1,094 research outputs found
A model based framework for air quality indices and population risk evaluation, with an application to the analysis of Scottish air quality data
The paper is devoted to the development of a statistical framework for air quality assessment at the country level and for the evaluation of the ambient population exposure and risk with respect to airborne pollutants. The framework is based on a multivariate space–time model and on aggregated indices defined at different levels of aggregation in space and time. The indices are evaluated, uncertainty included, by considering both the model outputs and the information on the population spatial distribution. The framework is applied to the analysis of air quality data for Scotland for 2009 referring to European and Scottish air quality legislation
Graphics for uncertainty
Graphical methods such as colour shading and animation, which are widely available, can be very effective in communicating uncertainty. In particular, the idea of a ‘density strip’ provides a conceptually simple representation of a distribution and this is explored in a variety of settings, including a comparison of means, regression and models for contingency tables. Animation is also a very useful device for exploring uncertainty and this is explored particularly in the context of flexible models, expressed in curves and surfaces whose structure is of particular interest. Animation can further provide a helpful mechanism for exploring data in several dimensions. This is explored in the simple but very important setting of spatiotemporal data
Adaptive Covariance Estimation with model selection
We provide in this paper a fully adaptive penalized procedure to select a
covariance among a collection of models observing i.i.d replications of the
process at fixed observation points. For this we generalize previous results of
Bigot and al. and propose to use a data driven penalty to obtain an oracle
inequality for the estimator. We prove that this method is an extension to the
matricial regression model of the work by Baraud
Re-thinking soil carbon modelling: a stochastic approach to quantify uncertainties
The benefits of sequestering carbon are many, including improved crop productivity, reductions in greenhouse gases, and financial gains through the sale of carbon credits. Achieving better understanding of the sequestration process has motivated many deterministic models of soil carbon dynamics, but none of these models addresses uncertainty in a comprehensive manner. Uncertainty arises in many ways - around the model inputs, parameters, and dynamics, and subsequently model predictions. In this paper, these uncertainties are addressed in concert by incorporating a physical-statistical model for carbon dynamics within a Bayesian hierarchical modelling framework. This comprehensive approach to accounting for uncertainty in soil carbon modelling has not been attempted previously. This paper demonstrates proof-of-concept based on a one-pool model and identifies requirements for extension to multi-pool carbon modelling. Our model is based on the soil carbon dynamics in Tarlee, South Australia. We specify the model conditionally through its parameters, soil carbon input and decay processes, and observations of those processes. We use a particle marginal Metropolis-Hastings approach specified using the LibBi modelling language. We highlight how samples from the posterior distribution can be used to summarise our knowledge about model parameters, to estimate the probabilities of sequestering carbon, and to forecast changes in carbon stocks under crop rotations not represented explicitly in the original field trials
Spatial vegetation patterns and neighborhood competition among woody plants in an East African savanna
The majority of research on savanna vegetation dynamics has focused on the coexistence of woody and herbaceous vegetation. Interactions among woody plants in savannas are relatively poorly understood. We present data from a 10-year longitudinal study of spatially explicit growth patterns of woody vegetation in an East African savanna following exclusion of large herbivores and in the absence of fire. We examined plant spatial patterns and quantified the degree of competition among woody individuals. Woody plants in this semi-arid savanna exhibit strongly clumped spatial distributions at scales of 1 - 5 m. However, analysis of woody plant growth rates relative to their conspecific and heterospecific neighbors revealed evidence for strong competitive interactions at neighborhood scales of up to 5 m for most woody plant species. Thus, woody plants were aggregated in clumps despite significantly decreased growth rates in close proximity to neighbors, indicating that the spatial distribution of woody plants in this region depends on dispersal and establishment processes rather than on competitive, density-dependent mortality. However, our documentation of suppressive effects of woody plants on neighbors also suggests a potentially important role for tree-tree competition in controlling vegetation structure and indicates that the balanced-competition hypothesis may contribute to well-known patterns in maximum tree cover across rainfall gradients in Africa
Nonlinear Reaction–Diffusion Process Models Improve Inference for Population Dynamics
Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long‐term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a logistic reaction component instead of a Malthusian component when population growth demonstrates asymptotic behavior. As a case study, we demonstrated that our model improves spatiotemporal abundance forecasts of sea otters in Glacier Bay, Alaska. Furthermore, we predicted spatially varying local equilibrium abundances as a result of environmentally driven diffusion and density‐regulated growth. Integrating equilibrium abundances over the study area in our application enabled us to infer the overall carrying capacity of sea otters in Glacier Bay, Alaska
Partially ordered models
We provide a formal definition and study the basic properties of partially
ordered chains (POC). These systems were proposed to model textures in image
processing and to represent independence relations between random variables in
statistics (in the later case they are known as Bayesian networks). Our chains
are a generalization of probabilistic cellular automata (PCA) and their theory
has features intermediate between that of discrete-time processes and the
theory of statistical mechanical lattice fields. Its proper definition is based
on the notion of partially ordered specification (POS), in close analogy to the
theory of Gibbs measure. This paper contains two types of results. First, we
present the basic elements of the general theory of POCs: basic geometrical
issues, definition in terms of conditional probability kernels, extremal
decomposition, extremality and triviality, reconstruction starting from
single-site kernels, relations between POM and Gibbs fields. Second, we prove
three uniqueness criteria that correspond to the criteria known as bounded
uniformity, Dobrushin and disagreement percolation in the theory of Gibbs
measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat.
Phy
Bayesian spatial extreme value analysis of maximum temperatures in County Dublin, Ireland
In this study, we begin a comprehensive characterisation of temperature
extremes in Ireland for the period 1981-2010. We produce return levels of
anomalies of daily maximum temperature extremes for an area over Ireland, for
the 30-year period 1981-2010. We employ extreme value theory (EVT) to model the
data using the generalised Pareto distribution (GPD) as part of a three-level
Bayesian hierarchical model. We use predictive processes in order to solve the
computationally difficult problem of modelling data over a very dense spatial
field. To our knowledge, this is the first study to combine predictive
processes and EVT in this manner. The model is fit using Markov chain Monte
Carlo (MCMC) algorithms. Posterior parameter estimates and return level
surfaces are produced, in addition to specific site analysis at synoptic
stations, including Casement Aerodrome and Dublin Airport. Observational data
from the period 2011-2018 is included in this site analysis to determine if
there is evidence of a change in the observed extremes. An increase in the
frequency of extreme anomalies, but not the severity, is observed for this
period. We found that the frequency of observed extreme anomalies from
2011-2018 at the Casement Aerodrome and Phoenix Park synoptic stations exceed
the upper bounds of the credible intervals from the model by 20% and 7%
respectively
- …