Beta

Beta distribution for binary data.

A Beta distribution is very similar to a Bernoulli distribution in that it counts occurrences of boolean events. The differences lies in what is being measured. A Binomial distribution models the probability of an event occurring, whereas a Beta distribution models the probability distribution itself. In other words, it's a probability distribution over probability distributions.

Parameters

• alpha (int) – defaults to 1

  Initial alpha parameter.

• beta (int) – defaults to 1

  Initial beta parameter.

• seed (int) – defaults to None

  Random number generator seed for reproducibility.

Attributes

• mode

  The most likely value in the distribution.

• n_samples

  The number of observed samples.

Examples

>>> from river import proba

>>> successes = 81
>>> failures = 219
>>> beta = proba.Beta(successes, failures)

>>> beta(.21), beta(.35)
(0.867..., 0.165...)

>>> for success in range(100):
...     beta = beta.update(True)
>>> for failure in range(200):
...     beta = beta.update(False)

>>> beta(.21), beta(.35)
(2.525...e-05, 0.841...)

Methods

call

Probability mass/density function.

Parameters

• p (float)

cdf

Cumulative density function, i.e. P(X <= x).

Parameters

• x (float)

revert

Reverts the parameters of the distribution for a given observation.

Parameters

• x (float)

sample

Sample a random value from the distribution.

update

Updates the parameters of the distribution given a new observation.

Parameters

• x (float)

References

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1. What is the intuition behind beta distribution? ↩