9,018 research outputs found
Stochastic partial differential equation based modelling of large space-time data sets
Increasingly larger data sets of processes in space and time ask for
statistical models and methods that can cope with such data. We show that the
solution of a stochastic advection-diffusion partial differential equation
provides a flexible model class for spatio-temporal processes which is
computationally feasible also for large data sets. The Gaussian process defined
through the stochastic partial differential equation has in general a
nonseparable covariance structure. Furthermore, its parameters can be
physically interpreted as explicitly modeling phenomena such as transport and
diffusion that occur in many natural processes in diverse fields ranging from
environmental sciences to ecology. In order to obtain computationally efficient
statistical algorithms we use spectral methods to solve the stochastic partial
differential equation. This has the advantage that approximation errors do not
accumulate over time, and that in the spectral space the computational cost
grows linearly with the dimension, the total computational costs of Bayesian or
frequentist inference being dominated by the fast Fourier transform. The
proposed model is applied to postprocessing of precipitation forecasts from a
numerical weather prediction model for northern Switzerland. In contrast to the
raw forecasts from the numerical model, the postprocessed forecasts are
calibrated and quantify prediction uncertainty. Moreover, they outperform the
raw forecasts, in the sense that they have a lower mean absolute error
Modeling and interpolation of the ambient magnetic field by Gaussian processes
Anomalies in the ambient magnetic field can be used as features in indoor
positioning and navigation. By using Maxwell's equations, we derive and present
a Bayesian non-parametric probabilistic modeling approach for interpolation and
extrapolation of the magnetic field. We model the magnetic field components
jointly by imposing a Gaussian process (GP) prior on the latent scalar
potential of the magnetic field. By rewriting the GP model in terms of a
Hilbert space representation, we circumvent the computational pitfalls
associated with GP modeling and provide a computationally efficient and
physically justified modeling tool for the ambient magnetic field. The model
allows for sequential updating of the estimate and time-dependent changes in
the magnetic field. The model is shown to work well in practice in different
applications: we demonstrate mapping of the magnetic field both with an
inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.Comment: 17 pages, 12 figures, to appear in IEEE Transactions on Robotic
An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data
Self-Exciting models are statistical models of count data where the
probability of an event occurring is influenced by the history of the process.
In particular, self-exciting spatio-temporal models allow for spatial
dependence as well as temporal self-excitation. For large spatial or temporal
regions, however, the model leads to an intractable likelihood. An increasingly
common method for dealing with large spatio-temporal models is by using Laplace
approximations (LA). This method is convenient as it can easily be applied and
is quickly implemented. However, as we will demonstrate in this manuscript,
when applied to self-exciting Poisson spatial-temporal models, Laplace
Approximations result in a significant bias in estimating some parameters. Due
to this bias, we propose using up to sixth-order corrections to the LA for
fitting these models. We will demonstrate how to do this in a Bayesian setting
for Self-Exciting Spatio-Temporal models. We will further show there is a
limited parameter space where the extended LA method still has bias. In these
uncommon instances we will demonstrate how a more computationally intensive
fully Bayesian approach using the Stan software program is possible in those
rare instances. The performance of the extended LA method is illustrated with
both simulation and real-world data
Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions
Exposure to high levels of air pollutant concentration is known to be associated with respiratory problems which can translate into higher morbidity and mortality rates. The link between air pollution and population health has mainly been assessed considering air quality and hospitalisation or mortality data. However, this approach limits the analysis to individuals characterised by severe conditions. In this paper we evaluate the link between air pollution and respiratory diseases using general practice drug prescriptions for chronic respiratory diseases, which allow to draw conclusions based on the general population.
We propose a two-stage statistical approach: in the first stage we specify a space-time model to estimate the monthly NO2 concentration integrating several data sources characterised by different spatio-temporal resolution; in the second stage we link the concentration to the β2-agonists prescribed monthly by general practices in England and we model the prescription rates through a small area approach
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