1,804 research outputs found
Spatio-Temporal Structured Sparse Regression With Hierarchical Gaussian Process Priors
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies between the components of the sparse signal of interest. A hierarchical Gaussian process describes such structure and the interdependencies are represented via the covariance matrices of the prior distributions. The inference is based on the expectation propagation method and the theoretical derivation of the posterior distribution is provided in this paper. The inference framework is thoroughly evaluated over synthetic, real video, and electroencephalography (EEG) data where the spatio-temporal evolving patterns need to be reconstructed with high accuracy. It is shown that it achieves 15% improvement of the F-measure compared with the alternating direction method of multipliers, spatio-temporal sparse Bayesian learning method and the one-level Gaussian process model. Additionally, the required memory for the proposed algorithm is less than in the one-level Gaussian process model. This structured sparse regression framework is of broad applicability to source localization and object detection problems with sparse signals
Structured Sparse Modelling with Hierarchical GP
In this paper a new Bayesian model for sparse linear regression with a
spatio-temporal structure is proposed. It incorporates the structural
assumptions based on a hierarchical Gaussian process prior for spike and slab
coefficients. We design an inference algorithm based on Expectation Propagation
and evaluate the model over the real data.Comment: SPARS 201
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
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
Latent Gaussian modeling and INLA: A review with focus on space-time applications
Bayesian hierarchical models with latent Gaussian layers have proven very
flexible in capturing complex stochastic behavior and hierarchical structures
in high-dimensional spatial and spatio-temporal data. Whereas simulation-based
Bayesian inference through Markov Chain Monte Carlo may be hampered by slow
convergence and numerical instabilities, the inferential framework of
Integrated Nested Laplace Approximation (INLA) is capable to provide accurate
and relatively fast analytical approximations to posterior quantities of
interest. It heavily relies on the use of Gauss-Markov dependence structures to
avoid the numerical bottleneck of high-dimensional nonsparse matrix
computations. With a view towards space-time applications, we here review the
principal theoretical concepts, model classes and inference tools within the
INLA framework. Important elements to construct space-time models are certain
spatial Mat\'ern-like Gauss-Markov random fields, obtained as approximate
solutions to a stochastic partial differential equation. Efficient
implementation of statistical inference tools for a large variety of models is
available through the INLA package of the R software. To showcase the practical
use of R-INLA and to illustrate its principal commands and syntax, a
comprehensive simulation experiment is presented using simulated non Gaussian
space-time count data with a first-order autoregressive dependence structure in
time
CARBayes: an R package for Bayesian spatial modeling with conditional autoregressive priors
Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping
- …