bayes_vs_frequentist_battle_0.1.py

#!/usr/bin/env python3
import random
from typing import Tuple
from tqdm import tqdm
import typer


def avgpos_bayes(l: int, r: int) -> float:
    return (l + 1) / (l + r + 2)


def avgfreq_pos(l: int, r: int) -> float:
    return l / (l + r)


def simulate_outcome(num_balls: int) -> Tuple[float, int]:
    first_ball = random.random()
    l = 0
    for _ in range(num_balls):
        if random.random() < first_ball:
            l += 1
    return first_ball, l


def one_run(num_balls: int) -> Tuple[float, float]:
    actual_pos, l = simulate_outcome(num_balls)
    r = num_balls - l
    bayes_pos = avgpos_bayes(l, r)
    freq_pos = avgfreq_pos(l, r)
    bayes_diff = abs(actual_pos - bayes_pos)
    freq_diff = abs(actual_pos - freq_pos)
    return bayes_diff, freq_diff


def main(num_balls: int, num_simulations: int = 1000000):
    bayes_diffs_sum = 0
    freq_diffs_sum = 0
    num_bayes_won = 0
    num_freq_won = 0
    for _ in tqdm(range(num_simulations)):
        bayes_diff, freq_diff = one_run(num_balls)
        bayes_diffs_sum += bayes_diff
        freq_diffs_sum += freq_diff
        num_bayes_won += bayes_diff < freq_diff
        num_freq_won += freq_diff < bayes_diff
    print(f"simulated {num_balls} balls {num_simulations} times")
    print(f"the Bayesian approach won over the Frequentist one {100 * num_bayes_won / num_simulations}% of the times")
    ties = num_simulations - (num_bayes_won + num_freq_won)
    if ties:
        print(f"{100 * ties / num_simulations}% of the simulations were ties, "
              f"so {100 * num_freq_won / num_simulations}% were Frequentist wins")
    print(f"the mean deviation from the real value for the Bayesian approach was:\t{bayes_diffs_sum / num_simulations}")
    print(f"the mean deviation from the real value for the Frequentist approach was:\t{freq_diffs_sum / num_simulations}")


if __name__ == "__main__":
    typer.run(main)