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We use the Dirichlet Process to construct a distribution on a potentially infinite number of bags. Each bag is associated with a discrete distribution on the three colors blue, green, and red. We draw marbles, with each marble drawn randomly from either a previously seen or a new bag.

(define colors '(blue green red))

(define samples
   200 100

   (define phi (dirichlet '(1 1 1)))
   (define alpha 0.1)
   (define prototype (map (lambda (w) (* alpha w)) phi))

   (define bag->prototype (mem (lambda (bag) (dirichlet prototype))))

   ;;the prior distribution on bags is simply a DPmem of gensym:
   (define get-bag (DPmem 1.0 gensym))

   ;;each observation comes from one of the bags:
   (define obs->bag (mem (lambda (obs-name) (get-bag))))

   (define draw-marble
     (mem (lambda (obs-name)
            (multinomial colors (bag->prototype (obs->bag obs-name))))))

   ;;did obs1 and obs2 come from the same bag? obs1 and obs3?
   (list (equal? (obs->bag 'obs1) (obs->bag 'obs2))
         (equal? (obs->bag 'obs1) (obs->bag 'obs3)))

    (equal? 'red (draw-marble 'obs1))
    (equal? 'red (draw-marble 'obs2))
    (equal? 'blue (draw-marble 'obs3))
    (equal? 'blue (draw-marble 'obs4))
    (equal? 'red (draw-marble 'obs5))
    (equal? 'blue (draw-marble 'obs6))

(hist (map first samples) "obs1 and obs2 same category?")
(hist (map second samples) "obs1 and obs3 same category?")