298 research outputs found
Visibility graph-based covariance functions for scalable spatial analysis in nonconvex domains
We present a new method for constructing valid covariance functions of
Gaussian processes over irregular nonconvex spatial domains such as water
bodies, where the geodesic distance agrees with the Euclidean distance only for
some pairs of points. Standard covariance functions based on geodesic distances
are not positive definite on such domains. Using a visibility graph on the
domain, we use the graphical method of "covariance selection" to propose a
class of covariance functions that preserve Euclidean-based covariances between
points that are connected through the domain. The proposed method preserves the
partially Euclidean nature of the intrinsic geometry on the domain while
maintaining validity (positive definiteness) and marginal stationarity over the
entire parameter space, properties which are not always fulfilled by existing
approaches to construct covariance functions on nonconvex domains. We provide
useful approximations to improve computational efficiency, resulting in a
scalable algorithm. We evaluate the performance of competing state-of-the-art
methods using simulations studies on a contrived nonconvex domain. The method
is applied to data regarding acidity levels in the Chesapeake Bay, showing its
potential for ecological monitoring in real-world spatial applications on
irregular domains
Detailed study of the Bootes field using 300-500 MHz uGMRT observations: Source Properties and radio--infrared correlations
The dominant source of radio continuum emissions at low frequencies is
synchrotron radiation, which originates from star-forming regions in disk
galaxies and from powerful jets produced by active galactic nuclei (AGN). We
studied the Bootes field using the upgraded Giant Meterwave Radio Telescope
(uGMRT) at 400 MHz, achieving a central minimum off-source RMS noise of
35Jy beam and a catalogue of 3782 sources in sq. degrees of
the sky. The resulting catalogue was compared to other radio frequency
catalogues, and the corrected normalised differential source counts were
derived. We use standard multi-wavelength techniques to classify the sources in
star-forming galaxies (SFGs), radio-loud (RL) AGN, and radio-quiet (RQ) AGN
that confirm a boost in the SFGs and RQ\,AGN AGN populations at lower flux
levels. For the first time, we investigated the properties of the radio--IR
relations at 400\,MHz in this field. The --
relations for SFGs were found to show a strong correlation with non-linear
slope values of , and variation of with is given
as, . This indicates
that the non-linearity of the radio--IR relations can be attributed to the mild
variation of values with . The derived relationships exhibit
similar behaviour when applied to LOFAR at 150 MHz and also at 1.4 GHz. This
emphasises the fact that other parameters like magnetic field evolution with
or the number densities of cosmic ray electrons can play a vital role in
the mild evolution of values.Comment: 18 pages, 18 Figures; Accepted for publication in MNRA
Neural networks for geospatial data
Analysis of geospatial data has traditionally been model-based, with a mean
model, customarily specified as a linear regression on the covariates, and a
covariance model, encoding the spatial dependence. We relax the strong
assumption of linearity and propose embedding neural networks directly within
the traditional geostatistical models to accommodate non-linear mean functions
while retaining all other advantages including use of Gaussian Processes to
explicitly model the spatial covariance, enabling inference on the covariate
effect through the mean and on the spatial dependence through the covariance,
and offering predictions at new locations via kriging. We propose NN-GLS, a new
neural network estimation algorithm for the non-linear mean in GP models that
explicitly accounts for the spatial covariance through generalized least
squares (GLS), the same loss used in the linear case. We show that NN-GLS
admits a representation as a special type of graph neural network (GNN). This
connection facilitates use of standard neural network computational techniques
for irregular geospatial data, enabling novel and scalable mini-batching,
backpropagation, and kriging schemes. Theoretically, we show that NN-GLS will
be consistent for irregularly observed spatially correlated data processes. To
our knowledge this is the first asymptotic consistency result for any neural
network algorithm for spatial data. We demonstrate the methodology through
simulated and real datasets
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