Bayesian Model Research Articles

BAYESIAN NETWORKS AND STRUCTURAL EQUATION MODELLING TO INVESTIGATE THE PASSENGERS’ PERCEPTIONS IN HIGH-SPEED RAIL SYSTEMS

Ensuring sustainability in the global world today depends on perception management as well as financial management. In order to manage the perceptions, which are inherently latent variables as they are measured indirectly through their indicators, they must be accurately handled and modelled comprehensively. In the present study, a hybrid technique combining Bayesian Networks (BN) and Structural Equation Modelling (SEM), which are regarded as causal models, was used to investigate the perceptions of High-Speed Rail System (HSRS) passengers. In order to provide insight into the customer retention strategy for HSRS, the analyses were performed on the survey data gathered from the frequent users of HSRS operating between 2 cities of Turkey. After the measurement model of the perception variables through SEM was established, the relationships between the variables were learned using BN knowledge extraction algorithms. As a result, relationships from image to trust and loyalty, from trust to perceived value, from perceived value to satisfaction, and from satisfaction to loyalty were determined. Final interpretations were made in terms of risk management with the help of the probabilistic predictive ability of the BN by setting evidence on the satisfaction levels of the perceptions.

Impact of Sharing Imprecise Information on Fixed-Bin Selective Assembly

Fixed-Bin Selective Assembly (FBSA) is widely used to improve the assembly quality of single units of different component types. FBSA has parts with similar dimensions, but with slight deviations due to production variances, sorted into pre-determined bins. A selection is made from paired bins for assembly. To ensure enough components, assemblers adopt a proactive or reactive strategy. For the proactive, predictions of component usage quantities are used to adjust processes for the internally manufactured matched component prior to production. With the reactive, component inventory levels are adjusted after assembly. The performance of each can be improved with information about incoming part dimensions. However, the communicated information may be imprecise. We developed a Bayesian Measurement Error Model to evaluate the impact of imprecision, in the supplier’s communicated information, on the efficacy of FBSA with either strategy. The model was tested with parameters obtained from a US assembler of combustion engines. We find that in most scenarios, the proactive approach results in better FBSA efficacy on average. A key exception was when imprecise information about the mean was communicated, resulting in no significant difference. The reactive approach is typically easier to implement, therefore it may be preferred when communicated information about the mean of incoming part dimensions is often inaccurate.

New statistical framework for interlaboratory evaluation of anti-doping testing results by WADA

AbstractThe World Anti-doping Agency (WADA) International Standard for Laboratories (ISL), developed as part of the World Anti-Doping Program, requires satisfactory laboratory performance in the WADA External Quality Assessment Scheme (EQAS) in order to obtain and maintain WADA accreditation. Under this mandate, WADA regularly distributes urine and blood test samples to anti-doping laboratories to continuously monitor their proficiency. Over the years, WADA has employed classical, generic statistical methods, in accordance to ISO 13528, to evaluate quantitative EQAS results. Here, we set out the rationale for a modern statistical approach that recognizes and addresses the particular features of the measurement results typically obtained in such tests and present an approach involving Bayesian measurement models and statistical data analysis that is tailored specifically to anti-doping testing.

Fluctuations in emotion regulation as a mechanism linking stress and internalizing psychopathology among adolescents: An intensive longitudinal study

Stressful life events (SLEs) are tightly coupled with the emergence of anxiety and depression symptoms among adolescents, but the mechanisms underlying this relationship remain poorly understood. We investigated within-person fluctuations in emotion regulation as a mechanism linking SLEs and internalizing psychopathology in an intensive longitudinal study. We examined how monthly fluctuations in SLEs were related to engagement in three emotion regulation strategies—acceptance, reappraisal, and rumination—and whether these strategies were associated with changes in internalizing symptoms in adolescents followed for one year (N = 30; n = 355 monthly observations). Bayesian hierarchical models revealed that on months when adolescents experienced more SLEs than was typical for them, they also engaged in more rumination, which, in turn, was associated with higher anxiety and depression symptoms and mediated the prospective relationship between SLEs and internalizing symptoms. In contrast, greater use of acceptance and reappraisal selectively moderated the association between stressors and internalizing symptoms, resulting in stronger links between SLEs and symptoms. These results suggest that emotion regulation strategies play different roles in the stress-psychopathology relationship. Understanding how changes in emotion regulation contribute to increases in internalizing symptoms following experiences of stress may provide novel targets for interventions aimed at reducing stress-related psychopathology.

Geographical Disparities in Hypertension Incidence Rate in Iran 2004-2016: Bayesian Spatial Analysis

Introduction: Cardiovascular diseases such as coronary heart disease, heart failure, arrhythmia, and cardiomyopathy all include hypertension as a key risk factor. Research has shown that the early detection and treatment of hypertension and its risk factors, as well as public health policies to reduce behavioral risk factors, have led to a gradual reduction in mortality caused by heart disease and stroke in high-income countries in the past three decades. Trends in hypertension incidence have been monitored at the national level in Iran. The aim of this study examine province-level disparities in Hypertension incidence from 2004 to 2016. Methods: Use the Non-Communicable Diseases Risk-Factors Surveillance in the Islamic Republic of Iran STEPs registry data. to estimate the incidence rate of hypertension for all provinces in 2004, 2006-2009, 2011, and 2016 using a Bayesian spatial model with Markov chain Monte Carlo algorithm in OpenBUGS version 3.2.3 and R version 4.2.2. Results: The estimated Hypertension incidence rate in total increased from 19.87 per 1000 people (95% credible interval 14.28, 25.48) in 2004 to 193.02 (171.92, 220.48) in 2016. According to the estimates of 2016, we found that the provinces of Markazi, Ardabil, and Semnan had the highest rate of hypertension, and the provinces of Hormozgan, and Sistan-Baluchistan had the lowest rate. Our findings show that Khorasan, North, Alborz, and Semnan have the most significant percentage change in incidence rate from 2004-2016. Conclusion: To reduce the prevalence of hypertension in Iranian regions, it is crucial to develop regular hypertension screening programs, especially among the elderly

Task-Dependent Brain Activity in Generalized Anxiety Disorder Determined By Bayesian Spatio-Temporal Single Case Model

Introduction: Data obtained from functional magnetic resonance imaging (fMRI) have a complex structure. Considering the special features of this type of data in analyses is of particular importance. Previous studies on generalized anxiety disorder (GAD) as a prevalent mental disorder using functional neuroimaging have had conflicting results. In this study, we apply a Bayesian spatiotemporal model to this type of data which considers both spatial and temporal dependence among regions which is one of the most essential features to consider. Methods: In this single-subject study, we analyze data from a patient with GAD and a healthy participant. Both participants are 24-year-old women who are assigned an emotion reactivity task (matching neutral and negative facial expressions) inside a scanner. The spatial Bayesian variable selection method is used to detect blood oxygen level-dependent activation in fMRI data. Results: Activation areas in neutral and negative facial expressions are provided for both participants by posterior probability map. The results of our study show a greater level of activity in the GAD participant in comparison to the healthy participant in responding to the negative matching task. Conclusion: the GAD patient showed more neural activity in response to negative facial expressions than the healthy participant in brain regions related to emotional response in the areas of the frontal Pole, middle frontal gyrus, insular cortex, and frontal orbital cortex. Moreover, the inferior frontal gyrus in the patient with GAD showed more reaction to negative emotional stimuli.

Information content of JWST spectra of WASP-39b

The era of James Webb Space Telescope (JWST) transmission spectroscopy of exoplanetary atmospheres commenced with the study of the Saturn-mass gas giant WASP-39b as part of the Early Release Science (ERS) program. WASP-39b was observed using several different JWST instrument modes (NIRCam, NIRISS, NIRSpec G395H and NIRSpec PRISM) and the spectra were published in a series of papers by the ERS team. The current study examines the information content of these spectra measured using the different instrument modes, focusing on the complexity of the temperature-pressure profiles and number of chemical species warranted by the data. We examine if the molecules H2O CO CO2 K H2S CH4 and SO2 are detected in each of the instrument modes. Two Bayesian inference methods are used to perform atmospheric retrievals: the standard nested sampling method, as well as the supervised machine learning method of the random forest (trained on a model grid). For nested sampling, Bayesian model comparison is used as a guide to identify the set of models with the required complexity to explain the data. Generally, non-isothermal transit chords are needed to fit the transmission spectra of WASP-39b, although the complexity of the temperature-pressure profile required is mode-dependent. The minimal set of chemical species needed to fit a spectrum is mode-dependent as well, and also depends on whether grey or non-grey clouds are assumed. When a non-grey cloud model is used to fit the NIRSpec G395H spectrum, it generates a spectral continuum that compensates for the water opacity. The same compensation is absent when fitting the non-grey cloud model to the NIRSpec PRISM spectrum (which has broader wavelength coverage), suggesting that it is spurious. The interplay between the cloud spectral continuum and the water opacity determines if sulphur dioxide is needed to fit either spectrum. The inferred elemental abundances of carbon and oxygen and the carbon-to-oxygen (C/O) ratios are all mode- and model-dependent, and should be interpreted with caution. Bayesian model comparison does not always offer a clear path forward for favouring specific retrieval models (e.g. grey versus non-grey clouds) and thus for enabling unambiguous interpretations of exoplanet spectra.

Four-of-a-kind? Comprehensive atmospheric characterisation of the HR 8799 planets with VLTI/GRAVITY

With four companions at separations from 16 to 71 au, HR 8799 is a unique target for direct imaging, presenting an opportunity for a comparative study of exoplanets with a shared formation history. Combining new VLTI/GRAVITY observations obtained within the ExoGRAVITY program with archival data, we performed a systematic atmospheric characterisation across all four planets. We explored different levels of model flexibility to understand the temperature structure, chemistry, and clouds of each planet using both petitRADTRANS atmospheric retrievals and fits to self-consistent radiative--convective equilibrium models. Using Bayesian model averaging to combine multiple retrievals (a total of 89 across all four planets), we find that the HR 8799 planets are highly enriched in metals, with M/H gtrsim 1, and have stellar to superstellar atmospheric C/O ratios. The C/O ratio increases with increasing separation from $0.55^ $ for d to $0.78^ $ for b, with the exception of the innermost planet, which has a C/O ratio of $0.87 Such high metallicities are unexpected for these massive planets, and challenge planet-formation models. By retrieving a quench pressure and using a disequilibrium chemistry model, we derive vertical mixing strengths compatible with predictions for high-metallicity, self-luminous atmospheres. Bayesian evidence comparisons strongly favour the presence of HCN in HR 8799 c and e, as well as in HR 8799 c, with detections at $>5 confidence. All of the planets are cloudy, with no evidence of patchiness. The clouds of c, d, and e are best fit by silicate clouds lying above a deep iron cloud layer, while the clouds of the cooler HR 8799 b are more likely composed of $S. With well-defined atmospheric properties, future exploration of this system is well positioned to unveil further details of these planets, extending our understanding of the composition, structure, and formation history of these siblings.

A Bayesian latent variable model for the optimal identification of disease incidence rates given information constraints

Abstract We present an original approach for measuring infections as a latent variable and making use of serological and expert surveys to provide ground truth identification during the early pandemic period. Compared to existing approaches, our model relies more on empirical information than strong structural forms, permitting inference with relatively few assumptions of cumulative infections. We also incorporate a range of political, economic, and social covariates to richly parameterize the relationship between epidemic spread and human behaviour. To show the utility of the model, we provide robust estimates of total infections that account for biases in COVID-19 cases and tests counts in the U.S. from March to July of 2020, a period of time when accurate data about the nature of the SARS-CoV-2 virus was of limited availability. In addition, we can show how sociopolitical factors like the Black Lives Matter protests and support for President Donald Trump are associated with the spread of the virus via changes in fear of the virus and cell phone mobility. A reproducible version of this article is available as an Rmarkdown file at https://github.com/CoronaNetDataScience/covid_model.

Using multi‐scale spatial models of dendritic ecosystems to infer abundance of a stream salmonid

Abstract Understanding patterns of species abundance is essential for planning landscape‐level conservation. The complex hierarchies of dendritic ecosystems result in different levels of heterogeneity at distinct geographic scales. Species responses to dynamic environmental drivers may also vary spatially depending on their interactions with landscape features. Monitoring abundance by explicitly quantifying their spatial and temporal variation is important for strategic management. We analysed brook trout (Salvelinus fontinalis) count data collected from 173 sites in western North Carolina between 1989 and 2015. We developed a Bayesian hierarchical model that used single‐ and multi‐pass electro‐fishing data and characterized their respective capture probabilities. We quantified spatial variation using a multi‐scale process model representative of the nested stream habitats, and we investigated differences in population temporal trends and responses to seasonal weather patterns by space and life stage. Trout abundance was lower on the Atlantic slope of the Eastern Continental Divide than in the interior, on average, and the Atlantic slope juveniles were more adversely affected by high winter flows. However, Atlantic slope populations of both lifestages demonstrated positive temporal trends, whereas Interior juveniles demonstrated a negative trend. We found higher spatial variation than temporal variation in abundance when conditioned on the covariates, where the primary source of spatial heterogeneity was revealed at the segment level, compared to watershed or network levels. Our multi‐scale spatial model outperformed simpler models in abundance estimation and out‐of‐sample prediction. The inferred per‐pass capture probabilities indicated that single‐pass surveys were as efficient as multi‐pass surveys. Synthesis and applications. Our study suggested conservation priority should involve multiple criteria, including present‐day abundance, temporal trend and sensitivity to environmental drivers. Based on the inferred scale‐specific variations in trout abundance, we recommend that future surveys strategically combine single‐pass surveys with multi‐pass surveys to optimize abundance estimation. Our approach is widely applicable to other species and ecosystems occupying dendritic habitats.

Human molybdenum exposure risk in industrial regions of China: New critical effect indicators and reference dose

Evidence increasingly suggests molybdenum exposure at environmental levels is still associated with adverse human health, emphasizing the necessity to establish a more protective reference dose (RfD). Herein, we conducted a study measuring 15 urinary metals and 30 clinical health indicators in 2267 participants residing near chemical enterprises across 11 Chinese provinces to investigate their relationships. The kidney and cystatin-C emerged as the most sensitive organ and critical effect indicator of molybdenum exposure, respectively. Odds of cystatin-C-defined chronic kidney disease (CKD) in the highest quantile of molybdenum exposure significantly increased by 133.5% (odds ratio [OR]: 2.34, 95% CI: 1.78, 3.11) and 75.8% (OR: 1.76, 95% CI: 1.24, 2.49) before and after adjusting for urinary 14 metals, respectively. Intriguingly, cystatin-C significantly mediated 15.9–89.5% of molybdenum's impacts on liver and lung function, suggesting nephrotoxicity from molybdenum exposure may trigger hepatotoxicity and pulmonary toxicity. We derived a new RfD for molybdenum exposure (0.87 μg/kg-day) based on cystatin-C-defined estimated glomerular filtration rate by employing Bayesian Benchmark Dose modeling analysis. This RfD is significantly lower than current exposure guidance values (5–30 μg/kg-day). Remarkably, >90% of participants exceeded the new RfD, underscoring the significant health impacts of environmental molybdenum exposure on populations in industrial regions of China.

A Bayesian adversarial probsparse Transformer model for long-term remaining useful life prediction

Long-term remaining useful life (RUL) prediction is essential for the maintenance of safety-crucial engineering assets. Deep learning (DL) models, especially Transformer-based models have achieved outstanding performance in long-term RUL prediction. However, existing Transformer models neglect the impact of discrepancy loss in model training. The accumulation of the discrepancy loss during the inference will hamper the generalization of prediction model, resulting in an overfitting problem. To address the problem, this paper proposes a Bayesian Adversarial Probsparse Transformer (BAPT) model for long-term RUL prediction. Firstly, the adversarial learning method is leveraged to mitigate the impact of accumulated discrepancy loss caused by varying working conditions in long-term prediction, thus diminishing the error accumulation. Secondly, the Probsparse multi-head attention is adopted to enhance the efficiency of feature extraction. The Probsparse multi-head attention focuses on the significant degradation features in long time-series to reduce the computation complexity. Lastly, the Bayesian neural network is introduced to quantify the uncertainty in RUL prediction. The effectiveness of the proposed model is verified using two commercial aircraft turbofan engine datasets. The results indicate that BAPT model for long-term RUL prediction demonstrates better performance than the existing state-of-the-art models.

Bayesian Hierarchical Modelling for Histology-Independent Time-to-Event Outcomes in the NICE Single Technology Appraisal of Pembrolizumab for Solid Tumours with MSI-H/dMMR: External Assessment Group Perspective.

Bayesian Hierarchical Modelling for Histology-Independent Time-to-Event Outcomes in the NICE Single Technology Appraisal of Pembrolizumab for Solid Tumours with MSI-H/dMMR: External Assessment Group Perspective.

Causal association of blood cell traits with inflammatory bowel diseases: a Mendelian randomization study.

Observational studies have found associations between blood cell traits and inflammatory bowel diseases (IBDs), whereas the causality and dose-effect relationships are still undetermined. Two-sample Mendelian randomization (MR) analyses using linear regression approaches, as well as Bayesian model averaging (MR-BMA), were conducted to identify and prioritize the causal blood cell traits for Crohn's disease (CD) and ulcerative colitis (UC). An observational study was also performed using restricted cubic spline (RCS) to explore the relationship between important blood cell traits and IBDs. Our uvMR analysis using the random effects inverse variance weighted (IVW) method identified eosinophil (EOS) as a causal factor for UC (OR = 1.36; 95% CI: 1.13, 1.63). Our MR-BMA analysis further prioritized that high level of lymphocyte (LYM) decreased CD risk (MIP = 0.307; MACE = -0.059; PP = 0.189; = -0.173), whereas high level of EOS increased UC risk (MIP = 0.824; MACE = 0.198; PP = 0.627; = 0.239). Furthermore, the observational study clearly depicts the nonlinear relationship between important blood cell traits and the risk of IBDs. Using MR approaches, several blood cell traits were identified as risk factors of CD and UC, which could be used as potential targets for the management of IBDs. Stratified genome-wide association studies (GWASs) based on the concentration of traits would be helpful owing to the nonlinear relationships between blood cell traits and IBDs, as demonstrated in our clinical observational study. Together, these findings could shed light on the clinical strategies applied to the management of CD and UC.

A Bayesian spatio-temporal model of COVID-19 spread in England

Exploring the spatio-temporal variations of COVID-19 transmission and its potential determinants could provide a deeper understanding of the dynamics of disease spread. This study aimed to investigate the spatio-temporal spread of COVID-19 infections in England, and examine its associations with socioeconomic, demographic and environmental risk factors. We obtained weekly reported COVID-19 cases from 7 March 2020 to 26 March 2022 at Middle Layer Super Output Area (MSOA) level in mainland England from publicly available datasets. With these data, we conducted an ecological study to predict the COVID-19 infection risk and identify its associations with socioeconomic, demographic and environmental risk factors using a Bayesian hierarchical spatio-temporal model. The Bayesian model outperformed the ordinary least squares model and geographically weighted regression model in terms of prediction accuracy. The spread of COVID-19 infections over space and time was heterogeneous. Hotspots of infection risk exhibited inconsistent clustering patterns over time. Risk factors found to be positively associated with COVID-19 infection risk were: annual household income [relative risk (RR) = 1.0008, 95% Credible Interval (CI) 1.0005–1.0012], unemployment rate [RR = 1.0027, 95% CI 1.0024–1.0030], population density on the log scale [RR = 1.0146, 95% CI 1.0129–1.0164], percentage of Caribbean population [RR = 1.0022, 95% CI 1.0009–1.0036], percentage of adults aged 45–64 years old [RR = 1.0031, 95% CI 1.0024–1.0039], and particulate matter (PM2.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {PM}_{2.5}$$\\end{document}) concentrations [RR = 1.0126, 95% CI 1.0083–1.0167]. The study highlights the importance of considering socioeconomic, demographic, and environmental factors in analysing the spatio-temporal variations of COVID-19 infections in England. The findings could assist policymakers in developing tailored public health interventions at a localised level.

Fecal calprotectin and platelet count predict histologic disease activity in pediatric ulcerative colitis: results from a projection-predictive feature selection.

Especially for pediatric patients, proxies of mucosal inflammation are needed. The Pediatric Ulcerative Colitis Activity Index (PUCAI) has been established to predict clinical and endoscopic disease activity. However, histologic inflammation might persist. We applied a special variable selection technique to predict histologic healing in pediatric ulcerative colitis (UC) as parsimoniously (but still as precisely) as possible. The retrospective analysis included data from two study cohorts, comprising 91 visits from 59 pediatric patients with UC. A Bayesian ordinal regression model was used in combination with a projection-predictive feature selection (PPFS) to identify a minimal subset of clinical and laboratory parameters sufficient for the prediction of histologic disease activity. Following the PPFS, CEDATA-GPGE patient registry data were analyzed to investigate the relevance of the selected predictors in relation to PUCAI and Physician Global Assessment (PGA) in up to 6697 patient visits. Fecal calprotectin (FC) and platelet count were identified as the minimal subset of predictors sufficient for prediction of histologic disease activity in pediatric UC. FC and platelet count also appeared to be associated with increasing disease activity as measured by PUCAI and PGA in the CEDATA-GPGE registry. Based on the selected model, predictions can be performed with a Shiny web app. Conclusion: Our statistical approach constitutes a reproducible and objective tool to select a minimal subset of the most informative parameters to predict histologic inflammation in pediatric UC. A Shiny app shows how physicians may predict the histologic activity in a user-friendly way using FC and platelet count. To generalize the findings, further prospective studies will be needed. What is Known: • Histologic healing is a major endpoint in the therapy of ulcerative colitis (UC). • The PUCAI score has been established to predict disease activity in pediatric UC but is not suitable for the prediction of histologic healing. What is New: • Our Bayesian ordinal regression model in combination with a projection-predictive feature selection is a reproducible and objective tool to select the minimal subset of clinical and laboratory parameters to predict histologic inflammation in pediatric UC. • Histologic inflammation in pediatric UC can be non-invasively predicted based on the combination of fecal calprotectin levels and platelet count.

A deep learning method for comparing Bayesian hierarchical models.

Bayesian model comparison (BMC) offers a principled approach to assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Reservoir temperature prediction based on characterization of water chemistry data—case study of western Anatolia, Turkey

Reservoir temperature estimation is crucial for geothermal studies, but traditional methods are complex and uncertain. To address this, we collected 83 sets of water chemistry and reservoir temperature data and applied four machine learning algorithms. These models considered various input factors and underwent data preprocessing steps like null value imputation, normalization, and Pearson coefficient calculation. Cross-validation addressed data volume issues, and performance metrics were used for model evaluation. The results revealed that our machine learning models outperformed traditional fluid geothermometers. All machine learning models surpassed traditional methods. The XGBoost model, based on the F-3 combination, demonstrated the best prediction accuracy with an R2 of 0.9732, while the Bayesian ridge regression model using the F-4 combination had the lowest performance with an R2 of 0.8302. This study highlights the potential of machine learning for accurate reservoir temperature prediction, offering geothermal professionals a reliable tool for model selection and advancing our understanding of geothermal resources.

A Bayesian Spatio-Temporal Modeling Approach to the Inverse Heat Conduction Problem

Abstract A wide range of science and engineering problems involve inferring the system behavior and physical models from indirect observations. These are known as inverse problems. Unlike forward problems (predictive models), inverse problems are difficult to solve due to ill-posedness arising from one or more of non-existence, non-uniqueness (existence of many solutions), or instability (small perturbations in the measurements emerging from noise could lead to large changes in the solution). Therefore, direct inversion of the inverse problem in complex real-world systems is impractical. Several modeling approaches have been developed and adopted in the literature. However, the existing approaches do not consider spatio-temporal relationships. Meanwhile, various real systems and processes exist whose inverse problems can be comfortably modeled using spatio-temporal modeling techniques. We present a spatio-temporal inverse model considering interaction effects for modeling this type of inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the parameter of interest. Finally, we evaluate the proposed methodology through case studies on a 1D heat simulation and pool boiling experiment, using multi-sensor thermocouple measurements to reconstruct heat flux. Compared to the conventional methods, the proposed method performs better and can be adopted for solving inverse heat conduction problems. Moreover, incorporating the spatio-temporal interaction term notably improved the model's performance.

Major axes of variation in tree demography across global forests

The future trajectory of global forests is closely intertwined with tree demography, and a major fundamental goal in ecology is to understand the key mechanisms governing spatio‐temporal patterns in tree population dynamics. While previous research has made substantial progress in identifying the mechanisms individually, their relative importance among forests remains unclear mainly due to practical limitations. One approach to overcome these limitations is to group mechanisms according to their shared effects on the variability of tree vital rates and quantify patterns therein. We developed a conceptual and statistical framework (variance partitioning of Bayesian multilevel models) that attributes the variability in tree growth, mortality, and recruitment to variation in species, space, and time, and their interactions – categories we refer to as organising principles (OPs). We applied the framework to data from 21 forest plots covering more than 2.9 million trees of approximately 6500 species. We found that differences among species, the species OP, proved a major source of variability in tree vital rates, explaining 28–33% of demographic variance alone, and 14–17% in interaction with space, totalling 40–43%. Our results support the hypothesis that the range of vital rates is similar across global forests. However, the average variability among species declined with species richness, indicating that diverse forests featured smaller interspecific differences in vital rates. Moreover, decomposing the variance in vital rates into the proposed OPs showed the importance of unexplained variability, which includes individual variation, in tree demography. A focus on how demographic variance is organized in forests can facilitate the construction of more targeted models with clearer expectations of which covariates might drive a vital rate. This study therefore highlights the most promising avenues for future research, both in terms of understanding the relative contributions of groups of mechanisms to forest demography and diversity, and for improving projections of forest ecosystems.