Integrated Nested Laplace Approximation Research Articles

Designing a Bayesian adaptive clinical trial to evaluate novel mechanical ventilation strategies in acute respiratory failure using integrated nested Laplace approximations

BackgroundAdaptive trials usually require simulations to determine values for design parameters, demonstrate error rates, and establish the sample size. We designed a Bayesian adaptive trial comparing ventilation strategies for patients with acute hypoxemic respiratory failure using simulations. The complexity of the analysis would usually require computationally expensive Markov Chain Monte Carlo methods but this barrier to simulation was overcome using the Integrated Nested Laplace Approximations (INLA) algorithm to provide fast, approximate Bayesian inference. MethodsWe simulated two-arm Bayesian adaptive trials with equal randomization that stratified participants into two disease severity states. The analysis used a proportional odds model, fit using INLA. Trials were stopped based on pre-specified posterior probability thresholds for superiority or futility, separately for each state. We calculated the type I error and power across 64 scenarios that varied the probability thresholds and the initial minimum sample size before commencing adaptive analyses. Two designs that maintained a type I error below 5%, a power above 80%, and a feasible mean sample size were evaluated further to determine the optimal design. ResultsPower generally increased as the initial sample size and the futility threshold increased. The chosen design had an initial recruitment of 500 and a superiority threshold of 0.9925, and futility threshold of 0.95. It maintained high power and was likely to reach a conclusion before exceeding a feasible sample size. ConclusionsWe designed a Bayesian adaptive trial to evaluate novel strategies for ventilation using the INLA algorithm to efficiently evaluate a wide range of designs through simulation.

Spatiotemporal Bayesian modeling of the risk of congenital syphilis in São Paulo, SP, Brazil

The aim of this study is to analyze the spatiotemporal risk of congenital syphilis (CS) in high-prevalence areas in the city of São Paulo, SP, Brazil, and to evaluate its relationship with socioeconomic, demographic, and environmental variables. An ecological study was conducted based on secondary CS data with spatiotemporal components collected from 310 areas between 2010 and 2016. The data were modeled in a Bayesian context using the integrated nested Laplace approximation (INLA) method. Risk maps showed an increasing CS trend over time and highlighted the areas that presented the highest and lowest risk in each year. The model showed that the factors positively associated with a higher risk of CS were the Gini index and the proportion of women aged 18–24 years without education or with incomplete primary education, while the factors negatively associated were the proportion of women of childbearing age and the mean per capita income.

Impact of Indoor Radon Exposure on Lung Cancer Incidence in Slovenia.

Indoor radon is an important risk factor for lung cancer, as 3-14% of lung cancer cases can be attributed to radon. The aim of our study was to estimate the impact of indoor radon exposure on lung cancer incidence over the last 40 years in Slovenia. We analyzed the distribution of lung cancer incidence across 212 municipalities and 6032 settlements in Slovenia. The standardized incidence ratios were smoothed with the Besag-York-Mollie model and fitted with the integrated nested Laplace approximation. A categorical explanatory variable, the risk of indoor radon exposure with low, moderate and high risk values, was added to the models. We also calculated the population attributable fraction. Between 2.8% and 6.5% of the lung cancer cases in Slovenia were attributable to indoor radon exposure, with values varying by time period. The relative risk of developing lung cancer was significantly higher among the residents of areas with a moderate and high risk of radon exposure. Indoor radon exposure is an important risk factor for lung cancer in Slovenia in areas with high natural radon radiation (especially in the southern and south-eastern parts of the country).

Exploring the effects of temperature on demersal fish communities in the Central Mediterranean Sea using INLA-SPDE modeling approach

AbstractClimate change significantly impacts marine ecosystems worldwide, leading to alterations in the composition and structure of marine communities. In this study, we aim to explore the effects of temperature on demersal fish communities in the Central Mediterranean Sea, using data collected from a standardized monitoring program over 23 years. Computationally efficient Bayesian inference is performed using the integrated nested Laplace approximation and the stochastic partial differential equation approach to model the spatial and temporal dynamics of the fish communities. We focused on the mean temperature of the catch (MTC) as an indicator of the response of fish communities to changes in temperature. Our results showed that MTC decreased significantly with increasing depth, indicating that deeper fish communities may be composed of colder affinity species, more vulnerable to future warming. We also found that MTC had a step-wise rather than linear increase with increasing water temperature, suggesting that fish communities may be able to adapt to gradual changes in temperature up to a certain threshold before undergoing abrupt changes. Our findings highlight the importance of considering the non-linear dynamics of fish communities when assessing the impacts of temperature on marine ecosystems and provide important insights into the potential impacts of climate change on demersal fish communities in the Central Mediterranean Sea.

Spatio-Temporal Marked Point Process Model to Understand Forest Fires in the Mediterranean Basin

AbstractUnderstanding and predicting forest fires have proved a highly difficult endeavour, which requires extending and adapting complex models used in different fields. Here, we apply a marked point process approach, commonly used in ecology, which uses multiple Gaussian random fields to represent dynamics of Mediterranean forest fires in a spatio-temporal distribution model. Inference is carried out using Integrated Nested Laplace Approximation (INLA) with , an accessible and computationally efficient approach for Bayesian hierarchical modelling, which is not yet widely used in species distribution models. Using the marked point process approach, intensity of forest fires and dispersion were predicted using socioeconomic factors and environmental and fire-related variables. This demonstrates the advantage of complex model components in accounting for spatio-temporal dynamics that are not explained by environmental variables. Introduction of spatio-temporal marked point process can provide a more realistic perspective of a system, which is of particular importance for a practical and impact-focused worldwide problem such as forest fires.Supplementary materials accompanying this paper appear online.

Abstract P322: Mapping Geographic Variation in Hypertension Prevalence in United States Congressional Districts Using Spatial Modeling

Introduction: Using spatial methods to explore drivers of hypertension (HTN) risks, commonalities, and differences across geographical areas can be assessed to inform future public health research and advocacy efforts. Objectives: To examine ecological associations between social determinants of health (SDoH), space, and HTN across congressional districts (CDs) in effect for the 118th US Congress. Methods: We obtained aggregate district-level data from Congressional District Health Dashboard on health behaviors, exposures, and outcomes for US CDs in 2019. Primary outcome was HTN prevalence, defined as proportion of adults who self-reported diagnosed HTN. Exposure variables were SDoH: health outcomes (diabetes, obesity, frequent physical and mental distress), health behaviors (physical activity, binge drinking, smoking), clinical care (routine checkups), and physical environment (air pollution). We fitted a hierarchical Bayesian Besag-York-Mollié model using the integrated nested Laplace approximation (INLA) method, which allowed the estimation of spatial autocorrelation of HTN prevalence at CDs level, accounting for SDoH. Results: Across 421 CDs, we found a variation in the modeled linear proportion of 83% across the CDs in the United States after adjusting for known HTN risk factors at the CDs level. A notable degree of variation in HTN prevalence exists within specific CDs, independent of recognized risk factors ( Figure ). These unmeasured variables act as confounding elements, and districts with darker shading indicate increased HTN attributed to the district, while lighter, red-shaded districts exhibit a reduced district-specific proportion of HTN. Conclusions: Our findings show significant geographic variation of HTN beyond known risk factors which underscores the significance of adopting a spatial perspective to understand HTN prevalence. It emphasizes the necessity for tailored public health interventions that consider the unique geographic context of each CDs.

Statistical stream temperature modelling with SSN and INLA: an introduction for conservation practitioners

Statistical stream temperature models predicting the fine-scale spatial distribution of water temperatures (i.e., “thermalscape”) can guide aquatic species recovery and habitat restoration efforts. However, stream temperature modelling is complicated by spatial autocorrelation arising from non-independence of sampling sites within dendritic networks. We used August mean temperature data from miniature sensors deployed in Canadian Rocky Mountain streams to demonstrate two statistical stream temperature modelling techniques that account for spatial autocorrelation. The first was a spatial steam network (SSN) model specifically developed to account for spatial autocorrelation in dendritic stream networks. The second was an integrated nested Laplace approximation (INLA) model that accounts for spatial autocorrelation but was not designed to address anisotropic stream network data. We evaluated the best-fitting SSN and INLA models using leave-one-out cross-validation. Relative to INLA, SSN models had lower RMSE (1.23 vs. 1.45 C) and higher r2 (0.71 vs. 0.61); however, the SSN models required more preprocessing steps before incorporating spatially correlated random errors. We provide practical advice, an open-access r-script, and data to help non-experts develop statistical stream temperature models.

Spatio-temporal characteristics of Tuberculosis in Ghana

Background Tuberculosis (TB) continues to be a prominent contributor to global mortality, standing as the second most fatal infectious disease and holding the seventh position among the top ten causes of death in Ghana. There is insufficient literature regarding the utilization of Bayesian hierarchical models, specifically within the framework of Integrated Nested Laplace Approximation (INLA), for examining the spatial and spatio-temporal dynamics of tuberculosis risk in Ghana. This study addresses this gap by determining TB hotspots regions in Ghana using the Bayesian modeling framework within the INLA. Methods TB data were sourced from the Ghana Health Service and National Tuberculosis Programme for the 10 administrative regions of Ghana, from 2008 to 2017. The relative risk of TB for each region and year was estimated utilizing Bayesian spatial and spatio-temporal modeling frameworks. Baseline predictors of TB risk were also considered. Maps for TB risks were created to visualized regions with TB hotspots. Model fitting and parameter estimation were conducted using R version 4.3.2. Results Among the baseline predictors, factors such as TB cure rate, TB success rate, knowledge about TB, HIV prevalence, percentage of literacy, and high income were found to be most significant in influencing the TB risk across the ten regions in Ghana. We noted an increased risk of TB infection in the Northern zone and the Eastern and Greater Accra regions in the Southern zone. Spatio-temporal distribution of TB infection risk was predominantly concentrated in the Southern zone. Clustering of TB risk was observed among neighboring regions. Conclusion To achieve a significant reduction in TB cases, it is essential to allocate resources to TB hotspots regions and also implement measures to control significant predictors of TB infection risk.

ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

A shiny R app for spatial analysis of species distribution models

In ecology, Species Distribution Models (SDMs) are a statistical tool whose use has expanded considerably over the last two decades. As their use has grown, so has the complexity of the data analysed and the structures of the models used.This has led to the development of various tools to facilitate the incorporation and use of these new data and statistical methodologies, mostly embodied in new R packages and Shiny applications that allow different types of SDMs to be solved. However, the Integrated Nested Laplace Approximation (INLA) approach, which has become increasingly popular in the field of ecological sciences, has not yet been integrated into an application that can synthesise the complexity of its code into a user-friendly interface for continuous spatial modelling.To overcome this shortcoming, we present in this paper a novel application, called BAYSPINS (BAYesian SPatial INla for SDMs), which allows the use of INLA for those who are not very experienced, or for those who are experienced and prefer a tool that allows them to carry out an initial analysis quickly, avoiding the process of writing code.BAYSPINS allows both geostatistical and preferential modelling, as well as a mixture of the two. It integrates the complex and hard coded SPDE-FEM (Stochastic Partial Differential Equation, along with the Finite Elements Method) approach to perform continuous spatial analysis with a visual interface. It also allows the use of default settings that automate the process or the customisation of a large number of elements that drive the modelling process. In this way, quick initial evaluations or more rigorous studies of the data provided by the user can be carried out, depending on the user's skill and understanding of the fundamentals underpinning the application.

Bayesian spatio-temporal analysis of malaria prevalence in children between 2 and 10 years of age in Gabon

BackgroundGabon still bears significant malaria burden despite numerous efforts. To reduce this burden, policy-makers need strategies to design effective interventions. Besides, malaria distribution is well known to be related to the meteorological conditions. In Gabon, there is limited knowledge of the spatio-temporal effect or the environmental factors on this distribution. This study aimed to investigate on the spatio-temporal effects and environmental factors on the distribution of malaria prevalence among children 2–10 years of age in Gabon.MethodsThe study used cross-sectional data from the Demographic Health Survey (DHS) carried out in 2000, 2005, 2010, and 2015. The malaria prevalence was obtained by considering the weighting scheme and using the space–time smoothing model. Spatial autocorrelation was inferred using the Moran’s I index, and hotspots were identified with the local statistic Getis-Ord General Gi. For the effect of covariates on the prevalence, several spatial methods implemented in the Integrated Nested Laplace Approximation (INLA) approach using Stochastic Partial Differential Equations (SPDE) were compared.ResultsThe study considered 336 clusters, with 153 (46%) in rural and 183 (54%) in urban areas. The prevalence was highest in the Estuaire province in 2000, reaching 46%. It decreased until 2010, exhibiting strong spatial correlation (P < 0.001), decreasing slowly with distance. Hotspots were identified in north-western and western Gabon. Using the Spatial Durbin Error Model (SDEM), the relationship between the prevalence and insecticide-treated bed nets (ITNs) coverage was decreasing after 20% of coverage. The prevalence in a cluster decreased significantly with the increase per percentage of ITNs coverage in the nearby clusters, and per degree Celsius of day land surface temperature in the same cluster. It slightly increased with the number of wet days and mean temperature per month in neighbouring clusters.ConclusionsIn summary, this study showed evidence of strong spatial effect influencing malaria prevalence in household clusters. Increasing ITN coverage by 20% and prioritizing hotspots are essential policy recommendations. The effects of environmental factors should be considered, and collaboration with the national meteorological department (DGM) for early warning systems is needed.

Lung Cancer Prevalence in Virginia: A Spatial Zipcode-Level Analysis via INLA.

Examining lung cancer (LC) cases in Virginia (VA) is essential due to its significant public health implications. By studying demographic, environmental, and socioeconomic variables, this paper aims to provide insights into the underlying drivers of LC prevalence in the state adjusted for spatial associations at the zipcode level. We model the available VA zipcode-level LC counts via (spatial) Poisson and negative binomial regression models, taking into account missing covariate data, zipcode-level spatial association and allow for overdispersion. Under latent Gaussian Markov Random Field (GMRF) assumptions, our Bayesian hierarchical model powered by Integrated Nested Laplace Approximation (INLA) considers simultaneous (spatial) imputation of all missing covariates through elegant prediction. The spatial random effect across zip codes follows a Conditional Autoregressive (CAR) prior. Zip codes with elevated smoking indices demonstrated a corresponding increase in LC counts, underscoring the well-established connection between smoking and LC. Additionally, we observed a notable correlation between higher Social Deprivation Index (SDI) scores and increased LC counts, aligning with the prevalent pattern of heightened LC prevalence in regions characterized by lower income and education levels. On the demographic level, our findings indicated higher LC counts in zip codes with larger White and Black populations (with Whites having higher prevalence than Blacks), lower counts in zip codes with higher Hispanic populations (compared to non-Hispanics), and higher prevalence among women compared to men. Furthermore, zip codes with a larger population of elderly people (age ≥ 65 years) exhibited higher LC prevalence, consistent with established national patterns. This comprehensive analysis contributes to our understanding of the complex interplay of demographic and socioeconomic factors influencing LC disparities in VA at the zip code level, providing valuable information for targeted public health interventions and resource allocation. Implementation code is available at GitHub.

Bayesian spatio-temporal analysis of the COVID-19 pandemic in Catalonia

In this study, we modelled the incidence of COVID-19 cases and hospitalisations by basic health areas (ABS) in Catalonia. Spatial, temporal and spatio-temporal incidence trends were described using estimation methods that allow to borrow strength from neighbouring areas and time points. Specifically, we used Bayesian hierarchical spatio-temporal models estimated with Integrated Nested Laplace Approximation (INLA). An exploratory analysis was conducted to identify potential ABS factors associated with the incidence of cases and hospitalisations. High heterogeneity in cases and hospitalisation incidence was found between ABS and along the waves of the pandemic. Urban areas were found to have a higher incidence of COVID-19 cases and hospitalisations than rural areas, while socio-economic deprivation of the area was associated with a higher incidence of hospitalisations. In addition, full vaccination coverage in each ABS showed a protective effect on the risk of COVID-19 cases and hospitalisations.

Multivariate Stochastic Volatility Modeling via Integrated Nested Laplace Approximations: A Multifactor Extension

This study introduces a multivariate extension to the class of stochastic volatility models, employing integrated nested Laplace approximations (INLA) for estimation. Bayesian methods for estimating stochastic volatility models through Markov Chain Monte Carlo (MCMC) can become computationally burdensome or inefficient as the dataset size and problem complexity increase. Furthermore, issues related to chain convergence can also arise. In light of these challenges, this research aims to establish a computationally efficient approach for estimating multivariate stochastic volatility models. We propose a multifactor formulation estimated using the INLA methodology, enabling an approach that leverages sparse linear algebra and parallelization techniques. To evaluate the effectiveness of our proposed model, we conduct in-sample and out-of-sample empirical analyses of stock market index return series. Furthermore, we provide a comparative analysis with models estimated using MCMC, demonstrating the computational efficiency and goodness of fit improvements achieved with our approach.

Modelling spatiotemporal patterns of visceral leishmaniasis incidence in two endemic states in India using environment, bioclimatic and demographic data, 2013-2022.

As of 2021, the National Kala-azar Elimination Programme (NKAEP) in India has achieved visceral leishmaniasis (VL) elimination (<1 case / 10,000 population/year per block) in 625 of the 633 endemic blocks (subdistricts) in four states. The programme needs to sustain this achievement and target interventions in the remaining blocks to achieve the WHO 2030 target of VL elimination as a public health problem. An effective tool to analyse programme data and predict/ forecast the spatial and temporal trends of VL incidence, elimination threshold, and risk of resurgence will be of use to the programme management at this juncture. We employed spatiotemporal models incorporating environment, climatic and demographic factors as covariates to describe monthly VL cases for 8-years (2013-2020) in 491 and 27 endemic and non-endemic blocks of Bihar and Jharkhand states. We fitted 37 models of spatial, temporal, and spatiotemporal interaction random effects with covariates to monthly VL cases for 6-years (2013-2018, training data) using Bayesian inference via Integrated Nested Laplace Approximation (INLA) approach. The best-fitting model was selected based on deviance information criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC) and was validated with monthly cases for 2019-2020 (test data). The model could describe observed spatial and temporal patterns of VL incidence in the two states having widely differing incidence trajectories, with >93% and 99% coverage probability (proportion of observations falling inside 95% Bayesian credible interval for the predicted number of VL cases per month) during the training and testing periods. PIT (probability integral transform) histograms confirmed consistency between prediction and observation for the test period. Forecasting for 2021-2023 showed that the annual VL incidence is likely to exceed elimination threshold in 16-18 blocks in 4 districts of Jharkhand and 33-38 blocks in 10 districts of Bihar. The risk of VL in non-endemic neighbouring blocks of both Bihar and Jharkhand are less than 0.5 during the training and test periods, and for 2021-2023, the probability that the risk greater than 1 is negligible (P<0.1). Fitted model showed that VL occurrence was positively associated with mean temperature, minimum temperature, enhanced vegetation index, precipitation, and isothermality, and negatively with maximum temperature, land surface temperature, soil moisture and population density. The spatiotemporal model incorporating environmental, bioclimatic, and demographic factors demonstrated that the KAMIS database of the national programmme can be used for block level predictions of long-term spatial and temporal trends in VL incidence and risk of outbreak / resurgence in endemic and non-endemic settings. The database integrated with the modelling framework and a dashboard facility can facilitate such analysis and predictions. This could aid the programme to monitor progress of VL elimination at least one-year ahead, assess risk of resurgence or outbreak in post-elimination settings, and implement timely and targeted interventions or preventive measures so that the NKAEP meet the target of achieving elimination by 2030.

Modeling multivariate positive‐valued time series using R‐INLA

AbstractIn this article, we describe fast Bayesian statistical analysis of vector positive‐valued time series, with application to interesting financial data streams. We discuss a flexible level correlated model (LCM) framework for building hierarchical models for vector positive‐valued time series. The LCM allows us to combine marginal gamma distributions for the positive‐valued component responses, while accounting for association among the components at a latent level. We introduce vector autoregression evolution of the latent states, deriving its precision matrix and enabling its estimation using integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling via the R‐INLA package, building custom functions to handle this setup. We use the proposed method to model interdependencies between intraday volatility measures from several stock indexes.

Thermal tolerance and habitat preferences mediate how freshwater fish body sizes respond to warming

Recent studies have linked ecosystem warming to decreased mean body size in aquatic ectotherms but have often relied on experimental approaches. This study explores how climate change modifies adult body sizes in natural communities for five culturally, commercially, and recreationally important freshwater fish species that vary in thermal preferences (lake trout ( Salvelinus namaycush), lake whitefish ( Coregonus clupeaformis), walleye ( Sander vitreus), yellow perch ( Perca flavescens), and smallmouth bass ( Micropterus dolomieu)). Using data for &gt;170 000 sampling records from &gt;600 lakes spanning the entire province of Ontario, Canada, we employ a spatial analysis technique based on Integrated Nested Laplace Approximation to detect body size changes due to warming lake conditions. With warming conditions, cold-adapted species (lake whitefish) decreased in adult body size, while cool- and warm-adapted species (walleye and smallmouth bass) increased in adult body size. Our study, like others recently conducted in marine and freshwater systems, demonstrates that the responses of fish body sizes to warming are not a unidirectional shift and may be linked to the habitat and thermal preferences of individual fish species.

A novel statistical approach to deal with spatial bias in maturity ogive estimation

The proportion of mature fish at length is one of the most important population attributes when evaluating reproductive potential for fish stock assessment purposes. Bias in maturity ogive parameters can lead to fishery management decisions based on misspecified biological reference points. These parameters can vary spatially and temporally, and this variability should be understood and included in the assessment models. However, integrating this variability becomes challenging when specific spatial-dependent ogives cannot be used in the stock assessment model. Hence, this study proposes a novel use of a multivariate response Bayesian regression model, employing an integrated nested Laplace approximation to estimate a single global maturity ogive using data from various spatial areas. This model explicitly accounts for differences in the sampling process and combines information from different areas to estimate shared maturity ogive parameters using joint-likelihood procedures. The model is applied to the European hake stock in ICES (International Council for the Exploration of the Sea) Divisions 27.8.c and 27.9.a, serving as a practical guide. In this model, we have considered different predictors to handle the relationship between the probability of being mature and the length and year covariates. Our results suggest that the logistic formulation correctly captures the relationship between the probability of being mature and length. For year variability, including a year factor covariate or year random effect in the predictor model produces similar values of goodness of fit measures.

Major ions in Central European precipitation – Insight into changes in NO3−/SO42−, NH4+/NO3− and NH4+/SO42− ratios over the last four decades

Knowledge of precipitation composition is important, among other things, to reveal changes in atmospheric chemistry. Here we present the long-term time trends in ratios of major ions in precipitation, namely nitrate to sulphate (NO3−/SO42−), ammonium to sulphate (NH4+/SO42−) and ammonium to nitrate (NH4+/NO3−). For this we explore the long-term time series recorded by the Czech Hydrometeorological Institute at eight monitoring sites situated in urban, rural and mountain regions of the Czech Republic between 1980 and 2020. To that end, we use innovative Bayesian inference with the Integrated Nested Laplace Approximation (INLA) computational method appropriate for investigating complicated large-scale data. Our results indicated: (i) increasing NO3−/SO42− ratio in precipitation over time and distinct seasonal behaviour with higher values in winter and lower values in summer, (ii) increasing NH4+/SO42− ratio in precipitation and distinct seasonal behaviour with higher values in summer and lower values in winter and (iii) relatively stable NH4+/NO3− ratio in precipitation with a mild recent increase and distinct seasonal behaviour with higher values in summer and lower values in winter. This behaviour pattern holds true for all the sites analysed, irrespective of their geographical position, altitude or environment. Though explored in detail rarely, the ion ratios are important to study as they reflect changes in atmospheric chemistry, mirroring changes in emissions and meteorology and suggesting changing impacts on ecosystems and the environment.

Assessing drivers of estuarine debris using a Bayesian spatial modelling approach (INLA-SPDE)

Estuaries are under increasing pressure from urbanization, including through the release of domestic wastes such as anthropogenic debris. Growing concern over environmental contamination has led to management interventions, aimed at reducing the further release of debris. Effective strategies, however, require an understanding of the factors influencing the abundance and distribution of debris. Estuaries pose a challenge to assess debris trends due to the myriad of factors that influence debris patterns. Here we present a Bayesian approach to assess spatial patterns in debris across four estuaries of New South Wales, Australia. We provide an overview of debris composition and employ Integrated Nested Laplace Approximation (INLA) alongside Stochastic Partial Differential Equation (SPDE) to produce three models testing predictors of debris abundance: (i) non spatial, (ii) a model accounting for spatial autocorrelation and (iii) accounting for spatial autocorrelation and introducing the estuarine foreshore as a barrier. Data was sourced from cleanups reported within the Australian Marine Debris Initiative (AMDI), a national citizen science program coordinated by the Tangaroa Blue Foundation. The data, from 169 sampling events between 2012 and 2017 was used. All models tested predictors against the abundance of hard plastic, expanded plastic, plastic bags, and plastic drink bottles. Plastic was the dominant component, ranging from 69% to 82% of total debris within the study estuaries. Important predictors differed across debris types and included ‘distance to estuary mouth’, access to foreshore, population, and site substrate. Specific factors differed in importance when accounting for spatial autocorrelation, demonstrating the need for spatial approaches when assessing debris trends within estuaries. The present Bayesian approach could be used to better understand drivers of estuarine debris and inform interventions for effective management.