score.py

from __future__ import division
from math import *
from random import random, gauss

def p_smooth(c, n):
        return (c + 1) / (n + 2)

def binomial(c, n):
        p = p_smooth(c, n)
        return 2*sqrt((1/n if n > 0 else 1) * p * (1-p))

def wilson(c, n):
        z = 1.96
        z2 = 1.96 ** 2
        phat = c / n
        plus_minus = z * sqrt((1/n) * phat * (1-phat) + z2/(4 * (n**2)))
        return [
                        1 / (1 + (z2/n)) * (phat + 1/(2*n) * z2 - plus_minus),
                        1 / (1 + (z2/n)) * (phat + 1/(2*n) * z2 + plus_minus)]


c = 0
n = 0

alpha = 0.75 # Exp smoothing factor

last_score = 0
v_smooth = 0
for i in range(0,100):
        r = gauss(0.5 + sin(i/10)/2, 0.01)
        if (random() < r):
                v = 1
                print "+ ",
        else:
                v = 0
                print "- ",

        # v_smooth = v_smooth + alpha * (v - v_smooth)

        c += v
        n += 1


        # score = sum([p_smooth(c, n), -binomial(c, n)])
        score = wilson(c, n)[0]

        print "%2.1f %4f %4f -- %3d %3d" % (
                        r,
                        c/n,
                        wilson(c, n)[0],
                        int(100*round(score,2)),
                        int(100*round(score-last_score,2))

                        )
        last_score = score