#| 

  BUGS book, 3.3.2 in Racket Gamble.
  Example 3.3.2 Surgery (continued): beta-binomial analysis using BUGS

var : p_crit
#f: 0.5850000000000004
#t: 0.4150000000000003
mean: 0.4150000000000003
Min: 0 Mean: 0.44 Max: 1 Variance: 0.2464 Stddev: 0.4963869458396343
Credible interval (0.84): 0..1

var : y_pred
0: 0.2950000000000002
1: 0.2900000000000002
2: 0.22400000000000017
3: 0.10800000000000007
4: 0.05400000000000002
5: 0.01799999999999999
6: 0.007999999999999995
8: 0.0019999999999999987
7: 0.0009999999999999994
mean: 1.4390000000000007
Min: 0 Mean: 1.528 Max: 7 Variance: 2.139216 Stddev: 1.4626058936022375
Credible interval (0.84): 0..3

var : theta
0.11358878049205051: 0.0009999999999999994
0.2044581574146713: 0.0009999999999999994
0.03559794917668811: 0.0009999999999999994
0.09538904980935774: 0.0009999999999999994
0.023888109644223086: 0.0009999999999999994
0.14115320693653635: 0.0009999999999999994
0.06753741906450797: 0.0009999999999999994
0.0914887633211163: 0.0009999999999999994
0.0651717446685267: 0.0009999999999999994
0.0556042259094008: 0.0009999999999999994
0.056270702337000496: 0.0009999999999999994
0.08012999711622149: 0.0009999999999999994
0.03221692824899702: 0.0009999999999999994
0.04946764613231722: 0.0009999999999999994
0.060797802307496734: 0.0009999999999999994
...
0.010547518854914352: 0.0009999999999999994
0.03640752092362645: 0.0009999999999999994
0.04242600842765503: 0.0009999999999999994
0.05705981955277175: 0.0009999999999999994
0.07008151787016471: 0.0009999999999999994
0.07591665245329911: 0.0009999999999999994
0.050485341509400684: 0.0009999999999999994
0.044794708702821755: 0.0009999999999999994
0.1386426607793571: 0.0009999999999999994
0.05183508392111952: 0.0009999999999999994
0.05957614898765729: 0.0009999999999999994
0.10093068159790196: 0.0009999999999999994
0.0884172841474261: 0.0009999999999999994
0.040899588765462035: 0.0009999999999999994
0.0502601564597627: 0.0009999999999999994
mean: 0.07465483246394995
Min: 0.005793805261303277 Mean: 0.07665855066080236 Max: 0.2547678006621886 Variance: 0.0016365676361203279 Stddev: 0.040454513173690865
Credible interval (0.84): 0.01793537221166915..0.12315574171372284

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Racket page: http://www.hakank.org/racket/

|#

#lang gamble

(require racket)
(require "gamble_utils.rkt")

(define (bugs-book-3-3-2)
  (rejection-sampler
   ; importance-sampler
   ; mh-sampler

   (define a 3)
   (define b 27)
   (define n 10)
   (define n_pred 20)
   (define n_crit 2)
    
   (define theta (beta a b))
   (define y (binomial n theta))
   (define y_pred (binomial n_pred theta))
   (define p_crit (> (+ y_pred 0.5) n_crit)) ;; toReal(y_pred - n_crit) + 0.5 > 0.0;

   (observe/fail y 0)

   (list p_crit y_pred theta)
   
   )
  )

(show-marginals (bugs-book-3-3-2)
                (list "p_crit" "y_pred" "theta")
                #:truncate-output 15
                #:show-stats? #t
                #:credible-interval 0.84
                )