We consider the problem of predicting values of a random process or field satisfying a linear model y(x)=θ⊤f(x)+ε(x), where errors ε(x)are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous...

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical...

The main result of the paper is the following characterization of the generalized arcsine density p <Subscript> γ </Subscript>(t) = t <Superscript> γ−1</Superscript>(1 − t)<Superscript> γ−1</Superscript>/B(γ, γ)   with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${t \in (0, 1)}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\gamma \in(0,\frac12) \cup (\frac12,1)}$$</EquationSource> </InlineEquation> : a r.v. ξ supported on [0, 1] has the generalized arcsine density...</equationsource></inlineequation></equationsource></inlineequation></superscript></superscript></subscript>