8.26 But first, BART notation:

  • Let \(K\) be the total number of regression trees and
  • \(B\) be the number of iterations the BART algorithm will run for
  • Let \(\hat{f}^b_k(x)\) be the prediction at \(x\) for the \(k\)th regression tree used in the \(b\)th iteration of the BART algorithm
  • At the end of each iteration, the \(K\) trees from that iteration will be summed:

\[\hat{f}^b(x) = \sum_{k=1}^{K}\hat{f}^b_k(x)\] for \(b=1,...,B\)