Good modelling practice in ecology, the hierarchical Bayesian perspective

Structural equation models are highly suited for evaluating ecosystem-level hypotheses, but to be effective, structural equation models need to be able to accommodate spatial and temporal data. Here, the importance of different abiotic and biotic drivers on wet heathland vegetation is investigated using a spatio-temporal structural equation model in a hierarchical Bayesian framework. Ecological data from 39 Danish sites, each with several wet heathland plots, were sampled in the period 2007–2014. Including resampling over the years, 1322 plots were sampled. Plant cover was measured using the pin-point method and the joint distribution of the key plant species in the wet heathland ecosystem, Erica tetralix, Calluna vulgaris, Molinia caerulea, and an aggregate class of other higher plants was estimated assuming a Dirichlet-multinomial mixture distribution. The investigated drivers of wet heathland vegetation include nitrogen deposition, soil type, pH, precipitation and grazing. Generally, the two dwarf shrubs, E. tetralix and C. vulgaris, responded in qualitatively similar ways to the abiotic variables and qualitatively oppositely to the way the grass M. caerulea and the aggregate class of other higher plants. Furthermore, the spatial effects were qualitatively similar to the temporal effects. The two dwarf shrub species were most likely positively affected by nitrogen deposition, soil pH, sandy soils, low precipitation, and the absence of grazing. The study demonstrated that important insight on ecosystem dynamics and regulation can be obtained by spatial and temporal structural equation modeling in a hierarchical Bayesian framework and that the proper statistical modeling of the joint species abundance is a key feature of such models. Furthermore, the advantages of partitioning different types of uncertainties become clear when the fitted structural equation model is used for predictive purposes at a specific site.

This brief communication reports on the main findings of the LEMTOX workshop, held from 9 to 12 September 2007, at the Helmholtz Centre for Environmental Research (UFZ) in Leipzig, Germany. The workshop brought together a diverse group of stakeholders from academia, regulatory authorities, contract research organizations, and industry, representing Europe, the United States, and Asia, to discuss the role of ecological modeling in risk assessments of pesticides, particularly under the European regulatory framework. The following questions were addressed: What are the potential benefits of using ecological models in pesticide registration and risk assessment? What obstacles prevent ecological modeling from being used routinely in regulatory submissions? What actions are needed to overcome the identified obstacles? What recommendations should be made to ensure good modeling practice in this context? The workshop focused exclusively on population models, and discussion was focused on those categories of population models that link effects on individuals (e.g., survival, growth, reproduction, behavior) to effects on population dynamics. The workshop participants concluded that the overall benefits of ecological modeling are that it could bring more ecology into ecological risk assessment, and it could provide an excellent tool for exploring the importance of, and interactions among, ecological complexities. However, there are a number of challenges that need to be overcome before such models will receive wide acceptance for pesticide risk assessment, despite having been used extensively in other contexts (e.g., conservation biology). The need for guidance on Good Modeling Practice (on model development, analysis, interpretation, evaluation, documentation, and communication), as well as the need for case studies that can be used to explore the added value of ecological models for risk assessment, were identified as top priorities. Assessing recovery potential of exposed nontarget species and clarifying the ecological relevance of standard laboratory test results are two areas for which ecological modeling may be able to provide considerable benefits.

Transport affordability defined as the share of household income devoted to transport expenditure is a key dimension of urban equity and social inclusion, particularly in contexts characterised by spatial inequality and income disparities. This study examines provincial variation in public transport affordability across South Africa using a hierarchical Bayesian regression framework applied to province–year data from 2015 to 2022 (n = 72). Affordability is operationalised as a transport cost burden, with higher values indicating a greater proportion of household income spent on transport, and is modelled as a function of household income, trip frequency, household population, and total provincial employment, with province-level random intercepts capturing unobserved regional heterogeneity. The results indicate that household income is negatively associated with transport cost burden, suggesting that provinces with higher average income devote a smaller share of income to transport and therefore experience better affordability. In contrast, household population and aggregate provincial employment are positively associated with transport cost burden, reflecting higher overall mobility and commuting demands in larger and more economically active provinces rather than improved affordability. Trip frequency shows no statistically meaningful association with affordability once household composition and income capacity are accounted for. After accounting for observed characteristics, between-province variation is limited, indicating that affordability dynamics are broadly similar across provinces over the study period. Methodologically, the hierarchical Bayesian framework enables partial pooling across provinces and supports probabilistic inference through credible intervals, thereby improving the stability of estimates in a small-sample multilevel context. While the analysis is associational rather than causal, the findings provide policy-relevant evidence for monitoring transport affordability, including benchmarking the prevalence of affordability burdens relative to the commonly used 10% threshold.

Improved hierarchical Bayesian modeling framework with arbitrary polynomial chaos for probabilistic model updating

Occupational exposure assessment is important in preventing occupational coal worker’s diseases. Methods have been proposed to assess compliance with exposure limits which aim to protect workers from developing diseases. A Bayesian framework with informative prior distribution obtained from historical or expert judgements has been highly recommended for compliance testing. The compliance testing is assessed against the occupational exposure limits (OEL) and categorization of the exposure, ranging from very highly controlled to very poorly controlled exposure groups. This study used a Bayesian framework from historical and expert elicitation data to compare the posterior probabilities of the 95th percentile (P95) of the coal dust exposures to improve compliance assessment and decision-making. A total of 10 job titles were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation was used to draw a full posterior probability of finding a job title to an exposure category. A modified IDEA (“Investigate”, “Discuss”, “Estimate”, and “Aggregate”) technique was used to conduct expert elicitation. The experts were asked to give their subjective probabilities of finding coal dust exposure of a job title in each of the exposure categories. Sensitivity analysis was done for parameter space to check for misclassification of exposures. There were more than 98% probabilities of the P95 exposure being found in the poorly controlled exposure group when using expert judgments. Historical data and non-informative prior tend to show a lower probability of finding the P95 in higher exposure categories in some titles unlike expert judgments. Expert judgements tend to show some similarity in findings with historical data. We recommend the use of expert judgements in occupational risk assessment as prior information before a decision is made on current exposure when historical data are unavailable or scarce.

EEG based emotion recognition by hierarchical bayesian spectral regression framework

Recent decades have seen tremendous increases in the quantity of empirical ecological data collected by individual investigators, as well as through research networks such as FLUXNET (Baldocchi et al., 2001). At the same time, advances in computer technology have facilitated the development and implementation of large and complex land surface and ecological process models. Separately, each of these information streams provides useful, but imperfect information about ecosystems. To develop the best scientific understanding of ecological processes, and most accurately predict how ecosystems may cope with global change, integration of empirical and modeling approaches is necessary. However, true integration - in which models inform empirical research, which in turn informs models (Fig. 1) - is not yet common in ecological research (Luo et al., 2011). The goal of this workshop, sponsored by the Department of Energy, Office of Science, Biological and Environmental Research (BER) program, was to bring together members of the empirical and modeling communities to exchange ideas and discuss scientific practices for increasing empirical - model integration, and to explore infrastructure and/or virtual network needs for institutionalizing empirical - model integration (Yiqi Luo, University of Oklahoma, Norman, OK, USA). The workshop included presentations and small group discussions that coveredmore » topics ranging from model-assisted experimental design to data driven modeling (e.g. benchmarking and data assimilation) to infrastructure needs for empirical - model integration. Ultimately, three central questions emerged. How can models be used to inform experiments and observations? How can experimental and observational results be used to inform models? What are effective strategies to promote empirical - model integration?« less

Mitochondrial dysfunction is involved in many complex diseases. Efficient and accurate evaluation of mitochondrial functionality is crucial for understanding pathology as well as facilitating novel therapeutic developments. As a popular platform, Seahorse extracellular flux (XF) analyzer is widely used for measuring mitochondrial oxygen consumption rate (OCR) in living cells. A hidden feature of Seahorse XF OCR data is that it has a complex data structure, caused by nesting and crossing between measurement cycles, wells and plates. Surprisingly, statistical analysis of Seahorse XF data has not received sufficient attention, and current methods completely ignore the complex data structure, impairing the robustness of statistical inference. To rigorously incorporate the complex structure into data analysis, here we developed a Bayesian hierarchical modeling framework, OCRbayes, and demonstrated its applicability based on analysis of published data sets. We showed that OCRbayes can analyze Seahorse XF OCR experimental data derived from either single or multiple plates. Moreover, OCRbayes has potential to be used for diagnosing patients with mitochondrial diseases.

Earth and Space Science Open Archive Presented WorkOpen AccessYou are viewing the latest version by default [v1]A space–time Bayesian hierarchical modeling framework for projection of seasonal high flow riskAuthorsÁlvaroOssandóniDBalajiRajagopalanSee all authors Álvaro OssandóniDCorresponding Author• Submitting AuthorUniversity of Colorado at BoulderiDhttps://orcid.org/0000-0003-2165-8736view email addressThe email was not providedcopy email addressBalaji RajagopalanUniversity of Colorado at Boulderview email addressThe email was not providedcopy email address

Personalized federated learning (PFL) based on Bayesian approach tackle the challenges from statistical heterogeneity of client data by computing a personalized posterior distribution over the parameters of each client's local model and constructing a global distribution by aggregating the parameters of these personalized posteriors. However, the heuristic aggregation methods introduce strong biases and result in global models with poor generalization. We thus propose a novel hierarchical Bayesian inference framework for PFL by specifying a conjugate hyper-prior over the parameters of the personalized posteriors. This allows us to jointly compute a global posterior distribution for aggregation and the personalized ones at local level. This hierarchical Bayesian inference framework achieves elegant balance between local personalization and global model robustness. Extensive empirical study shows that by effectively sharing the heterogeneous statistical strength across the local models while retaining their distinctive characteristics, our framework yields state-of-the-art performance. We also show that existing Bayesian PFLs are special cases of our framework.

In this brief, a hierarchical Bayesian network modeling framework is formulated for large-scale process monitoring and decision making, which includes a basic layer and a functional layer. First, the whole process is decomposed into different units, where local Bayesian networks are constructed, providing monitoring information and decision-making capability for the upper layer. The network structure is determined automatically based on the process data in each local unit of the basic layer. Then, through incorporating the topological structure of the process, a functional Bayesian network is further constructed to infer the information from the basic layer, which can be customized according to user demands, such as fault detection, fault diagnosis, and classification of operating status. The performance of the proposed method is evaluated through a benchmark process.

Stable isotopes are valuable tools for partitioning the components contributing to ecological processes of interest, such as animal diets and trophic interactions, plant resource use, ecosystem gas fluxes, streamflow, and many more. Stable isotope data are often analyzed with simple linear mixing (SLM) models to partition the contributions of different sources, but SLM models cannot incorporate a mechanistic understanding of the underlying processes and do not accommodate additional data associated with these processes (e.g., environmental covariates, flux data, gut contents). Thus, SLM models lack predictive ability. We describe a process-based mixing (PBM) model approach for integrating stable isotopes, other data sources, and process models to partition different sources or process components. This is accomplished via a hierarchical Bayesian framework that quantifies multiple sources of uncertainty and enables the incorporation of process models and prior information to help constrain the source-specific proportional contributions, thereby potentially avoiding identifiability issues that plague SLM models applied to "too many" sources. We discuss the application of the PBM model framework to three diverse examples: temporal and spatial partitioning of streamflow, estimation of plant rooting profiles and water uptake profiles (or water sources) with extension to partitioning soil and ecosystem CO2 fluxes, and reconstructing animal diets. These examples illustrate the advantages of the PBM modeling approach, which facilitates incorporation of ecological theory and diverse sources of information into the mixing model framework, thus enabling one to partition key process components across time and space.

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Speech enhancement using a Bayesian evidence approach

Global and regional numerical models for terrestrial ecosystem dynamics require fine spatial resolution and temporally complete historical climate fields as input variables. However, because climate observations are unevenly spaced and have incomplete records, such fields need to be estimated. In addition, uncertainty in these fields associated with their estimation are rarely assessed. Ecological models are usually driven with a geostatistical model's mean estimate (kriging) of these fields without accounting for this uncertainty, much less evaluating such errors in terms of their propagation in ecological simulations. We introduce a Bayesian statistical framework to model climate observations to create spatially uniform and temporally complete fields, taking into account correlation in time and space, spatial heterogeneity, lack of normality, and uncertainty about all these factors. A key benefit of the Bayesian model is that it generates uncertainty measures for the generated fields. To demonstrate this method, we reconstruct historical monthly precipitation fields (a driver for ecological models) on a fine resolution grid for a climatically heterogeneous region in the western United States. The main goal of this work is to evaluate the sensitivity of ecological models to the uncertainty associated with prediction of their climate drivers. To assess their numerical sensitivity to predicted input variables, we generate a set of ecological model simulations run using an ensemble of different versions of the reconstructed fields. We construct such an ensemble by sampling from the posterior predictive distribution of the climate field. We demonstrate that the estimated prediction error of the climate field can be very high. We evaluate the importance of such errors in ecological model experiments using an ensemble of historical precipitation time series in simulations of grassland biogeochemical dynamics with an ecological numerical model, Century. We show how uncertainty in predicted precipitation fields is propagated into ecological model results and that this propagation had different modes. Depending on output variable, the response of model dynamics to uncertainty in inputs ranged from uncertainty in outputs that matched that of inputs to those that were muted or that were biased, as well as uncertainty that was persistent in time after input errors dropped.