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Schiphol
Schiphol

Reputation: 1151

Noisy OR-gate in PyMC3

I am trying to create a PyMC3 model of a noisy OR-gate (a common-effect Bayes net, see graph below), as characterized in Rehder (1999):

The resulting probability distribution should be as in the table below, under "Common Effect Causal Model". q is the unconditional probability of parents.

I could easily hard code the dependence of a4 on the other three random variables, of course, but I wonder if PyMC3 has a more compact way to express this kind of disjunctive interaction.

common-effect netenter image description here

Reference: Rehder, B. (1999). A causal model theory of categorization. In *Proceedings of the 21st annual meeting of the Cognitive Science Society *(pp. 595–600).

Upvotes: 1

Views: 539

Answers (1)

merv
merv

Reputation: 76780

The most compact way I can think of capturing the relationship, assuming that c is a shared value, is to reduce down to a single probability for a_4. That is, something along these lines:

import pymc3 as pm
import theano.tensor as tt

with pm.Model() as model:
    # prior probabilities
    q = pm.Beta('q', alpha=1, beta=1)
    c = pm.Beta('c', alpha=1, beta=1)
    u = pm.Beta('u', alpha=1, beta=1)

    # input nodes
    a_i = pm.Bernoulli('a_i', p=q, shape=3)

    # prob for a_4
    p = pm.math.switch(tt.any(a_i), 1.0 - (1.0 - c)**tt.sum(a_i), u)

    # output node
    a_4 = pm.Bernoulli('a_4', p=p)

    prior = pm.sample_prior_predictive(samples=1000)

where, if any of the a_i succeed, then we compute the probability of any success in sum(a_i) tries (i.e., 1-(1-c)^sum(a_i)), otherwise just use u.

Obviously, the prior probabilities can be fixed or made independent as needed (e.g., maybe you want independent q values, which would be done by adding shape=3).

If this isn't what you're looking for, then maybe add some clarification to the question.

Upvotes: 1

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