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In community ecology studies the goal is to evaluate the effect of environmental covariates on a response variable while investigating the nature unobserved heterogeneity. We focus on onefactor mixed models in a Bayesian setting and introduce an intuitive Penalized Complexity (PC) prior to balance the variance components of the model. We start with the simple one-way anova and discuss extension to spatially structured residuals, following a Matern exponential covariance.

In this work we discuss a novel framework for modelling complex inter- actions in spatio-temporal datasets. The joint effect due to the space and time (in- teraction term) is separated out by the marginal effects. To implement these models in a Bayesian framework we find convenient to work under the Penalized Complexity (PC) prior framework. In this way, the degree with which the interaction model shrinks to the marginal model can intuitively be tuned at prior.

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.

Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models, discussing several correlation structures for the within group residuals. All the considered group models are parametrized in terms of a single correlation (hyper-)parameter, controlling the shrinkage towards the case of independent residuals (iid). We derive a penalized complexity (PC) prior for the correlation parameter of a generic group model. This prior has desirable properties from a practical point of view: (i) it ensures appropriate shrinkage to the iid case; (ii) it depends on a scaling parameter whose choice only requires a prior guess on the proportion of total variance explained by the grouping factor; (iii) it is defined on a distance scale common to all group models, thus the scaling parameter can be chosen in the same manner regardless the adopted group model. We show the benefit of using these PC priors in a case study in community ecology where different group models are compared.

Spatial data collected worldwide from a huge number of locations is 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 in order 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 as is the precision matrix of the GMRF prior, thus computational efficiency is gained by construction. We illustrate the approach with a real climate study, where the goal is to identify the Intertropical Convergence Zone using high-resolution remote sensing data.

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., 14 pages

The Inter Tropical Convergence Zone (ITCZ) is the region of the Earth's atmosphere where the trade winds converge. This region is characterized by rising air, strong convection, clouds and heavy precipitation and it is tightly related to changes in climate patterns on a global scale. For these reasons assessing the ITCZ migrations is of extreme importance for climate monitoring. This can be achieved through the use of satellite data of different kind. In the last decades several quantities have been used as proxies for this purpose, e.g. infrared radiance measured at the top of atmosphere (TOA), precipitation datasets or vertical and horizontal wind components. In this work the ITCZ position is determined and its time evolution is analysed using the Total Column Water Vapour (TCWV) data, retrieved using the Advanced Infra-Red Water Vapour Estimator algorithm (AIRWAVE). AIRWAVE was developed for the retrieval of the TCWV from the Along Track Scanning Radiometer (ATSR) instrument series, operational from 1991 to 2012. It allows the TCWV retrieval from infra-red channels at 11 and 12 μm exploiting the ATSR nadir and forward viewing geometries, for day/night and cloud-free sea surface scenarios. The information on cloud coverage from ATSRs is used as correlative information in order to expand the ITCZ analysis to land scenes. The TCWV and cloud frequency datasets are analysed with a Geodesic P-spline efficient spatial smoothing method specifically developed to extract information from large datasets. The posterior distribution of the model is considered for identification of the ITCZ both over sea and land with associated uncertainty quantification. The resulting AIRWAVE/cloud frequency monthly fields are analysed to detect trends in the ITCZ latitudinal displacement over the 20 years of the ATSR family lifetime. Results indicate that no significant trends can be detected in the 1991–2012 time period.

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] 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.

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.

Land use maps are a powerful resource to study the dynamics of urban growth. Official land use data, routinely produced by a wide range of institutions, are usually the result of processing remote sensing images. After complex elaborations, maps are provided to the public in two possible spatial formats: vector and raster. Vector maps are a collection of polygons, where each polygon belongs to a land use category. Raster maps result from converting polygons into a regular lattice or grid, where each grid box is assigned a land use category. Visual inspection of raster maps can immediately provide important information on the urban distribution over space, however, formal methods for the detection of spatio-temporal trends in this type of data are required. Modelling the spatial dependencies using the traditional Matern class of covariance functions is problematic because of the high dimensionality of these maps. We discuss efficient P-spline smoothing models for raster maps, which give computational advantages and therefore allows urbanization trends to be investigated, even in relatively large regions such as a city or a metropolitan area. An application of the proposed models is illustrated on urban data on the metropolitan area around Bologna, Italy. One of the most challenging application goals is the detection of regions showing a significant change in the urbanisation process over time.