Bayes' Rule, reframed "odds" instead of "chances"

bayesodds.py

"""
Bayes rule, reframed as "odds" instead of "chances".

https://twitter.com/florimondmanca/status/1342119381573238789

Inspired by 3Blue1Brown's "The medical test paradox: Can redesigning Bayes rule help?".
"""
from fractions import Fraction
from typing import Any


def bayesfactor(accuracy: float, false_positive_rate: float) -> float:
    return accuracy / false_positive_rate


class Odds:
    # Run tests: $ python -m doctest bayesodds.py
    """
    >>> prior = Odds[1:9]
    >>> prior
    Odds[1:9]
    >>> prior.prob
    0.1
    >>> b = bayesfactor(accuracy=0.9, false_positive_rate=0.01)
    >>> b
    90.0
    >>> posterior = prior * b
    >>> posterior
    Odds[10:1]
    >>> posterior.prob
    0.9090909090909091
    """

    def __init__(self, fraction: Fraction) -> None:
        self._fraction = fraction

    @classmethod
    def __class_getitem__(cls, item: Any) -> "Odds":
        if not isinstance(item, slice):
            raise NotImplementedError
        positive = item.start
        negative = item.stop
        return Odds(Fraction(positive, negative))

    def __mul__(self, other: Any) -> "Odds":
        try:
            other = float(other)
        except (TypeError, ValueError):
            raise NotImplementedError
        return Odds(self._fraction * other)

    def __rmul__(self, other: Any) -> "Odds":
        return self.__mul__(other)

    def __repr__(self) -> str:
        positive, negative = self._fraction.as_integer_ratio()
        return f"Odds[{positive}:{negative}]"

    @property
    def prob(self) -> float:
        positive, negative = self._fraction.as_integer_ratio()
        return positive / (positive + negative)