434 research outputs found
A note on intrinsic Conditional Autoregressive models for disconnected graphs
In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR)
models for disconnected graphs, with the aim of providing practical guidelines
for how these models should be defined, scaled and implemented. We show how
these suggestions can be implemented in two examples on disease mapping.Comment: 14 page
Quasi-periodic spatiotemporal models of brain activation in single-trial MEG experiments
Magneto-encephalography (MEG) is an imaging technique which measures neuronal activity in the brain. Even when a subject is in a resting state, MEG data show characteristic spatial and temporal patterns, resulting from electrical current at specific locations in the brain. The key pattern of interest is a ‘dipole’, consisting of two adjacent regions of high and low activation which oscillate over time in an out-of-phase manner. Standard approaches are based on averages over large numbers of trials in order to reduce noise. In contrast, this article addresses the issue of dipole modelling for single trial data, as this is of interest in application areas. There is also clear evidence that the frequency of this oscillation in single trials generally changes over time and so exhibits quasi-periodic rather than periodic behaviour. A framework for the modelling of dipoles is proposed through estimation of a spatiotemporal smooth function constructed as a parametric function of space and a smooth function of time. Quasi-periodic behaviour is expressed in phase functions which are allowed to evolve smoothly over time. The model is fitted in two stages. First, the spatial location of the dipole is identified and the smooth signals characterizing the amplitude functions for each separate pole are estimated. Second, the phase and frequency of the amplitude signals are estimated as smooth functions. The model is applied to data from a real MEG experiment focusing on motor and visual brain processes. In contrast to existing standard approaches, the model allows the variability across trials and subjects to be identified. The nature of this variability is informative about the resting state of the brain
P-spline smoothing for spatial data collected worldwide
Spatial data collected worldwide at a huge number of locations are frequently
used in environmental and climate studies. Spatial modelling for this type of
data presents both methodological and computational challenges. In this work we
illustrate a computationally efficient non parametric framework to model and
estimate the spatial field while accounting for geodesic distances between
locations. The spatial field is modelled via penalized splines (P-splines)
using intrinsic Gaussian Markov Random Field (GMRF) priors for the spline
coefficients. The key idea is to use the sphere as a surrogate for the Globe,
then build the basis of B-spline functions on a geodesic grid system. The basis
matrix is sparse and so is the precision matrix of the GMRF prior, thus
computational efficiency is gained by construction. We illustrate the approach
on a real climate study, where the goal is to identify the Intertropical
Convergence Zone using high-resolution remote sensing data
Non-parametric regression on compositional covariates using Bayesian P-splines
Methods to perform regression on compositional covariates have recently
been proposed using isometric log-ratios (ilr) representation of compositional parts.
This approach consists of first applying standard regression on ilr coordinates and
second, transforming the estimated ilr coefficients into their contrast log-ratio counterparts.
This gives easy-to-interpret parameters indicating the relative effect of each
compositional part. In this work we present an extension of this framework, where compositional
covariate effects are allowed to be smooth in the ilr domain. This is achieved
by fitting a smooth function over the multidimensional ilr space, using Bayesian Psplines.
Smoothness is achieved by assuming random walk priors on spline coefficients
in a hierarchical Bayesian framework. The proposed methodology is applied to spatial
data from an ecological survey on a gypsum outcrop located in the Emilia Romagna
Region, Italy
Smoothing of land use maps for trend and change detection in urbanization
Urban sprawl and its evolution over relatively short periods of time demands that we develop statistical tools to make best use of the routinely produced land use data from satellites. An efficient smoothing framework to estimate spatial patterns in binary raster maps derived from land use datasets is developed and presented in this paper. The framework is motivated by the need to model urbanization, specifically urban sprawl, and also its temporal evolution. We frame the problem as estimation of a probability of urbanization surface and use Bayesian P-splines as the tool of choice. Once such a probability map is produced, with associated uncertainty, we develop exploratory tools to identify regions of significant change across space and time. The proposal is used to study urbanisation and its development around the city of Bologna, Emilia Romagna, Italy, using land use data from the Cartography Archive of Emilia Romagna Region for the period 1976–2008
Variance partitioning in spatio-temporal disease mapping models
: Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that we name the variance partitioning model. The variance partitioning model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a penalized complexity prior on the mixing parameter aids in coding prior information in an intuitive way. We illustrate the advantages of the variance partitioning model using two case studies
Variance partitioning in spatio-temporal disease mapping models
Bayesian disease mapping, yet if undeniably useful to describe variation in
risk over time and space, comes with the hurdle of prior elicitation on
hard-to-interpret precision parameters. We introduce a reparametrized version
of the popular spatio-temporal interaction models, based on Kronecker product
intrinsic Gaussian Markov Random Fields, that we name variance partitioning
(VP) model. The VP model includes a mixing parameter that balances the
contribution of the main and interaction effects to the total (generalized)
variance and enhances interpretability. The use of a penalized complexity prior
on the mixing parameter aids in coding any prior information in a intuitive
way. We illustrate the advantages of the VP model on two case studies
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