6,504 research outputs found
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
A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced
orthogonal array-based space-filling designs are useful experimental designs in
several contexts, including computer experiments with categorical in addition
to quantitative inputs and cross-validation. Here, we provide a straightforward
construction of doubly orthogonal quasi-Sudoku Latin squares which can be used
to generate sliced space-filling designs which achieve uniformity in one and
two-dimensional projections for both the full design and each slice. A
construction of quasi-sliced orthogonal arrays based on these constructed
doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn,
be used to generate sliced space-filling designs which achieve uniformity in
one and two-dimensional projections for the full design and and uniformity in
two-dimensional projections for each slice. These constructions are very
practical to implement and yield a spectrum of design sizes and numbers of
factors not currently broadly available.Comment: 15 pages, 9 figure
Recreation in Swedish agricultural areas - public attitudes to multifunctional greenway design
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
High-speed observation of sprite streamers
This article is distributed under the terms of the Creative Commons Attribution License
which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the
source are credited.Sprites are optical emissions in the mesosphere mainly at altitudes 50–90 km.
They are caused by the sudden re-distribution of charge due to lightning in the troposphere which can produce electric fields in the mesosphere in excess of the local breakdown field. The resulting optical displays can be spectacular and this has led to research into the physics and chemistry involved. Imaging at faster than 5,000 frames per second has revealed streamer discharges to be an important and very dynamic part of sprites, and this paper will review high-speed observations of sprite streamers. Streamers are initiated in the 65–85 km altitude range and observed to propagate both down and up at velocities normally in the 106–5 9 107 m/s range. Sprite streamer heads are small, typically less than a few hundreds of meters, but very bright and appear in images much like stars with signals up to that expected of a magnitude -6 star. Many details of streamer formation have been modeled and successfully compared with observations. Streamers frequently split into multiple sub-streamers. The splitting is very fast. To resolve details will require framing
rates higher than the maximum 32,000 fps used so far. Sprite streamers are similar to
streamers observed in the laboratory and, although many features appear to obey simple
scaling laws, recent work indicates that there are limits to the scaling.Research funding has been provided by
the US National Science Foundation grants to the University of Alaska Fairbanks, and the US Air Force Academy, and by DARPA through a grant to the University of Florida
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
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