ABSTRACT This study employs Bayesian regression and Bayesian Model Averaging (BMA) to analyze the determinants of the production‐based ecological footprint (EF) of Finland during 1990–2022. Using Hamiltonian Monte Carlo estimation and enumeration of the 256‐model space with the Bayesian Adaptive Sampling algorithm, the analysis accounts for parameter uncertainty and nonlinearity among the predictors (GDP and its square, renewable energy, foreign direct investment, urbanization, nuclear energy, and innovation), together with an FDI × urbanization interaction. To ensure the findings do not hinge on an arbitrary prior, inclusion probabilities are assessed across prior specifications. Three predictors are robust under every specification: renewable energy (negatively associated with EF), foreign direct investment (positively associated), and the FDI × urbanization interaction (negative), implying that the footprint‐raising effect of inward investment is attenuated in more urbanized settings. Support for an Environmental Kuznets Curve is weak once model uncertainty is accounted for: neither GDP nor its square is a robust driver. An out‐of‐sample comparison shows that BMA delivers better‐calibrated predictions than any single selected model, and information criteria (LOOIC preferred over WAIC, with reliable Pareto‐ k diagnostics) confirm model adequacy. The paper provides a robust framework for inference under model uncertainty and clarifies the production‐side drivers of Finland's environmental pressure.
ABSTRACT We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed‐linear combinations of independent regularly varying random variables. Under a reasonable modeling assumption, the matrix of inner products corresponds to the tail pairwise dependence matrix, which can be easily estimated. We derive the optimal transformed‐linear predictor via the projection theorem, which yields a predictor with the same form as the best linear unbiased predictor in non‐extreme settings. We quantify uncertainty for prediction errors by constructing prediction intervals based on the geometry of regular variation. We demonstrate the effectiveness of our method through a simulation study and its applications to predicting high pollution levels, and extreme precipitation.
ABSTRACT Cellular automata (CA) have become an invaluable tool for simulating complex ecological processes, offering a computationally efficient approach to modeling spatially explicit dynamics. In ecological contexts, CA models can capture the emergent behaviors and nonlinear interactions that characterize real‐world ecosystems. This paper introduces a hands‐on, code‐driven approach to using CA in ecology through the development of the R package cellulaR . The package provides three core functions for simulating species and vegetation spread: c.neutral() , which models neutral spread on a homogeneous grid; c.fractal() , which generates a heterogeneous fractal landscape to simulate spatial variability; and c.weighted() , which combines the fractal landscape with terrain‐based effects, such as slope and habitat suitability, to simulate more ecologically realistic spread and mortality patterns. By demonstrating the practical implementation of these functions, this paper illustrates how cellulaR provides a lightweight and accessible framework for exploring selected ecological cellular‐automata concepts, including neutral spread, landscape heterogeneity, and environmentally weighted colonization dynamics. Ultimately, this work provides a practical introduction to ecological modeling with cellular automata, illustrating how simple CA rules can be implemented and extended within ecological simulation workflows.
ABSTRACT Forecasting is a central objective in time series analysis, with increasing interest in obtaining accurate predictions and reliable prediction intervals. State‐space models provide a natural framework for this purpose through the Kalman filter, although conventional predictive inference often relies on Gaussian innovations and time‐invariant system matrices. We propose a state‐space bootstrap (SSB) procedure for constructing prediction intervals that accommodates time‐varying system matrices, incorporates parameter estimation uncertainty through bootstrap reestimation, and relaxes the Gaussian assumption by resampling standardized innovations. The methodology is applied to daily concentrations in Coyhaique, Chile, using a regression– model formulated within the SS framework. The systematic component accounts for trend and annual seasonality through Fourier harmonics, while the stochastic component captures short‐ and long‐range dependence, allowing the fractional memory parameter and innovation scale to evolve smoothly over time.
ABSTRACT Ecological monitoring programmes and palaeoecological analyses play a key role in understanding how biodiversity, including plants and wildlife, respond to environmental factors such as climate change or biotic competition. Such data are typically compositional in nature, and a common challenge in the analysis of ecological compositional data is the interpretation and modeling of datasets containing a high proportion of zeros and 's. Such data frequently occur in ecological applications where counts of species are collected until a sum total imposed by sampling cost or sampling effort is reached. In the bivariate count (two‐species) setting we focus on in this article, zero‐inflation of one species will result in ‐inflation of the other. This can lead to species absence being attributed to an unsuitable habitat as opposed to missingness by chance. Similarly, an excess of 's will lead to misleading inferences about habitat preference and abundance estimates. Our contribution is to identify that two independent zero‐inflated Poisson processes subject to a sum constraint provide a novel biologically‐motivated generating mechanism for the occurrence of binomial count data exhibiting zero and ‐inflation. We identify an extension to the model to capture additional overdispersion within the data resulting in a novel zero and ‐inflated beta‐binomial model. We consider two motivating datasets, one involving a pesticide treatment for an invasive species, and a second involving the abundance of two plant species. We demonstrate that incorporation of covariates in each case enable learning about sources of zero and ‐inflation as well as abundance. We show that the proposed models provide for an improved understanding of the biological processes underlying ecological patterns and support more accurate biodiversity assessment, environmental monitoring, and palaeoclimate reconstruction.
