Discrete Bayes

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Copyright 2015 Roger R Labbe Jr.

FilterPy library. http://github.com/rlabbe/filterpy

Documentation at: https://filterpy.readthedocs.org

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.

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filterpy.discrete_bayes.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:

pdf : ndarray

discrete distribution that needs to be converted to a pdf. Converted in-place, i.e., this is modified.

Returns:

pdf : ndarray

The converted pdf.

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filterpy.discrete_bayes.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:

likelihood : ndarray, dtype=flaot

array of likelihood values

prior : ndarray, dtype=flaot

prior pdf.

Returns:

posterior : ndarray, dtype=float

Returns array representing the posterior.

Examples

# 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)

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filterpy.discrete_bayes.predict(pdf, offset, kernel, mode=u'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

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