An exogenous variable distribution specifies uncertainty about an exogenous variable in a structural causal model. In a generative SCM, it supplies variation so assignment functions can reproduce the joint distribution. section 6.4.2 section 8.4.2
Choose distributions in relation to the model’s assumptions and estimation workflow:
- After selecting assignment-function classes, compare canonical distributions by post-estimation fit, model comparison, and cross-validation. section 6.4.2
- Parameterize the noise distribution, for example nᵧ ~ N(0, δ), or fix it at nᵧ ~ N(0, 1) and learn the scale through y = α + βx + δnᵧ. section 6.4.2
- Treat either approach as acceptable when the resulting choice captures the modeler’s assumptions about how outcomes are generated. section 6.4.2
Monty Hall in pgmpy
A discrete SCM assigns TabularCPD distributions to Host Inclination and Strategy with probabilities [.5, .5], and to Door with Car and Player First Choice with probabilities [1/3, 1/3, 1/3]. These distributions combine with deterministic assignment functions to produce winning probabilities of 1/3 for staying and 2/3 for switching. section 6.3.3
