Bayesian Models

Nonparametric Bayesian ensemble method that combines many weak learners (decision trees) through a sum-of-trees model. Automatically handles nonlinearities, interactions, and variable selection. Provides uncertainty estimates via posterior distributions over tree structures and leaf parameters.

A multilevel modeling approach that incorporates partial pooling to estimate group-level effects while accounting for data hierarchy. Uses Bayesian inference to provide full posterior distributions for all parameters, enabling probabilistic interpretation of effects across levels (e.g., students within schools). Particularly useful for datasets with nested structures and when dealing with small sample sizes at higher levels.

Accounts for model uncertainty by averaging over multiple plausible models weighted by their posterior probabilities. Provides more robust inference than single-model approaches by incorporating model selection uncertainty into parameter estimates and predictions.

Extension of quantile regression that estimates conditional quantiles (e.g., median, 90th percentile) using Bayesian inference with asymmetric Laplace likelihood. Provides full posterior distributions for quantile-specific effects, allowing uncertainty quantification in tail relationships. Robust to outliers and heteroscedasticity.