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;; Bayesian inference of multinomial distribution parameters
(use '(incanter core stats bayes charts))
(def y [727 583 137])
(div y 1447.) ;; (0.502 0.403 0.095)
(def theta (sample-multinomial-params 1000 y))
(def theta1 (sel theta :cols 0))
(def theta2 (sel theta :cols 1))
(def theta3 (sel theta :cols 2))
;; view means, 95% CI, and histograms of the proportion parameters
(mean theta1) ;; 0.502
(sd theta1) ;; 0.0129
(quantile theta1 :probs [0.025 0.975]) ;; (0.476 0.528)
(view (histogram theta1
:title "Bush, Sr. Support"))
(mean theta2) ;; 0.403
(sd theta2) ;; 0.013
(quantile theta2 :probs [0.025 0.975]) ;; (0.376 0.427)
(view (histogram theta2
:title "Dukakis Support"))
(mean theta3) ;; 0.095
(sd theta3) ;; 0.008
(quantile theta3 :probs [0.025 0.975]) ;; (0.082 0.111)
(view (histogram theta3
:title "Other/Undecided"))
;; view a histogram of the difference in proportions between the first
;; two candidates
(view (histogram (minus theta1 theta2)
:title "Bush, Sr. and Dukakis Diff"))
;; sample the proportions directly from a Dirichlet distribution
(def alpha [1 1 1])
(def props (sample-dirichlet 1000 (plus y alpha)))
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