Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

Gått ut på dato? Landløftene, Midtøsten-konflikten og jødisk–kristne relasjoner

I 2009 ga palestinske kirkeledere ut dokumentet Et sannhetens øyeblikk - Kairos Palestina, et rop til kristne over hele verden, og en bønn om solidaritet med en befolkning som lider under en undertrykkende okkupasjon. Konflikten i området og israelsk okkupasjon av palestinske områder er sentrale i den kirkelige debatten i Norge. Forfatterne drøfter i denne boken spørsmål som reises i Kairos Palestina ut fra historiske, teologiske, menneskerettslige og politiske vinklinger. Dokumentet Et sannhetens øyeblikk - Kairos Palestina er gjengitt på norsk til slutt i boken

Accuracy of multi-point boundary crossing time analysis

Recent multi-spacecraft studies of solar wind discontinuity crossings using the timing (boundary plane triangulation) method gave boundary parameter estimates that are significantly different from those of the well-established single-spacecraft minimum variance analysis (MVA) technique. A large survey of directional discontinuities in Cluster data turned out to be particularly inconsistent in the sense that multi-point timing analyses did not identify any rotational discontinuities (RDs) whereas the MVA results of the individual spacecraft suggested that RDs form the majority of events. To make multi-spacecraft studies of discontinuity crossings more conclusive, the present report addresses the accuracy of the timing approach to boundary parameter estimation. Our error analysis is based on the reciprocal vector formalism and takes into account uncertainties both in crossing times and in the spacecraft positions. A rigorous error estimation scheme is presented for the general case of correlated crossing time errors and arbitrary spacecraft configurations. Crossing time error covariances are determined through cross correlation analyses of the residuals. The principal influence of the spacecraft array geometry on the accuracy of the timing method is illustrated using error formulas for the simplified case of mutually uncorrelated and identical errors at different spacecraft. The full error analysis procedure is demonstrated for a solar wind discontinuity as observed by the Cluster FGM instrument

Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table