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Bayesian Additive Regression Trees (ISL ch 8.2.4, Chipman-George-McCulloch 2010)
— a sum-of-trees regression model y = Σⱼ gⱼ(x) + ε fit by Bayesian
backfitting MCMC: each tree is updated in turn against the partial residual via
a grow/prune Metropolis-Hastings step with conjugate-normal leaves, and the noise
variance is drawn from its inverse-gamma full conditional.
The trees are kept deliberately small by the depth prior p_split(d) = α(1+d)^{−β}, so the ensemble is a sum of weak learners (like boosting, but with
a full posterior). Prediction is the posterior-mean over retained MCMC draws,
giving a smooth fit with built-in uncertainty. Kernel-class Divergent (the MCMC).
Structs§
- Bart
- A fitted BART model: the retained posterior draws (each a forest of trees).