;; Here is a simple Bayesian network consisting of five nodes, one of which
;; depends on two parents, both of which depend on a single ancestor.  This
;; forms an undirected loop.  The example is originally from Cooper, and
;; models consequences of a brain tumor.  For binary variables, the #f value
;; comes before the #t value.

(define mcbn1
  (define-bnet 'mcbn1
    '((a () (0.8 0.2))                  ;; P(A) = 0.2
      (b (a) ((0.9 0.1) (0.3 0.7)))     ;; P(B|~A) = 0.1, P(B|A) = 0.7
      (c (a) ((0.7 0.3) (0.4 0.6)))     ;; ...
      (d (b c) (((0.9 0.1) (0.7 0.3)) ((0.6 0.4) (0.2 0.8)))) 
      ;; P(D|~B,~C) = 0.1, P(D|~B,C) = 0.3, P(D|B,~C) = 0.4, P(D|B,C) = 0.8
      (e (c) ((0.9 0.1) (0.6 0.4))))))

;; Here are a few simple example calculations to try:
;;
;; (infer mcbn1 '((a #t)))
;; (infer mcbn1 '((a #f) (e #t)))
;; (infer mcbn1 '((a #t) (b #f) (c #t) (d #t) (e #t)))
;;
;; A conditional probability, say P(e=#t|a=#f) is P(e=#t,a=#f)/P(a=#f)
;; Thus,
;; (/ (infer mcbn1 '((a #f) (e #t))) (infer mcbn1 '((a #f))))

(define mcbn2
  (define-bnet 'mcbn2
    '((a () (0.8 0.2))
      (b (a) (noisy-or 0.1 0.9))
      (c (a) (noisy-or 0.05 0.8))
      (d (b c) (noisy-or 0.0 0.9 0.75))
      (e (c) (noisy-or 0.1 0.6)))))