Adding billiards.py

billiards.py

@@ -0,0 +1,68 @@
+"""This file contains code used in "Think Stats",
+by Allen B. Downey, available from greenteapress.com
+
+Copyright 2015 Allen B. Downey
+License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
+"""
+
+from __future__ import print_function, division
+
+import numpy
+import thinkbayes
+import thinkplot
+
+
+"""
+This problem presents a solution to the "Bayesian Billiards Problem",
+presented in this video:
+
+https://www.youtube.com/watch?v=KhAUfqhLakw
+
+Based on the formulation in this paper:
+
+http://www.nature.com/nbt/journal/v22/n9/full/nbt0904-1177.html
+
+Of a problem originally posed by Bayes himself.
+"""
+
+class Billiards(thinkbayes.Suite):
+
+    def Likelihood(self, data, hypo):
+        """Computes the likelihood of the data under the hypothesis.
+
+        data: tuple (#wins, #losses)
+        hypo: float probability of win
+        """
+        p = hypo
+        win, lose = data
+        like = p**win * (1-p)**lose
+        return like
+
+
+def ProbWinMatch(pmf):
+    total = 0
+    for p, prob in pmf.Items():
+        total += prob * (1-p)**3
+    return total
+
+
+def main():
+    ps = numpy.linspace(0, 1, 101)
+    bill = Billiards(ps)
+    bill.Update((5, 3))
+    thinkplot.Pdf(bill)
+    thinkplot.Save(root='billiards1',
+                   xlabel='probability of win',
+                   ylabel='PDF',
+                   formats=['png'])
+
+    bayes_result = ProbWinMatch(bill)
+    print(thinkbayes.Odds(1-bayes_result))
+
+    mle = 5 / 8
+    freq_result = (1-mle)**3
+    print(thinkbayes.Odds(1-freq_result))
+
+
+if __name__ == '__main__':
+    main()