probability_monte_carlo#

actinvoting.probability_monte_carlo(factory, n_samples, test, conditional_on=None)[source]#

Probability that a random something meets some given test.

Parameters:

  • factory (callable or tuple of callable) –

    This can be:

    • Either a callable that takes no input and that outputs a (random) something,

    • Or a tuple of such factories (cf. examples below).

  • n_samples (int) – Number of samples.

  • test (callable or tuple of callable) –

    This can be:

    • Either a function that take as input(s) the output(s) of the factory(ies) and that returns a Boolean.

    • Or a tuple of such functions (cf. examples below).

  • conditional_on (callable) – A function that take as input(s) the output(s) of the factory(ies) and that returns a Boolean. Default: always True.

Returns:

This can be:

  • Either the probability that the output(s) generated by factory meet(s) test, conditional on the fact that it meets conditional_on, based on a Monte-Carlo estimation of n_samples trials.

  • Or a tuple giving this probability for each member of test, when test is a tuple itself.

Return type:

float or tuple of float

Examples

In this basic example with one factory, we estimate the probability that a random float between 0 and 1 is greater than .5, conditionally on being greater than .25:

>>> np.random.seed(0)
>>> def rand_number():
...     return np.random.rand()
>>> probability_monte_carlo(factory=rand_number, n_samples=1000,
...                         test=lambda x: x > .5, conditional_on=lambda x: x > .25)
0.657

In this example with a tuple of factories, we estimate the probability that a random 2*2 matrix and a random vector of size 2, both with integer coefficients between -10 included and 11 excluded, have a dot product that is null, conditionally on not being null themselves:

>>> np.random.seed(0)
>>> def rand_matrix():
...     return np.random.randint(-10, 11, (2, 2))
>>> def rand_vector():
...     return np.random.randint(-10, 11, 2)
>>> def test_dot_zero(matrix, vector):
...     return np.all(np.dot(matrix, vector) == 0)
>>> def test_non_trivial(matrix, vector):
...     return not np.all(matrix == 0) and not np.all(vector == 0)
>>> probability_monte_carlo(factory=(rand_matrix, rand_vector), n_samples=10000,
...                         test=test_dot_zero, conditional_on=test_non_trivial)
0.0003

In the following example, we estimate the probability that a random float between 0 and 1 is greater than .5, and the probability that it is greater than .75, conditionally on being greater than .25:

>>> np.random.seed(0)
>>> def rand_number():
...     return np.random.rand()
>>> probability_monte_carlo(factory=rand_number, n_samples=1000,
...                         test=(lambda x: x > .5, lambda x: x > .75), conditional_on=lambda x: x > .25)
(0.657, 0.342)

When using a tuple of tests, the same sample is used to estimate each probability.