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Functional ANOVA using Gaussian Process priors.

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# Gaussian Process Functional ANOVA

Implementation of a functional ANOVA (FANOVA) model, based partly on the model in

[Bayesian functional ANOVA modeling using Gaussian process prior distributions]( To implement a FANOVA model, an underlying general framework is defined for modeling functional observations:

$$ Y(t) = X beta(t),$$

where $$ Y(t) = [y_1(t),dots,y_m(t)]^T, $$ $$beta(t) = [beta_1(t),dots,beta_f(t)]^T,$$ $$ X: m times f$$ for a given time $t$. The design matrix $X$ defines the relation between the functions $beta$ and observations $y$. In general, the rank of $X$ should match the number of functions $f$. The FANOVA model can then be described by a specific form of $X$ such that

$$ y_{i,j}(t) = mu(t) + alpha_i(t) + beta_j(t) + alphabeta_{i,j}(t). $$

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