kristovatlas · October 23, 2020 20:10 · kristovatlas · Oct 23, 2020
diff --git a/evidence.py b/evidence.py
 """
 https://twitter.com/elliot_olds/status/1319364546880942080

 To keep calculations simple, let's fix population size to 100
 """
 POPULATION = 100
 FRED_PROB_FIRST = 1/(0.6 * POPULATION)
 NOT_FRED_PROB_FIRST = 1-FRED_PROB_FIRST

 def prob_no_blood_type(population, num_crime_scene):
    """
    Suppose there are p people in the population and n people at the scene of
    the crime. If we have no idea how many people are at the scene of the crime
    (n is between 1 and p, inclusive), then the probability that Fred was one of
    the people at the scene of the crime is n/p.
    """
    return num_crime_scene * 1.0 / population

 def prob_blood_type(population, num_crime_scene):
    """
    If we know that there were at least two people at the scene of the crime
    with blood types O (60%) and AB (1%) respectively, and that Fred has blood
    type O, then the probability is changed. Since order does not matter, let's
    fix the first person at the scene as blood type O, the second as blood type
    AB, and the remainder (if any) as being any remaining member of the
    population.

    The probability that Fred is the O type (first) is 1/(0.6p)
    The probability that Fred isn't the O type (first) is 1-(1/(0.6p))
    The probability that Fred is the AB type (second) is 0
    The probability that is third or later is based on the probability that
        Fred was in none of the previous places multiplied by probability that
        he was at a specific place. He cannot appear in multiple places, of
        course.

    We will calculate the total probability that one of the suspects is Fred.
    """
    fred_prob_first = 1/(0.6 * population)
    not_fred_prob_first = 1-fred_prob_first

    fred_total_prob = fred_prob_first

    # The probability that all previous suspects were not Fred. We will add to
    # this list as we continue to calculate from N=3 to N=num_crime_scene
    not_fred_lookup_table = [not_fred_prob_first, not_fred_prob_first]

    # nth_person_at_scene is 0-based; starting at 2 since Fred can't be the
    # second person given his blood type of O
    for nth_person_at_scene in range(2, num_crime_scene):
        not_fred_prev = not_fred_lookup_table[nth_person_at_scene - 1]


        new_prob_fred = 1.0 / (population - nth_person_at_scene)
        new_prob_not_fred = 1 - new_prob_fred
        not_fred_lookup_table.append(not_fred_prev * new_prob_not_fred)

        current_prob = not_fred_prev * new_prob_fred
        fred_total_prob += current_prob

    return fred_total_prob

 def main():
    """
    Let's compare likelihoods for Fred given fixed P = 100 and various N's
    We can skip N=1 since there's no comparison for the blood type scenario
    """

    print("p,n,prob_no_blood,prob_blood")
    #num_crime_scene is 1-based
    for num_crime_scene in range(2, POPULATION + 1):
        prob_no_blood = prob_no_blood_type(POPULATION, num_crime_scene)
        prob_blood = prob_blood_type(POPULATION, num_crime_scene)
        if prob_blood > 1:
            prob_blood = 1 #correct rounding error


        print("{p},{n},{prob_no_blood},{prob_blood}".format(
            p=POPULATION, n=num_crime_scene, prob_no_blood=prob_no_blood,
            prob_blood=prob_blood))

 if __name__ == '__main__':
    main()
	"""
	https://twitter.com/elliot_olds/status/1319364546880942080

	To keep calculations simple, let's fix population size to 100
	"""
	POPULATION = 100
	FRED_PROB_FIRST = 1/(0.6 * POPULATION)
	NOT_FRED_PROB_FIRST = 1-FRED_PROB_FIRST

	def prob_no_blood_type(population, num_crime_scene):
	"""
	Suppose there are p people in the population and n people at the scene of
	the crime. If we have no idea how many people are at the scene of the crime
	(n is between 1 and p, inclusive), then the probability that Fred was one of
	the people at the scene of the crime is n/p.
	"""
	return num_crime_scene * 1.0 / population

	def prob_blood_type(population, num_crime_scene):
	"""
	If we know that there were at least two people at the scene of the crime
	with blood types O (60%) and AB (1%) respectively, and that Fred has blood
	type O, then the probability is changed. Since order does not matter, let's
	fix the first person at the scene as blood type O, the second as blood type
	AB, and the remainder (if any) as being any remaining member of the
	population.

	The probability that Fred is the O type (first) is 1/(0.6p)
	The probability that Fred isn't the O type (first) is 1-(1/(0.6p))
	The probability that Fred is the AB type (second) is 0
	The probability that is third or later is based on the probability that
	Fred was in none of the previous places multiplied by probability that
	he was at a specific place. He cannot appear in multiple places, of
	course.

	We will calculate the total probability that one of the suspects is Fred.
	"""
	fred_prob_first = 1/(0.6 * population)
	not_fred_prob_first = 1-fred_prob_first

	fred_total_prob = fred_prob_first

	# The probability that all previous suspects were not Fred. We will add to
	# this list as we continue to calculate from N=3 to N=num_crime_scene
	not_fred_lookup_table = [not_fred_prob_first, not_fred_prob_first]

	# nth_person_at_scene is 0-based; starting at 2 since Fred can't be the
	# second person given his blood type of O
	for nth_person_at_scene in range(2, num_crime_scene):
	not_fred_prev = not_fred_lookup_table[nth_person_at_scene - 1]


	new_prob_fred = 1.0 / (population - nth_person_at_scene)
	new_prob_not_fred = 1 - new_prob_fred
	not_fred_lookup_table.append(not_fred_prev * new_prob_not_fred)

	current_prob = not_fred_prev * new_prob_fred
	fred_total_prob += current_prob

	return fred_total_prob

	def main():
	"""
	Let's compare likelihoods for Fred given fixed P = 100 and various N's
	We can skip N=1 since there's no comparison for the blood type scenario
	"""

	print("p,n,prob_no_blood,prob_blood")
	#num_crime_scene is 1-based
	for num_crime_scene in range(2, POPULATION + 1):
	prob_no_blood = prob_no_blood_type(POPULATION, num_crime_scene)
	prob_blood = prob_blood_type(POPULATION, num_crime_scene)
	if prob_blood > 1:
	prob_blood = 1 #correct rounding error


	print("{p},{n},{prob_no_blood},{prob_blood}".format(
	p=POPULATION, n=num_crime_scene, prob_no_blood=prob_no_blood,
	prob_blood=prob_blood))

	if __name__ == '__main__':
	main()