#| 

  BUGS book, 2.5.1 in Racket Gamble.
  "The how many trick"

var : number
26181.209136598904: 0.0009999999999999994
30135.43182499509: 0.0009999999999999994
31532.69204534173: 0.0009999999999999994
36934.82740997929: 0.0009999999999999994
30731.95202277405: 0.0009999999999999994
33896.830238383765: 0.0009999999999999994
33035.38588974109: 0.0009999999999999994
27536.56772546697: 0.0009999999999999994
37809.02648610869: 0.0009999999999999994
30953.367381930126: 0.0009999999999999994
...
30233.2389587696: 0.0009999999999999994
31814.638729164304: 0.0009999999999999994
32332.08915092479: 0.0009999999999999994
30088.729315394245: 0.0009999999999999994
40822.727961353085: 0.0009999999999999994
27721.507629055683: 0.0009999999999999994
31623.607310119995: 0.0009999999999999994
32523.24307708477: 0.0009999999999999994
39352.93917013385: 0.0009999999999999994
24754.154029673686: 0.0009999999999999994
mean: 33060.87053387217

var : ix
12: 0.2970000000000002
11: 0.2590000000000002
13: 0.16900000000000012
10: 0.1360000000000001
14: 0.07700000000000004
9: 0.028
15: 0.026
16: 0.004999999999999997
8: 0.0019999999999999987
17: 0.0009999999999999994
mean: 11.80300000000001

var : x-all
(1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0): 0.21000000000000016
(1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0): 0.11500000000000007
(1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0): 0.11400000000000007
(1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0): 0.06500000000000003
(1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0): 0.058000000000000024
(1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0): 0.034
(1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0): 0.033
(1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0): 0.031000000000000003
(1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0): 0.030000000000000002
(1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0): 0.028
...
(1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0): 0.0009999999999999994
(1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0): 0.0009999999999999994


  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-2-5-1)
  (rejection-sampler
   ; importance-sampler
   ; mh-sampler
   
   (define n 20) 

    (define (y i) (gamma 3.0 (/ 0.04)) )
    
    (define (cum i)
      ; (displayln (list "cum " i ":" (cum i)))
      (if (= i 0)
          (+ (y 0) 1)
          (+ (cum (sub1 i)) (y i) i)
          ))
    
    (define (cum-step i)
      (if (> (cum i) 1000.0)
          (* i (cum i))
          0))

    ;; A changepoint.
    (define (x i) (if (< (cum i) 1001.0) 1 0))

    (define number
      (apply max (for/list ([i (range n)]) (cum-step i) )))
    
    (define ix
      (apply max (for/list ([i (range n)])
                   (if (= (x i) 1) i 0))))

    (define x-all
      (for/list ([i (range n)]) (x i)))
    
   
    (list number
          ix 
          x-all 
          )
    )
  )

(show-marginals (bugs-book-2-5-1) (list "number" "ix" "x-all" ) #:truncate-output 10)
; (show-model (bugs-book-2-5-1) #:no-stats? #t #:no-cred? #t)