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Causal Bayes Theorem
Extension of Bayes' theorem applied to causal inference, using conditional probabilities to update beliefs about observed causal relationships between variables and their effects.
Causal Prior Distribution
Initial probability distribution encapsulating pre-existing knowledge or hypotheses about causal parameters before observing data, serving as a starting point for causal Bayesian inference.
Causal Posterior
Updated probability distribution of causal parameters after incorporating observed data, combining prior information with data likelihood to estimate causal effects.
Directed Acyclic Graphical Models
Mathematical representation of causal relationships using directed graphs without cycles, where nodes represent variables and directed edges represent direct causal influences.
Bayesian Confounding
Probabilistic treatment of confounding variables in causal inference, using probability distributions to model uncertainty about confounding factors and their impact on estimated causal relationships.
Bayesian Latent Variables
Unobserved variables modeled by probability distributions in Bayesian causal models, allowing capture of underlying factors influencing relationships between observable variables.
Causal Gibbs Sampling
MCMC algorithm adapted for inference in Bayesian causal models, generating samples from conditional distributions to explore the space of causal structures and parameters.
Bayesian Structural Models
Theoretical framework combining causal structural models and Bayesian inference to simultaneously estimate the structure of causal relationships and effect magnitudes while quantifying uncertainty.
Bayesian Score Functions
Probabilistic metrics evaluating the quality of candidate causal models by calculating the marginal probability of the data given the structure, such as Bayesian BIC or evidence lower bound (ELBO).
Bayesian Structure Learning
Process of automatically inferring the causal graph structure from observed data using Bayesian methods to explore the space of possible DAGs and their probabilities.
Bayesian Counterfactuals
Probabilistic computation of hypothetical counterfactual scenarios within the Bayesian framework, estimating what would have occurred if a different causal intervention had been applied with uncertainty quantification.
Bayesian Instrumental Variables
Bayesian approach to instrumental variables addressing uncertainty about instrument validity and estimating causal effects through probability distributions rather than point estimates.
Expert-Elicited Prior
Prior distribution constructed from domain expert knowledge to guide Bayesian causal inference, translating qualitative expertise into quantitative probabilistic constraints.
Causal Bayes Factor
Marginal likelihood ratio comparing two competing causal models, enabling Bayesian causal model selection and quantifying the strength of evidence in favor of each hypothesis.
Bayesian Causal Meta-Analysis
Bayesian integration of multiple causal studies to combine their evidence by quantifying heterogeneity between studies and producing overall causal estimates with propagated uncertainty.
Bayesian Propensity
Propensity score treated within a Bayesian framework with prior and posterior distribution, allowing modeling of uncertainty in estimating treatment probabilities and its impact on causal effects.
Bayesian Causal Hierarchy
Multi-level structure of Bayesian causal models where higher-level parameters govern the distribution of lower-level parameters, capturing the hierarchical complexity of causal systems.
Approximate Causal Inference
Bayesian variational methods adapted for large-scale causal inference, approximating complex posterior distributions with simpler distributions to accelerate computations while preserving uncertainty.
Causal Convergence Diagnostics
Set of techniques evaluating the convergence of MCMC algorithms in Bayesian causal models, ensuring that generated samples adequately represent the posterior distribution of causal parameters.