Discrete Bayes Module

The discrete_bayes module contains discrete Bayesian filter implementations.

discrete_bayes

Copyright 2015 Roger R Labbe Jr.

FilterPy library. https://github.com/GeorgePearse/bayesian_filters

Documentation at: https://georgepearse.github.io/bayesian_filters

Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

This is licensed under an MIT license. See the readme.MD file for more information.

__all__ = ['discrete_bayes'] module-attribute

normalize(pdf)

Normalize distribution pdf in-place so it sums to 1.0.

Returns pdf for convienence, so you can write things like:

kernel = normalize(randn(7))

Parameters:

Name	Type	Description	Default
pdf	ndarray	discrete distribution that needs to be converted to a pdf. Converted in-place, i.e., this is modified.	required

Returns:

Name	Type	Description
pdf	ndarray	The converted pdf.

predict(pdf, offset, kernel, mode='wrap', cval=0.0)

Performs the discrete Bayes filter prediction step, generating the prior.

pdf is a discrete probability distribution expressing our initial belief.

offset is an integer specifying how much we want to move to the right (negative values means move to the left)

We assume there is some noise in that offset, which we express in kernel. For example, if offset=3 and kernel=[.1, .7., .2], that means we think there is a 70% chance of moving right by 3, a 10% chance of moving 2 spaces, and a 20% chance of moving by 4.

It returns the resulting distribution.

If mode='wrap', then the probability distribution is wrapped around the array.

If mode='constant', or any other value the pdf is shifted, with cval used to fill in missing elements.

Examples:

.. code-block:: Python

belief = [.05, .05, .05, .05, .55, .05, .05, .05, .05, .05]
prior = predict(belief, offset=2, kernel=[.1, .8, .1])

update(likelihood, prior)

Computes the posterior of a discrete random variable given a discrete likelihood and prior. In a typical application the likelihood will be the likelihood of a measurement matching your current environment, and the prior comes from discrete_bayes.predict().

Parameters:

Name	Type	Description	Default
likelihood	ndarray, dtype=flaot	array of likelihood values	required
prior	ndarray, dtype=flaot	prior pdf.	required

Returns:

Name	Type	Description
posterior	ndarray, dtype=float	Returns array representing the posterior.

Examples:

.. code-block:: Python

# self driving car. Sensor returns values that can be equated to positions
# on the road. A real likelihood compuation would be much more complicated
# than this example.

likelihood = np.ones(len(road))
likelihood[road==z] *= scale_factor

prior = predict(posterior, velocity, kernel)
posterior = update(likelihood, prior)