gistfile1.txt

from __future__ import division
import itertools 
from scipy import stats
import numpy as np
from collections import Counter


# Define some functions to use later

def form_lineup(delta, foils, felons):
    foils = [i for i in stats.norm.rvs(loc=0, scale=1, size=foils)]
    if felons > 0:
        felons = [i for i in stats.norm.rvs(loc=delta, scale=1, size=felons)]
    else:
        felons = []
    return foils, felons

def worst_is_a_felon(lineup):
    foils, felons = lineup
    if len(felons)==0:
        return False
    return bool(max(felons) > max(foils))

def punters_worst_first(lineup):
    all = list(itertools.chain(*lineup))
    all.sort()
    all.reverse()
    return all

def worst_meets_criterion(lineup, criterion):
    all = punters_worst_first(lineup)
    return bool(all[0] > criterion)
    
def exceeds_margin(lineup, margin):
    all = punters_worst_first(lineup)
    return bool(all[0] - all[1] > margin)

def beats_average_by(lineup, margin):
    all = punters_worst_first(lineup)
    worst = all[0]
    rest = all[1:]                 
    av_rest = np.average(rest)
    return bool(worst - av_rest > margin)

def categorise_lineup(lineup, criterion, win_function, margin):
    a = worst_meets_criterion(lineup, criterion) and win_function(lineup, margin)
    b = worst_is_a_felon(lineup)
    if a and b:
        return 'hit'
    if a:
        return 'false_alarm'


# DEFINE SOME PARAMETERS

criterion = 1.5
delta = 3
nfelons = 1
nfoils = 5 
reps = 1000 
prob_felon = .5
prob_no_felon = 1 - prob_felon
win_function = exceeds_margin  # this might seem odd, but you choose the function to apply by assigning it to this variable


# GENERATE SOME LINEUPS

lineups_with_felons = [form_lineup(delta=delta, foils=nfoils, felons=nfelons) for i in range(0, int(reps * prob_felon))]
lineups_without = [form_lineup(delta=delta, foils=nfoils+nfelons, felons=0) for i in range(0, int(reps * prob_no_felon))]                                       
lineups = list(itertools.chain(lineups_with_felons, lineups_without))


# SIMULATE AT DIFFERENT VALUES OF MARGIN

for margin in [x * 0.3 for x in range(0, 10)]:
    c = Counter([categorise_lineup(i, criterion, win_function, margin) for i in lineups])
    n = len(lineups)
    phit = c['hit']/n
    pfa = c['false_alarm']/n
    dprime=stats.norm.ppf(phit) - stats.norm.ppf(pfa)      # norm.ppf is NORMSINV in excel

    print "margin: %g \t phit: %g \t pfa: %g \t dprime: %g" % (margin, phit, pfa, dprime)


# outputs:

# margin: 0      phit: 0.463     pfa: 0.181      dprime: 0.818682
# margin: 0.3    phit: 0.455     pfa: 0.157      dprime: 0.893826
# margin: 0.6    phit: 0.438     pfa: 0.123      dprime: 1.00408
# margin: 0.9    phit: 0.412     pfa: 0.078      dprime: 1.19625
# margin: 1.2    phit: 0.369     pfa: 0.045      dprime: 1.36089
# margin: 1.5    phit: 0.322     pfa: 0.023      dprime: 1.53328
# margin: 1.8    phit: 0.27      pfa: 0.015      dprime: 1.55728
# margin: 2.1    phit: 0.215     pfa: 0.007      dprime: 1.66807
# margin: 2.4    phit: 0.17      pfa: 0.003      dprime: 1.79362
# margin: 2.7    phit: 0.126     pfa: 0.002      dprime: 1.73266