#| 

  Mean inference in Racket.Gamble 

  From the SPPL model poisson_mean_inference.pynb

  Here is the PDF of Y = 0..20 (exact probabilities) from the SPPL model:
  (0, 0.19572329209779615),
  (1, 0.24541518485806976),
  (2, 0.15633363576277434),
  (3, 0.07275764007128807),
  (4, 0.03749784880330323),
  (5, 0.03225414602603766),
  (6, 0.036272539178041456),
  (7, 0.03919655164760693),
  (8, 0.03782130413444809),
  (9, 0.032547494609049904),
  (10, 0.025221805385485633),
  (11, 0.017769927037907036),
  (12, 0.011477227802063514),
  (13, 0.006844292955361095),
  (14, 0.00379364785941744),
  (15, 0.0019704640279916506),
  (16, 0.000975431521715664),
  (17, 0.0004844975064651556),
  (18, 0.0002799391781190319),
  (19, 0.00023526933546341676)
  (20, 0.0002864142016352986)

  This Gamble model

var : x
...
mean: -0.00208193575164102

var : y
1: 0.23691000000037568
0: 0.1846200000003234
2: 0.17141000000031018
3: 0.10304000000021132
4: 0.06221000000011403
5: 0.04217000000008008
6: 0.03086000000006079
7: 0.024370000000047545
8: 0.019680000000037973
9: 0.015660000000029768
10: 0.012490000000023841
11: 0.011170000000021376
12: 0.009340000000017959
13: 0.008230000000015886
14: 0.007190000000013889
15: 0.00586000000001129
16: 0.005490000000010567
17: 0.004600000000008828
18: 0.004230000000008105
19: 0.0038300000000073267
20: 0.0031000000000059318
21: 0.0027800000000053203
22: 0.002660000000005091
23: 0.0022400000000042885
24: 0.0021400000000040974
25: 0.0018800000000036004
26: 0.001850000000003543
27: 0.00166000000000318
28: 0.0014600000000027978
29: 0.0011300000000021672
30: 0.001110000000002129
31: 0.0009800000000018806
32: 0.0009400000000018038
33: 0.0008300000000015924
35: 0.0008200000000015732
39: 0.0007700000000014771
34: 0.0007500000000014386
36: 0.000720000000001381
37: 0.0007100000000013618
40: 0.0005700000000010927
38: 0.0005200000000009967
44: 0.00045000000000086236
41: 0.00043000000000082404
45: 0.00040000000000076655
46: 0.0003400000000006516
42: 0.0003300000000006324
43: 0.0003300000000006324
50: 0.0003000000000005749
48: 0.0002600000000004983
47: 0.0002500000000004791
49: 0.0002500000000004791
52: 0.0002500000000004791
54: 0.00024000000000045992
53: 0.00020000000000038328
56: 0.00020000000000038328
51: 0.0001700000000003258
65: 0.0001400000000002683
55: 0.00012000000000022996
58: 0.00012000000000022996
59: 0.00012000000000022996
63: 0.00010000000000019164
72: 0.00010000000000019164
60: 9.000000000017248e-5
61: 9.000000000017248e-5
62: 9.000000000017248e-5
57: 8.000000000015331e-5
66: 8.000000000015331e-5
67: 8.000000000015331e-5
64: 7.000000000013415e-5
73: 7.000000000013415e-5
78: 7.000000000013415e-5
69: 6.000000000011498e-5
70: 6.000000000011498e-5
90: 6.000000000011498e-5
71: 5.000000000009582e-5
74: 5.000000000009582e-5
79: 5.000000000009582e-5
80: 5.000000000009582e-5
82: 5.000000000009582e-5
88: 5.000000000009582e-5
75: 4.0000000000076656e-5
77: 4.0000000000076656e-5
81: 4.0000000000076656e-5
85: 4.0000000000076656e-5
87: 4.0000000000076656e-5
102: 4.0000000000076656e-5
68: 3.0000000000057494e-5
76: 3.0000000000057494e-5
89: 3.0000000000057494e-5
91: 3.0000000000057494e-5
93: 3.0000000000057494e-5
103: 3.0000000000057494e-5
84: 2.0000000000038328e-5
86: 2.0000000000038328e-5
95: 2.0000000000038328e-5
96: 2.0000000000038328e-5
98: 2.0000000000038328e-5
100: 2.0000000000038328e-5
107: 2.0000000000038328e-5
136: 1.0000000000019164e-5
94: 1.0000000000019164e-5
97: 1.0000000000019164e-5
99: 1.0000000000019164e-5
101: 1.0000000000019164e-5
106: 1.0000000000019164e-5
108: 1.0000000000019164e-5
109: 1.0000000000019164e-5
110: 1.0000000000019164e-5
111: 1.0000000000019164e-5
114: 1.0000000000019164e-5
116: 1.0000000000019164e-5
118: 1.0000000000019164e-5
122: 1.0000000000019164e-5
123: 1.0000000000019164e-5
124: 1.0000000000019164e-5
mean: 4.170010000007912


  This is a port of my WebPPL model mean_inference.wppl which in turn is
  a port of the SPPL model poisson_mean_inference.pynb

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

|#

#lang gamble

; (require gamble/viz)
(require racket)
(require "gamble_utils.rkt")
; (require "gamble_distributions.rkt")


(define (model)
  (; enumerate
   ; rejection-sampler
   importance-sampler
   ; mh-sampler

   ; x is truncated
   ;; (define x (normal 0 1))
   ;; (observe/fail (>= x -4))
   ;; (observe/fail (<= x 4))
   
   ; neater
   (define x (sample (clip-distx (normal-dist 0 1) -4 4 )))
   
   (define y (poisson (+ 1 (* 2 (abs (expt x 3))))))
   
   (list x
         y
         )
   )
)

(show-marginals (model)
                (list  "x"
                       "y"
                       )
                #:num-samples 100000
                ; #:truncate-output 5
                ; #:skip-marginals? #t
                ; #:show-stats? #t
                ; #:credible-interval 0.84
                ; #:show-histogram? #t
                ; #:show-percentiles? #t
                )