This model first samples a bias, splits the bias into red and black, and then defines how the urnsâ€™ proportions of red balls depend on the biases.

```
;;;fold: factor-equal?
(define (factor-eq x y)
(factor (if (equal? x y) 0.0 -1000))
#t)
(define (factor-equal? xs ys)
(if (and (null? xs) (null? ys))
#t
(and (factor-eq (first xs) (first ys))
(factor-equal? (rest xs) (rest ys)))))
;;;
(define samples
(mh-query 3000 10
;; model
(define bias (uniform 0 10))
(define red-bias (uniform 0 bias))
(define black-bias (- bias red-bias))
(define urn->proportion-red
(mem
(lambda (urn)
(beta (+ .4 red-bias) (+ .4 black-bias)))))
(define (sample-urn urn)
(if (flip (urn->proportion-red urn))
'red
'black))
;; query expression
(urn->proportion-red 3)
;; condition
(factor-equal? (repeat 15 (lambda () (sample-urn 1)))
'(red red red red red red red red
red red red red red red black))))
(density samples "Proportion of red balls in urn 3" true)
```

References:

- Cite:Stuhlmueller2013aa