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.

Spectral adjustment for spatial confounding.

Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the exposure to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matérn coherence function to more robust semiparametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.

Multiple testing on standardized mortality ratios: a Bayesian hierarchical model for FDR estimation.

The analysis of large data sets of standardized mortality ratios (SMRs), obtained by collecting observed and expected disease counts in a map of contiguous regions, is a first step in descriptive epidemiology to detect potential environmental risk factors. A common situation arises when counts are collected in small areas, that is, where the expected count is very low, and disease risks underlying the map are spatially correlated. Traditional p-value-based methods, which control the false discovery rate (FDR) by means of Poisson p-values, might achieve small sensitivity in identifying risk in small areas. This problem is the focus of the present work, where a Bayesian approach which performs a test to evaluate the null hypothesis of no risk over each SMR and controls the posterior FDR is proposed. A Bayesian hierarchical model including spatial random effects to allow for extra-Poisson variability is implemented providing estimates of the posterior probabilities that the null hypothesis of absence of risk is true. By means of such posterior probabilities, an estimate of the posterior FDR conditional on the data can be computed. A conservative estimation is needed to achieve the control which is checked by simulation. The availability of this estimate allows the practitioner to determine nonarbitrary FDR-based selection rules to identify high-risk areas according to a preset FDR level. Sensitivity and specificity of FDR-based rules are studied via simulation and a comparison with p-value-based rules is also shown. A real data set is analyzed using rules based on several FDR levels.

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.

Using invertebrate functional traits to improve flow variability assessment within European rivers.

Rivers are among the most threatened ecosystems worldwide and are experiencing rapid biodiversity loss. Flow alteration due to climate change, water abstraction and augmentation is a severe stressor on many aquatic communities. Macroinvertebrates are widely used for biomonitoring river ecosystems although current taxonomic approaches used to characterise ecological responses to flow have limitations in terms of generalisation across biogeographical regions. A new macroinvertebrate trait-based index, Flow-T, derived from ecological functional information (flow velocity preferences) currently available for almost 500 invertebrate taxa at the European scale is presented. The index was tested using data from rivers spanning different biogeographic and hydro-climatic regions from the UK, Cyprus and Italy. The performance of Flow-T at different spatial scales and its relationship with an established UK flow assessment tool, the Lotic-invertebrate Index for Flow Evaluation (LIFE), was assessed to determine the transferability of the approach internationally. Flow-T was strongly correlated with the LIFE index using both presence-absence and abundance weighted data from all study areas (r varying from 0.46 to 0.96). When applied at the river reach scale, Flow-T was effective in identifying communities associated with distinct mesohabitats characterised by their hydraulic characteristics (e.g., pools, riffles, glides). Flow-T can be derived using both presence/absence and abundance data and can be easily adapted to varying taxonomic resolutions. The trait-based approach facilitates research using the entire European invertebrate fauna and can potentially be applied in regions where information on taxa-specific flow velocity preferences is not currently available. The inter-regional and continental scale transferability of Flow-T may help water resource managers gauge the effects of changes in flow regime on instream communities at varying spatial scales.

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.

Spatiotemporal smoothing of single trial MEG data.

In MEG experiments an electromagnetic field is measured at a very high temporal resolution in many sensors located in a helmet-shaped dewar, producing a very large dataset. Filtering techniques are commonly used to reduce the noise in the data. In this paper, spatiotemporal smoothing across space and time simultaneously is used, not simply as a pre-processing step, but as the central focus of a modelling technique intended to estimate the structure of the spatial and temporal response to stimulus. A particular advantage of this approach is the ability to study responses from individual replicates, rather than averages. The benefits of this form of smoothing are discussed and simulation used to evaluate its performance. The methods are illustrated on an application with real data.