Massimo Ventrucci

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.

Spatio-temporal regression on compositional covariates: modeling vegetation in a gypsum outcrop

Investigating the relationship between vegetation cover and substrate typologies is important for habitat conservation. To study these relationships, common practice in modern ecological surveys is to collect information regarding vegetation cover and substrate typology over fine regular lattices, as derived from digital ground photos. Information on substrate typologies is often available as compositional measures, e.g., the area proportion occupied by a certain substrate. Two primary issues are of interest for ecologists: first, how much substrate typologies differ in terms of relative suitability for vegetation cover and, second, whether suitability varies over time. This paper develops a procedure for managing compositional covariates within a Bayesian hierarchical framework to effectively address the aforementioned issues. A spatio-temporal model is adopted to estimate the temporal pattern characterizing substrate relative suitability for vegetation cover and, at the same time, to account for spatio-temporal correlation. Relative suitability is modeled by time-varying regression coefficients, and spatial, temporal and spatio-temporal random effects are modeled using Gaussian Markov Random Field models.

Penalized complexity priors for degrees of freedom in Bayesian P-splines

Abstract Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter τ . Prior elicitation of τ is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

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.

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 P-splines. 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.

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.