Here, the posterior mean a kl j and variance b kl j are calculated based on the collection of data points in the l-th node of the k-th tree for the j-th component using the normal-inverse gamma conjugate formula with priors μ kl j ∼ N 0 0.25 k 2 m j. Conditional on Σ, m j, and h l≠ j the posterior distribution of M k j or μ kl j l = 1, … ∼ i i d N a kl j b kl j. However, the only difference will be the posterior distribution of M k j conditional on all other parameters. Step (ii)Įach individual tree parameters T k j M k j k = 1, …, m j in the regression function for the j-th component h j( x j) is updated identically as mentioned in Chipman et al. Conditional on Σ, m j, and h l≠ j we only need to update the Θ j = T 1 j M 1 j … T m j j M m j j parameters. Select the BART regression function for the j-th component h j x j = ∑ k = 1 m j g k j x j T k j M k j.
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