Probabilistic Programming

Probabilistic programming lets users describe generative models as programs, then compute posterior, predictive, or counterfactual quantities without hand-coding every inference step. Systems use exact methods such as weighted model counting for finite probabilistic logic, and approximate methods such as MCMC, Hamiltonian Monte Carlo, variational inference, and gradient estimators for larger or continuous models. Work also applies these methods to causal and neurosymbolic reasoning, dynamical systems, and language-model-generated Bayesian models, with predictive checks and calibration helping validate programs beyond whether they compile. A central tension is scaling inference while preserving sound semantics and reliable uncertainty: continuous models face dimensionality costs, and model selection can be sensitive to parameterization and misspecification.