laplace's rule of succession

rule_of_succession.clj

@@ -0,0 +1,52 @@
+(defn tosses[]
+  (let [p (rand)]
+    (cons p (map (fn[_](if (< (rand) p) :h :t)) (range)))))
+
+(def coins (for [i (range)] (tosses)))
+
+(defn select-tosses [sq]
+  (filter #(= (take (count sq) (drop 1 %)) sq) coins))
+
+(defn select-coins [sq]
+  (map first (select-tosses sq)))
+
+(def select-coins (memoize select-coins))
+
+(defn next-vals [sq]
+  (map #(nth % (inc (count sq))) (select-tosses sq)))
+
+(defn laplace-rule [sq]
+  (let [f (frequencies sq)]
+      (str (inc (get f :h 0)) ":" (inc (get f :t 0)))))
+
+(defn laplace-by-sampling [sq n]
+  (let [f (frequencies (take n (next-vals sq)))]
+    (str (get f :h 0) ":" (get f :t 0))))
+
+(laplace-rule '(:h :h))
+(laplace-by-sampling '(:h :h) 40000)
+
+(defn rangen[n] (map * (repeat (/ 1 n)) (range (+ n 1))))
+(defn intervals [n] (partition 2 1 (rangen 10.0)))
+
+(defn between [samples]
+  (let [st (sort samples)]
+    (fn [a b] (count (take-while #(< % b) (drop-while #(< % a) st))))))
+
+(defn histogram [sq samplesize bins]
+  (map (fn [[a b]] ((between (take samplesize (select-coins sq))) a b)) (intervals bins)))
+
+(histogram '()   10000 10) ; (972 971 1053 987 1000 1015 975 1013 1016 998)
+
+(histogram '(:h) 10000 10) ; (126 292 516 654 835 1152 1297 1526 1715 1887)
+(histogram '(:t) 10000 10) ; (1820 1653 1580 1295 1123 913 663 547 310 96)
+
+(map + 
+     (histogram '(:t :t) 10000 10) ; (2696 2181 1722 1262 906 649 326 167 81 10)
+     (histogram '(:t :h) 5000 10) ; (129 373 587 669 786 705 679 582 355 135)
+     (histogram '(:h :t) 5000 10) ; (160 350 565 634 694 767 699 620 363 148)
+     (histogram '(:h :h) 10000 10) ; (12 80 190 376 564 961 1234 1683 2175 2725)
+     ) ; (2997 2984 3064 2941 2950 3082 2938 3052 2974 3018)
+
+
+