti( theta[i,1:3], N[i]) # predictive dist

ev.pred[i] <- EV[i]*step(y.pred[i,2] - y.pred[i,1])

}

evsum.pred <- sum( ev.pred[] ) # predicted number of EVs

obama.prob <- step(evsum.pred - 270) # Estimate Posterior Pr(Obama wins)

}

# Initial values -> generate inits

# Data 1

list( alpha = c(1, 1, 1) ) # uniform prior for theta

# Data 2

M.pct[] O.pct[] EV[]

58 36 9

55 37 3

50 46 10

51 44 6

33 55 55

45 52 9

31 56 7

38 56 3

13 82 3

46 50 27

52 47 15

32 63 4

68 26 4

35 59 21

48 48 11

37 54 7

63 31 6

51 42 8

50 43 9

35 56 4

39 54 10

34 53 12

37 53 17

42 53 10

46 33 6

48 48 11

49 46 3

60 34 5

43 47 5

42 53 4

34 55 15

43 51 5

31 62 31

49 46 15

43 45 3

47 45 20

61 34 7

34 48 7

46 52 21

31 45 4

59 39 8

48 41 3

55 39 11

57 38 34

55 32 5

36 57 3

44 47 13

39 51 11

53 44 5

42 53 10

58 32 3

END