Probability Distributions (lib601.dist)

Discrete probability distributions

class lib601.dist.DDist(elts)

Discrete probability distribution. Can be sparse, in the sense that elements that are not explicitly contained in the dictionary are assumed to have zero probability.

Parameters:elts – A dictionary mapping support elements to their associated probabilities. The values of this dictionary (the probabilities) must be nonnegative, and they must sum to 1.
condition(testFunc)
Parameters:testFunc – a function mapping support elements to booleans: True if the element should be included in the resulting distribution, and False otherwise.
Returns:new distribution, conditioned on the event described by testfunc
draw()
Returns:A randomly drawn element from the distribution
expectation(f)
Returns:The expected value of function f, with respect to this distribution
max_prob_elt()
Returns:The element in this domain with maximum probability
prob(elt)
Parameters:elt – an element of the domain of this distribution
Returns:the probability associated with elt
project(mapFunc)
Parameters:mapFunc – a function mapping elements in the support to modified elements
Returns:a DDist over some new set of elements, where the probability associated with each element \(e\) in the original distribution is associated with \(e'\) = \(\mathtt{mapFunc}(e)\) in the new distribution.
support()
Returns:A list (in arbitrary order) of the elements of this distribution with non-zero probabability.
lib601.dist.bayes_rule(PA, prob_b_given_a, b)
Parameters:
  • PA – DDist over \(A\)
  • prob_b_given_a – conditional distribution over \(B\) given \(A\) (function from values of \(a\) to DDist over \(B\))
  • b – evidence value for \(B = b\)
Returns:

Updated distribution given evidence, \(\Pr(A~|~B=b)\)
lib601.dist.delta_dist(v)

Distribution with all of its probability mass on value v

Parameters:v – the element that should have probability 1
lib601.dist.make_joint_distribution(PA, prob_b_given_a)

Create a joint distribution on \(\Pr(A,~B)\) (in that order), represented as a DDist

Parameters:
  • PA – a DDist on some random var \(A\)
  • prob_b_given_a – a conditional probability distribution specifying \(\Pr(B~|~A)\) (that is, a function from elements of \(A\) to DDist on \(B\))
lib601.dist.mixture(d1, d2, p)

A mixture of two DDist instances, d1 and d2, with mixture parameter p. Probability of an element \(x\) under this distribution is \(p \cdot \mathtt{d1.prob}(x) + (1 - p) \cdot \mathtt{d2.prob}(x)\).

lib601.dist.square_dist(lo, hi, loLimit=None, hiLimit=None)

Construct and return a DDist over integers. The distribution will have a uniform distribution on integers from lo to hi-1 (inclusive). Any probability mass that would be below loLimit or above hiLimit is instead assigned to loLimit or hiLimit.

lib601.dist.total_probability(PA, prob_b_given_a)
Parameters:
  • prob_b_given_a – conditional distribution over \(B\) given \(A\) (function from values of \(a\) to DDist over \(B\))
  • PA – distribution over \(A\) (object of type DDist)
Returns:

\(\Pr(B)\), computed using the law of total probability.
lib601.dist.triangle_dist(peak, halfWidth, loLimit=None, hiLimit=None)

Construct and return a DDist over integers. The distribution will have its peak at index peak and fall off linearly from there, reaching 0 at an index halfWidth on either side of peak. Any probability mass that would be below loLimit or above hiLimit is instead assigned to loLimit or hiLimit

lib601.dist.uniform_dist(elts)

Uniform distribution over a given finite set of elts

Parameters:elts – list of any kind of item