Economical Models for Functional Covariation - SAMSI

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Overview Functional PCA finite element basis Estimation Examples Extensions and discussion Data fitting methods σ can be fit to data in many ways. A Wishart-based loss function can be used to estimate σ from a sample discrete variance-covariance matrix Σ by maximum likelihood. A Gaussian-based likelihood can be used to estimate σ directly from either discrete or continuous data.
Overview Functional PCA finite element basis Estimation Examples Extensions and discussion Tensor notation Computing functions, gradients and hessians for multi-index objects like R(s, t), which has six indices, is made much easier by using tensor notation. Einstein summation notation specifies that there is summation over repeated indices. Repeated indices usually occur in subscript/superscript pairs, called covariant and contravariant indices, respectively. Thus, in tensor notation σ(s i , t j ) = c k1 l 1 r k 1l 1 k 2 l 2 (s i , t j )c k2 l 2
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Economical Models for Functional Covariation - SAMSI

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