A simulator for spatially extended kappa models

Technometrics, 2021

Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via Markov chain Monte Carlo (MCMC). Each iteration of the MCMC algorithm is computationally expensive due to costly matrix operations. In addition, the MCMC algorithm needs to be run for more iterations because the strong cross-correlations among the spatial latent variables result in slow mixing Markov chains. To address these computational challenges, we propose a projection-based intrinsic conditional autoregression (PICAR) approach, which is a discretized and dimension-reduced representation of the underlying spatial random field using empirical basis functions on a triangular mesh. Our approach exhibits fast mixing as well as a considerable reduction in computational cost per iteration. PICAR is computationally efficient and scales well to high dimensions. It is also automated and easy to implement for a wide array of user-specified hierarchical spatial models. We show, via simulation studies, that our approach performs well in terms of parameter inference and prediction. We provide several examples to illustrate the applicability of our method, including (i) a highdimensional cloud cover dataset that showcases its computational efficiency, (ii) a spatially varying coefficient model that demonstrates the ease of implementation of PICAR in the probabilistic programming languages stan and nimble, and (iii) a watershed survey example that illustrates how PICAR applies to models that are not amenable to efficient inference via existing methods.

Ecological Applications, 1995

Spatially explicit population models are becoming increasingly useful tools for population ecologists, conservation biologists, and land managers. Models are spatially explicit when they combine a population simulator with a landscape map that describes the spatial distribution of landscape features. With this map, the locations of habitat patches, individuals, and other items of interest are explicitly incorporated into the model, and the effect of changing landscape features on population dynamics can be studied. In this paper we describe the structure of some spatially explicit models under development and provide examples of current and future research using these models. Spatially explicit models are important tools for investigating scale-related questions in population ecology, especially the response of organisms to habitat change occurring at a variety of spatial and temporal scales. Simulation models that incorporate real-world landscapes, as portrayed by landscape maps created with geographic information systems, are also proving to be crucial in the development of management strategies in response to regional land-use and other global change processes. Spatially explicit population models will increase our ability to accurately model complex landscapes, and therefore should improve both basic ecological knowledge of landscape phenomena and applications of landscape ecology to conservation and management.

2008

Nature is governed by local interactions among lower-level sub-units, whether at the cell, organ, organism, or colony level. Adaptive system behaviour emerges via these interactions, which integrate the activity of the sub-units. To understand the system level it is necessary to understand the underlying local interactions. Successful models of local interactions at different levels of biological organisation, including epithelial tissue and ant colonies, have demonstrated the benefits of such ‘agent-based ’ modelling [1–4]. Here we present an agent-based approach to modelling a crucial biological system – the intracellular NF-kB signalling pathway. The pathway is vital to immune response regulation, and is fundamental to basic survival in a range of species [5–7]. Alterations in pathway regulation underlie a variety of diseases, including atherosclerosis and arthritis. Our modelling of individual molecules, receptors and genes provides a more comprehensive outline of regulatory net...

Understanding the Dynamics of …, 2011

Systems biology aims at integrating processes at various time and spatial scales into a single and coherent formal description to allow analysis and computer simulation. In this context, we focus on rule-based modeling and its integration in the domain-specific language MGS. Through the notions of topological collections and transformations, MGS allows the modeling of biological processes at various levels of description. We validate our approach through the description of various models of a synthetic bacteria designed in the context of the iGEM competition, from a very simple biochemical description of the process to an individual-based model on a Delaunay graph topology. This approach is a first step into providing the requirements for the emerging field of spatial systems biology which integrates spatial properties into systems biology.

2015

BACK-CALCULATION, CLASSIFICATION AND EMULATION-BASED INFERENCE FOR SPATIAL INFECTIOUS DISEASES MODELS Gyanendra Pokharel Advisor: University of Guelph, 2015 Dr. Rob Deardon Individual-level models (ILMs) are a class of complex probabilistic models which can be used to model infectious disease data. They can incorporate the effects of time and space, the key risk factors of disease transmission, and inference for them is carried out easily within a Bayesian MCMC framework. They are thus useful for modelling individual-level spatial epidemic data. However, fitting these models to what are typically incomplete data can result in poor parameter estimation and can miss important characteristics of the disease systems. Additionally, the complex nature of such ILMs can cause significant computational expense when fitting them to large disease systems. Here, we propose methods and models which address both the incomplete history of epidemic data as well as the computational problem of infer...

Ecological Applications, 1995

Spatially explicit population models are becoming increasingly useful tools for population ecologists, conservation biologists, and land managers. Models are spatially explicit when they combine a population simulator with a landscape map that describes the spatial distribution of landscape features. With this map, the locations of habitat patches, individuals, and other items of interest are explicitly incorporated into the model, and the effect of changing landscape features on population dynamics can be studied. In this paper we describe the structure of some spatially explicit models under development and provide examples of current and future research using these models. Spatially explicit models are important tools for investigating scale-related questions in population ecology, especially the response of organisms to habitat change occurring at a variety of spatial and temporal scales. Simulation models that incorporate real-world landscapes, as portrayed by landscape maps created with geographic information systems, are also proving to be crucial in the development of management strategies in response to regional land-use and other global change processes. Spatially explicit population models will increase our ability to accurately model complex landscapes, and therefore should improve both basic ecological knowledge of landscape phenomena and applications of landscape ecology to conservation and management.

2008

Journal of Applied Ecology, 2006

1. Spatial autocorrelation is an important source of bias in most spatial analyses. We explored the bias introduced by spatial autocorrelation on the explanatory and predictive power of species' distribution models, and make recommendations for dealing with the problem. 2. Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the spatial structure of the original variables. Univariate models of species' distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with spatial autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with spatial autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3. Spatial autocorrelation was shown to represent a serious problem for niche-based species' distribution models. Significance values were found to be inflated up to 90-fold. 4. In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of spatial autocorrelation. 5. The procedures utilized to reduce the effects of spatial autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual spatial autocorrelation effects. 6. Synthesis and applications. Given the expected inflation in the estimates of significance when analysing spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.

Spatially-explicit individual-based models are important tools in forestry and plant ecology. They are commonly implemented through custom computer coding that is time-consuming, may cause compatibility and availability problems, and makes difficult the evaluation, comparison and re-use of model components.

Spatial and Spatio-temporal Epidemiology, 2013

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