Inference: Diagnosis, Prediction, and Simulation

Bayesian networks model uncertainty explicitly. In BayesiaLab, diagnosis, prediction, and simulation are all forms of evidence-conditioned inference.

• Diagnosis (abduction): infer likely causes from observed effects.
• Prediction/simulation: infer likely effects from observed causes.
• The interpretation depends on research perspective, while the underlying computation remains the same.

Observational Inference

• Bayesian networks represent a Joint Probability Distribution and support omnidirectional inference.
• Given evidence on any subset of nodes, BayesiaLab computes posterior probabilities for all other nodes.
• Both exact and approximate observational inference algorithms are available.

Evidence Types

• Hard Evidence: one state observed with certainty.
• Likelihood/Virtual Evidence: state-specific likelihoods.
• Probabilistic/Soft Evidence: evidence as marginal distributions.
• Numerical Evidence: numeric evidence for numeric or value-encoded symbolic variables.

Causal Inference

• Beyond observation, BayesiaLab can compute intervention effects.
• BayesiaLab includes Pearl’s Graph Surgery and Jouffe’s Likelihood Matching for causal estimation.

Effects Analysis

• In this nonparametric framework, effects are estimated through simulation rather than fixed coefficients.
• Because relationships are encoded in Conditional Probability Tables (CPT), effect size depends on simulated conditions.
• Functions such as Total Effects Analysis and Target Mean Analysis support nonlinear effect and interaction analysis.

Optimization

• Target Optimization searches for value combinations that optimize a target criterion.
• Combined with Direct Effects, this helps evaluate nonlinear trade-offs under dependence.
• Genetic Target Optimization can identify high-performing scenarios within constraints.