We suggest a general method for the construction of highly continuous interpolants for one-step methods applied to the numerical solution of initial value problems of ODEs of arbitrary order. For the construction of these interpolants one uses, along with the numerical data of the discrete solution of a problem provided by a typical one-step method at endstep points, high-order derivative appro...

In this review, we first set out the general linear model (GLM) for the non technical reader, as a tool able to do both linear regression and ANOVA within the same flexible framework. We present a short history of its development in the fMRI community, and describe some interesting examples of its early use. We offer a few warnings, as the GLM relies on assumptions that may not hold in all situ...

By using themethods of linear algebra andmatrix inequality theory, we obtain the characterization of admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set. In the classes of homogeneous and general linear estimators, the necessary and suffcient conditions that the estimators of regression coeffcient function are admissible are establi...

We investigate a general characteristic of the trade-off in learning problems between goodness-of-fit and model complexity. Specifically we characterize a general class of learning problems where the goodness-of-fit function can be shown to be convex within firstorder as a function of model complexity. This general property of "diminishing returns" is illustrated on a number of real data sets a...

Based on geometric invariance properties, we derive an explicit prior distribution for the parameters of multivariate linear regression problems in the absence of further prior information. The problem is formulated as a rotationally-invariant distribution of L-dimensional hyperplanes inN dimensions, and the associated system of partial differential equations is solved. The derived prior distri...

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