Laplace Approximation Research Articles

Bayesian Seismic Inversion with Implicit Neural Representations

Abstract Seismic inversion translates seismic data into subsurface elastic property models, enabling geophysicists to better understand underground rocks and fluids. Due to the inherently ill-posed nature of this inverse problem, accurately capturing the uncertainty associated with the solution is essential for reliable interpretations. Traditional Bayesian inversion methods, such as Markov Chain Monte Carlo (MCMC) and Laplace approximations, have been employed for this purpose but face significant limitations in terms of scalability and computational efficiency for large-scale problems. Combined with deep learning, Variational Inference (VI) has emerged as a promising alternative, striking a balance between computational efficiency and flexibility (i.e. the ability to approximate complex posterior distributions). However, selecting an appropriate proposal distribution remains a key challenge, as it directly influences the quality of the estimated posterior distribution. In this study, we extend IntraSeismic, an implicit neural representation (INR)-based framework for seismic inversion applications, to Bayesian inversion using VI with different parameterizations of the proposal distribution. We introduce two methods: B-IntraSeismic (BIS), which uses a mean-field Gaussian proposal, and B-IntraSeismic with Conditional Normalizing Flows (BIS-Flow), which utilizes a mean-field unparameterized proposal distribution to better capture deviations from Gaussianity in the posterior distribution. These methods are evaluated on a synthetic dataset (Marmousi) and two field data (Volve and Sleipner). Our results indicate that both BIS and BIS-Flow can accurately capture structural details and produce high-resolution mean models and standard deviation maps. BIS-Flow is also shown to be able to model complex posterior distributions, offering a more comprehensive characterization of uncertainty while maintaining computational feasibility.

The demise of the world's largest piedmont glacier: a probabilistic forecast

Abstract. Sít' Tlein, located in the St. Elias Range, which straddles Alaska's Wrangell–St. Elias National Park and Kluane National Park in the Yukon, is the world's largest piedmont glacier. Sít' Tlein has thinned considerably over 30 years of altimetry, yet its low-elevation piedmont lobe has remained intact in contrast to the glaciers that once filled neighboring Icy and Disenchantment bays. In an effort to forecast changes to Sít' Tlein over decadal to centennial timescales, we take a data-constrained dynamical modeling approach in which we infer the parameters of a higher-order model of ice flow – the bed elevation, basal traction, and surface mass balance – with a diverse but spatiotemporally sparse set of observations including satellite-derived, time-varying velocity fields; radar-derived bed and surface elevation measurements; and in situ and remotely sensed observations of accumulation and ablation. Nonetheless, such data do not uniquely constrain model behavior, so we adopt an approximate Bayesian approach based on the Laplace approximation and facilitated by low-rank parametric representations to quantify uncertainty in the bed, traction, and mass balance fields alongside the induced uncertainty in model-based predictions of glacier change. We find that Sít' Tlein is considerably out of balance with contemporary (and presumably future) climate, and we expect its piedmont lobe to largely disappear over the coming centuries. If warming ceases, and surface mass balance remains at 2023 levels, then by 2073 (2173) we forecast a mass loss (expressed in terms of 95 % credible interval) of 323–444 km3 (546–728 km3). If instead surface mass balance continues to change at the same rate as inferred over the historical period, then we forecast a 2073 (2173) mass loss of 383–505 km3 (740–900 km3). In either case, the resulting retreat and subsequent replacement of glacier ice with a marine embayment or lake will yield a significant modification to the regional landscape and ecosystem.

Burden of knee osteoarthritis in China and globally: 1990–2045

BackgroundKnee osteoarthritis (KOA) is a major global health challenge, with rising prevalence, incidence, and disability-adjusted life years (DALYs). This disease increasingly burdens healthcare systems worldwide, particularly as populations age and obesity rates rise. In China, the rapid demographic shift towards an aging population, combined with rising obesity rates, makes KOA a pressing public health issue. China is projected to experience a significant increase in the number of elderly individuals, who are particularly vulnerable to KOA. Additionally, gender disparities, with women being more affected, add further urgency. Addressing KOA in China requires targeted healthcare strategies, considering these unique demographic and lifestyle factors.MethodsWe utilized data from the Global Burden of Disease (GBD) 2021 database to assess the prevalence, incidence, and DALYs related to KOA both globally and in China. The decomposition analysis was used to evaluate the contributions of population aging, growth, and epidemiological changes. For prediction, we employed the Bayesian Age-Period-Cohort (BAPC) model, implemented using the Integrated Nested Laplace Approximation (INLA) method, to project future trends from 2022 to 2045.ResultsFrom 1990 to 2021, both China and globally experienced significant increases in the burden of KOA. In China, the age-standardized prevalence rate (ASPR) increased from 4,667.29 (95% UI: 3,996.06–5,359.85) per 100,000 in 1990 to 5,016.52 (95% UI: 4,265.22–5,758.38) per 100,000 in 2021. Globally, the ASPR rose from 3,964.75 (95% UI: 3,411.86–4,536.4) per 100,000 in 1990 to 4,294.27 (95% UI: 3,695.04–4,910.76) per 100,000 in 2021. Similarly, the age-standardized incidence rate (ASIR) in China increased from 377.93 (95% UI: 324.79–434.28) per 100,000 in 1990 to 406.42 (95% UI: 348.7–467.23) per 100,000 in 2021, compared to a global increase from 330.26 (95% UI: 284.34–375.75) to 353.67 (95% UI: 304.56–402.5). The age-standardized DALY rate (ASDR) in China rose from 151.24 (95% UI: 72.96–291.47) per 100,000 in 1990 to 162.44 (95% UI: 78.35–314.13) per 100,000 in 2021, whereas the global ASDR rose from 127.14 (95% UI: 62.17–246.99) per 100,000 in 1990 to 137.59 (95% UI: 67.08–266.87) per 100,000 in 2021. The prevalence, incidence, and DALYs of KOA were consistently higher in females compared to males. In both regions, population growth had the most significant impact on KOA burden, but population aging was a more significant factor in China. High BMI and metabolic risk factors, particularly in females, were identified as key contributors to KOA-related DALYs. This study projects the trends in knee osteoarthritis (KOA) burden in China and globally by 2045. In China, the Age-Standardized Prevalence Rate (ASPR) is projected to increase by approximately 2.5% (from 5016.52 to 5142.90), while the Age-Standardized Incidence Rate (ASIR) is expected to decrease by about 8.8% (from 406.43 to 370.72). Globally, the ASPR is expected to rise by around 7.8% (from 4294.26 to 4630.97), while the ASIR is projected to increase by 5.8% (from 353.67 to 374.13). The Age-Standardized Death Rate (ASDR) is expected to increase in both China (by 1.3%, from 162.44 to 164.61) and globally (by 5.7%, from 137.59 to 145.45). These projections suggest an overall rise in the burden of KOA, with regional variations.ConclusionKOA remains a significant and increasingly complex global health challenge, with its burden expected to rise sharply in the coming decades. This study highlights that in both China and globally, the escalating prevalence of KOA is closely linked to population aging and obesity, but the drivers vary across regions. In China, the rising burden is predominantly influenced by demographic aging, making it critical to develop targeted interventions that address the needs of an aging population. Globally, the expansion of the population is the primary contributor to the increased KOA burden, which underscores the importance of integrating KOA prevention into broader public health strategies aimed at managing population growth and associated lifestyle risks. The findings underscore the urgency of addressing obesity as a key risk factor for KOA, especially in women. Public health interventions should focus on obesity prevention, particularly in middle-aged and older populations, and include strategies such as promoting healthier diets, physical activity, and metabolic health management. Furthermore, policies aimed at improving joint health in aging populations, with a focus on early diagnosis and rehabilitation, could significantly alleviate the long-term societal and healthcare costs associated with KOA.

EXPLORING FACTORS INFLUENCING AVERAGE CALL NUMBERS IN OWL NESTLINGS: A GENERALIZED LINEAR MIXED MODEL STRUCTURE WITH LAPLACE APPROXIMATION AND ADAPTIVE GAUSSIAN-HERMITE QUADRATURE METHOD

Understanding the factors that influence the begging behavior of owl nestlings (or chicks) is critical for elucidating parent-offspring communication and resource allocation strategies. This study examines the average call numbers of owl nestlings, focusing on the effects of brood size, food treatment, and parental arrival time. Since the data conform to a Poisson distribution, it employs a generalized linear mixed model (GLMM) framework that incorporates both fixed and random effects to account for variability at the individual and nest levels. Laplace approximation and Adaptive Gaussian-Hermite Quadrature (AGHQ) method enhance the precision of parameter estimation. The results demonstrate significant interactions between brood size and food treatment, highlighting the adaptive nature of begging calls in response to parental provisioning strategies. The findings emphasize the importance of advanced statistical methodologies, such as GLMM with Laplace and AGHQ, in studying complex ecological behaviors. This approach provides a robust framework for ongoing research into the dynamics of avian communication and parental investment.

Global, regional, and national burden of older adults peripheral nervous system tumors (1990-2021): a systematic analysis of incidence, dalys, and deaths with projections to 2050.

Peripheral nervous system tumors are abnormal proliferations originating from neural tissues (such as the nerve sheath and nerve fibers), classified as either benign or malignant. Common subtypes encompass schwannomas, neurofibromas, and malignant peripheral nerve sheath tumors. Notably, malignant peripheral nerve sheath tumors are characterized by their high malignancy potential and have demonstrated a concerning rise in both incidence and mortality rates in recent epidemiological studies. Based on the Global Burden of Disease (GBD) 2021 database, we conducted a statistical analysis of the trends of incidence, disability-adjusted life years (DALYs) per 100,100 population along with 95% uncertainty intervals(UIs), as well as deaths among adults aged 70years and older from 1990 to 2021 in peripheral nervous system tumors. The date were subjected to stratified analyses across age, sex, socio-demographic index (SDI), 21 regions, and 204 countries. A Bayesian age- period- cohort (BAPC) model incorporating integrated nested Laplace approximations was applied to forecast the disease burden up to 2050. On a global scale, all stratified analyses demonstrated a consistent trajectory trend in incidence, DALYs, and deaths among older adults, with projections indicating this trend is likely to persist until 2050. Over the past three decades (1990-2021), the incidence rates of peripheral nervous system tumors have risen by 185%, with disability-adjusted life years (DALYs) rates increasing by 164% and deaths rates climbing by 167%. Notably, high SDI regions exhibited declining trends in incidence rates (-10.1%), DALYs rates (-14.3%), and mortality rates (-11.6%) after 2003, low- and middle SDI regions maintained annual increases. A significant gender reversal occurred in 2021, where male incidence numbers, DALYs and deaths numbers surpassed female rates. Bayesian age-period-cohort (BAPC) modelling predicts a 2.0-fold increase in ASIR by 2050 relative to 2021 levels, with DALY and mortality burdens projected to rise 2.2-fold and 1.8-fold respectively under current trajectories. The analysis results revealed that there were pronounced disparities across SDI regions, with high-middle SDI regions shouldering the greatest burden. These findings underscore the urgent need for region-specific prevention and control strategies to address the growing epidemiological and socioeconomic impacts of these malignancies in aging populations.

Bus-exposure matrix, a tool to assess bus drivers' exposure to physicochemical hazards.

Bus-exposure matrix, a tool to assess bus drivers' exposure to physicochemical hazards.

Interpretation of the connotation of Article 33 of the “Law on the Application of Law to Foreign-Related Civil Relations”: “Validity of Wills” - An empirical study based on 50 judgment documents

Article 33 of the Law on the Application of Law in Foreign-Related Civil Relations stipulates the applicable law for determining the validity of foreign-related wills. This paper conducts a comparative analysis of the conceptual differences in defining “testamentary validity” between domestic and foreign-related legal contexts in China. It finds that, in judicial practice, the requirements for the validity of wills in foreign-related civil law are ambiguously defined and overly broad in scope. Specifically, the concept of “testamentary validity” not only includes general elements such as formal requirements, the testator’s legal capacity, genuine intention and the legality of the will’s content but also extends to matters of testamentary succession, including the revocation, amendment and specific provisions of the will. In addressing certain foreign-related testamentary succession disputes, China faces a lack of legal provisions and has to turn to the Article 33. The root cause lies in the inherent deficiencies of China’s dual succession legal system. To address this issue, I propose two approaches for improvement: firstly, fundamentally restructuring the system into an “inheritance-will” model; and secondly, refining the rules of testamentary succession by introducing specialized provisions for matters not currently regulated by law. These measures aim to ensure the legality, reasonableness and fairness of foreign-related judicial adjudication.

Characterization and prediction of non-melanoma skin cancer incidence in China: Joinpoint regression and age-period-cohort model.

Understanding the non-melanoma skin cancer (NMSC) incidence and its trends in China is an important prerequisite for effective prevention and control of NMSC. NMSC incidence data was collected from the Annual Report of China Cancer Registry from 2005 to 2018. The Joinpoint regression model was used to estimate the average annual percent change (AAPC) and annual percent change (APC) to reflect the time trend. Age-period-cohort model with the intrinsic estimator algorithm was used to analyze age, period, and cohort effects. Bayesian age-period-cohort (BAPC) model with integrated nested laplace approximation was used for prediction. The age-standardized incidence rate (ASIR) of NMSC increased from 1.02/ 100,000 to 1.63/100,000 from 2005 to 2018, showing an increasing trend with AAPC of 3.7% (95% CI: 2.5%, 4.9%). The ASIR was higher in men than in women, while the increase rate was reversed, and it was lower in rural than in urban areas, while AAPC was 1.15 times higher. The risk of NMSC incidence increased with age. The cohort effect was first to increase and then to decrease and the inflection point appeared in 1930-1934. The ASIR of NMSC in China will continue to rise during 2019-2035. The ASIR of NMSC in China from 2005 to 2018 showed an increasing trend with age, gender, and regional differences, and will continue to increase in the future. NMSC remains a public health problem and requires continuous attention.

Characterization and prediction of non-melanoma skin cancer incidence in China: Joinpoint regression and age-period-cohort model

ObjectiveUnderstanding the non-melanoma skin cancer (NMSC) incidence and its trends in China is an important prerequisite for effective prevention and control of NMSC.MethodsNMSC incidence data was collected from the Annual Report of China Cancer Registry from 2005 to 2018. The Joinpoint regression model was used to estimate the average annual percent change (AAPC) and annual percent change (APC) to reflect the time trend. Age-period-cohort model with the intrinsic estimator algorithm was used to analyze age, period, and cohort effects. Bayesian age-period-cohort (BAPC) model with integrated nested laplace approximation was used for prediction.ResultsThe age-standardized incidence rate (ASIR) of NMSC increased from 1.02/ 100,000 to 1.63/100,000 from 2005 to 2018, showing an increasing trend with AAPC of 3.7% (95% CI: 2.5%, 4.9%). The ASIR was higher in men than in women, while the increase rate was reversed, and it was lower in rural than in urban areas, while AAPC was 1.15 times higher. The risk of NMSC incidence increased with age. The cohort effect was first to increase and then to decrease and the inflection point appeared in 1930-1934. The ASIR of NMSC in China will continue to rise during 2019-2035.ConclusionThe ASIR of NMSC in China from 2005 to 2018 showed an increasing trend with age, gender, and regional differences, and will continue to increase in the future. NMSC remains a public health problem and requires continuous attention.

An intelligent intrusion detection approach utilizing kernel-driven deep neural architectures for securing Internet of Things (IoT) infrastructure

ABSTRACT The Internet of Things provides advent services to people by sensing intelligent devices to perform real-time functionalities. The divergence of IoT offers enormous benefits to human society by node cooperation. Moreover, selecting reliable nodes for communication is essential, and the malicious nodes have to be identified. An innovative link-based mechanism for intrusion prediction employs the Kernel-based Deep Neural Model ( k -DNM) which includes the kernel functionality of a linear Support Vector Machine for pattern analysis and adaptive fuzzy rules (successive rules are generated for network weight analysis) for labeling and identification of lightweight linkage nodes. The proposed methodology uses topological analysis with improved generalization capacity to help forecast the network patterns. The pattern flow is measured for future research. In the MATLAB 2020a environment simulation is performed. The projected k -DNM model performs better than the six traditional methods by adopting a benchmark dataset for investigation. The detection rate is enhanced averagely by adopting k -DNM. This approach improves linkage connectivity to enable subsequent linking processes to be more effective and attain the goal in a unique way. An attack disturbs the community of linking nodes when it gets affected. By preserving higher energy efficiency while improving network resilience, the suggested k-DNM performs better than the current methods.

Geospatial analysis of immunisation outcomes in Nigeria using a Bayesian geostatistical approach and an interactive dashboard

BackgroundNigeria’s significant contribution to the global pool of zero-dose children persists despite ongoing immunisation investments. This coverage deficits in Kano and Lagos states serve as stark indicators of underlying structural and socio-economic obstacles hindering equitable immunisation access at the sub-national level.MethodsTo investigate these barriers, localised secondary data from various sources were collected including data from the State Routine Immunisation (RI) microplans, demographic and health survey data, supportive supervision data, immunisation coverage survey data, administrative data from health management information systems (HMIS), and vaccine security and logistics data to study the structural determinants of zero dose children and missed communities. This data was then visualised in an interactive geospatial dashboard deployed in Tableau to visualise and interpret key immunisation metrics. Using the Stochastic Partial Differential Equation (SPDE) approach in R Interface to Integrated Nested Laplace Approximations (R-INLA), a geostatistical model was developed to predict immunisation outcomes based on structural determinants identified from the literature.ResultsFindings show that in Kano state, urban health facilities are 39% (OR = 0.609, 95% CI: 0.406–0.906) less likely to have zero-dose children compared to rural ones with less significant impact of the type of settlement on under-immunisation (OR = 1.146. 95% CI: 0.724–1.869). In Lagos state, the distinction between urban and rural settings does not significantly impact zero-dose (OR = 2.117, 95% CI:0.473–10.001) or under-immunisation rates (OR = 1.136, 95% CI:0.300–4.722).ConclusionLocalised triangulation analysis of data from the two states demonstrates complex interaction between different structural determinants of immunisation outcomes. These findings emphasise the need to prioritise localised analysis of available data and invest in capacity for data analysis at lower levels of the health system, to enable the use of available data for decision-making and action.

Spatiotemporal impact of urban development on nighttime light intensity and its hotspot distribution.

Nighttime light (NTL) data serve as a valuable proxy for accessing urbanization and socio-economic activities at various scales. This study investigated the spatiotemporal evolution of NTL intensity in Taipei City from January 2018 to June 2023 using data from the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) via the Google Earth Engine (GEE) platform. A grid system comprising 1,211 cells (500-m resolution) was established to integrate land use, road networks, population, electricity consumption, and business prosperity into temporal, spatial, and spatiotemporal models using Integrated Nested Laplace Approximations (INLA). Additionally, spatiotemporal patterns were analyzed through the space-time cube in ArcGIS Pro. This finding highlights the strong influence of commercial activities and electricity consumption on NTL intensity, with persistent hotspots in commercial and industrial areas and cold spots in forested and agricultural zones. This study underscores the potential of NTL data to capture the interplay between urbanization, land use, and socioeconomic factors. Emphasizing land use as a central analytical focus provides a scalable framework for future urban studies and policy development that can be applied to diverse urban contexts.

Global, regional, and national burden of acute leukemia and its risk factors from 1990 to 2021 and predictions to 2040: findings from the global burden of disease study 2021

BackgroundDespite therapeutic advances, acute leukemia (AL) continues to impose a substantial global health burden, with persistently high incidence and mortality rates. Notably, the prediction is that the number of incidence and mortality of acute myeloid leukemia (AML) cases will continue to increase to 184,287.88 and 165,537.59, respectively, by 2040. Using Global Burden of Disease Study (GBD) 2021 data, we assessed the worldwide AL burden from 1990 to 2021, analyzing trends by sex to inform public health strategies. MethodsTo delineate the burden of AL, we reported incidence, prevalence, mortality, and disability-adjusted life year (DALY) rates at global, regional, and national levels, with these estimates including age-standardized rates (ASRs) per 100,000 population and average annual percentage changes (AAPCs) from 1990 to 2021 which were stratified by age, sex, and socio-demographic index (SDI), and computed ASRs and AAPCs using linear regression. Temporal trends were analyzed using an age-period-cohort (APC) model with intrinsic estimation (principal component regression). Risk factor attribution quantified contributions of 21 behavioral, environmental, and metabolic exposures to AL-related DALYs. For inequality assessment, we applied the Slope Index of Inequality and Concentration Index to evaluate absolute and relative disparities in AL burden across regions and countries. Future projections (2040) were modeled via a Bayesian APC framework with Integrated Nested Laplace Approximation. All statistical analyses were performed using R software (version R 4.4.1). The GATHER (Guidelines for Accurate and Transparent Health Estimates Reporting) statement provides a framework to ensure the transparency, reproducibility, and quality of health estimates reporting. ResultsBetween 1990 and 2021, global ASRs of AL declined, except for acute lymphoblastic leukemia (ALL) age-standardized prevalence rates (ASPR) (AAPC 0.84, 95% CI 0.59-1.10). Case numbers rose overall, though ALL mortality and DALYs decreased. AML burden correlated positively with SDI (ρ > 0, P < 0.001), with the highest number of incident and mortality cases in Western Europe. For ALL, SDI showed positive associations with ASIR and ASPR (ρ > 0, P < 0.001) but negative correlations with ASMR and ASDALR (ρ < 0, P < 0.001), with East Asia being the most severely affected region. High body mass index (BMI), smoking, and benzene/formaldehyde exposure were key AL DALY risk factors. High BMI and smoking predominate in developed countries, and the proportion of DALYs decreases progressively as SDI decreases. Occupational exposures prevailed in developing countries. Population growth drove most absolute increases. Males bore a greater AL burden. AML risk rose with age, whereas ALL displayed bimodal peaks (< 5 and > 40 years). Notably, while ASRs in AL are projected to decline slightly and the number of ALL to decrease by 2040, the number of AML is expected to increase, with the number of incidence and mortality cases increasing by 41.56% and 27.16%, respectively.ConclusionAs a major public health concern, despite declining ALL-related mortality and DALYs (1990–2021), AL remains a growing global health challenge, with AML cases projected to rise significantly by 2040. Region-specific intervention strategies are required: high-SDI nations should prioritize smoking cessation and metabolic control to address smoking and high BMI-related AML risks while preparing for aging populations, whereas low/middle-SDI countries urgently need enhanced pediatric ALL diagnosis, treatment capacity, and occupational safety measures. Effective mitigation demands evidence-based health planning, including resource allocation guided by projected AL burden trends and targeted policy interventions to reduce healthcare disparities.

Trends and burden of gout among adolescents aged 10–24 years: insights from the global burden of disease study 2021

BackgroundGout increasingly affects adolescents. However, comprehensive data on adolescent gout are scarce. This study aimed to analyse the incidence, prevalence, years lived with disability (YLDs), and risk factors for gout in adolescents aged 10–24 years via the Global Burden of Disease (GBD) database from 1990 to 2021.MethodsThis study employed cross-sectional data from the GBD 2021 study in adolescents aged 10–24 years. The incidence, prevalence, YLD, and risk factor rates or numbers for gout were extracted, and trends across different sociodemographic index (SDI) levels and exponential annualized percentage change (EAPC) rates were analysed via linear regression analysis. Bayesian age-period-cohot (BAPC) model with an integrated nested Laplace approximation to predict the age-standardized incidence rate of gout among adolescents over the next 15 years in Global, China, Taiwan (Province of China), Qatar, and Maldives.ResultsThe global incidence number of gout in adolescents increased by 23.47% (95% CI 21.66 to 25.92) from 1990 to 2021; by 2021, the incidence number of gout was 110664.59 (95% UI 62543.83 to 163447.37). High BMI was the leading risk factor for YLD. The higher the SDI is, the greater the incidence of gout and the greater the disease burden in adolescents. Taiwan (Province of China) had the highest rates in 2021, and an increasing trend is predicted by 2035.ConclusionAdolescent gout is an escalating global health issue, particularly in regions with increasing age-standardized incidence rates. Urgent dietary and weight interventions are recommended to reduce the disease burden in adolescents.

Impacts of ENSO on Spatiotemporal Variability of Rainfall and Crop Yield in the Agricultural Frontier of the Pampas, Argentina

Abstract Transitional climate zones between humid and semiarid regions are particularly vulnerable to climate change. Agricultural expansion in these zones over recent decades poses high risks for environmental degradation. The Pampean region in South America, a leading global agricultural area, faces productivity impacts from climate change and the El Niño–Southern Oscillation (ENSO) phenomenon, especially in the semiarid frontier. Our study aimed to (i) explore the associations between precipitation and crop yields over recent decades at a fine spatial scale and (ii) develop a spatiotemporal model of precipitation and its relationship with a quantitative multivariate ENSO index (MEI). We used monthly precipitation data from 74 rain gauges and crop yield data at the departmental level from 1965 to 2014. The relationship between MEI and precipitation was estimated using a Bayesian technique for mixed models [integrated nested Laplace approximation (INLA)]. The average correlations between yield and precipitation were moderate (0.41–0.47) with spatial variations among crops. Wheat showed the highest number of significant correlations (94%) with annual precipitation, reaching coefficients of 0.65. Sunflower showed correlations in fewer southern departments (60%), while maize and sorghum correlated better with growing season precipitation (September–March) and a higher number of departments (73%–87%). The MEI-estimated coefficient obtained from the spatiotemporal INLA model was 38 mm (24–58 mm) for growing season precipitation. Interpolated precipitation maps revealed a regional pattern following a southwest-to-northeast gradient. However, this pattern exhibited variability and inconsistency across different years and ENSO phases, underscoring the influence of random effects.

Dynamic causal modelling in probabilistic programming languages.

Understanding the intricate dynamics of brain activities necessitates models that incorporate causality and nonlinearity. Dynamic causal modelling (DCM) presents a statistical framework that embraces causal relationships among brain regions and their responses to experimental manipulations, such as stimulation. In this study, we perform Bayesian inference on a neurobiologically plausible generative model that simulates event-related potentials observed in magneto/encephalography data. This translates into probabilistic inference of latent and observed states of a system driven by input stimuli, described by a set of nonlinear ordinary differential equations (ODEs) and potentially correlated parameters. We provide a guideline for reliable inference in the presence of multimodality, which arises from parameter degeneracy, ultimately enhancing the predictive accuracy of neural dynamics. Solutions include optimizing the hyperparameters, leveraging initialization with prior information and employing weighted stacking based on predictive accuracy. Moreover, we implement the inference and conduct comprehensive model comparison in several probabilistic programming languages to streamline the process and benchmark their efficiency. Our investigation shows that model inversion in DCM extends beyond variational approximation frameworks, demonstrating the effectiveness of gradient-based Markov chain Monte Carlo methods. We illustrate the accuracy and efficiency of posterior estimation using a self-tuning variant of Hamiltonian Monte Carlo and the automatic Laplace approximation, effectively addressing parameter degeneracy challenges. This technical endeavour holds the potential to advance the inversion of state-space ODE models, and contribute to neuroscience research and applications in neuroimaging through automatic DCM.

Kernel generalized least squares regression for network-structured data.

In this paper, we study a class of non-parametric regression models for predicting graph signals [Formula: see text] as a function of explanatory variables [Formula: see text]. Recently, Kernel Graph Regression (KGR) and Gaussian Processes over Graph (GPoG) have emerged as promising techniques for this task. The goal of this paper is to examine several extensions to KGR/GPoG, with the aim of generalising them a wider variety of data scenarios. The first extension we consider is the case of graph signals that have only been partially recorded, meaning a subset of their elements is missing at observation time. Next, we examine the statistical effect of correlated prediction error and propose a method for Generalized Least Squares (GLS) on graphs. In particular, we examine Autoregressive AR(1) vector autoregressive processes, which are commonly found in time-series applications. Finally, we use the Laplace approximation to determine a lower bound for the out-of-sample prediction error and derive a scalable expression for the marginal variance of each prediction. These methods are tested on both real and synthetic data, with the former taken from a network of air quality monitoring stations across California. We find evidence that the generalised GLS-KGR algorithm is well-suited to such time-series applications, outperforming several standard techniques on this dataset.

Estimation of spatial panel data models with random effects using Laplace approximation methods

ABSTRACT This paper proposes using integrated nested Laplace approximations (INLAs), a full Bayesian approach, for estimating spatial panel data models with random effects. These models encompass Anselin’s model, Kapoor’s model and the generalised spatial random effects model. We show that a spatial autoregressive process in the error terms is a special case of Gaussian Markov random fields (GMRFs), thereby reducing computational costs. The computational benefit is further enhanced through the use of INLAs to compute the posterior marginals of model parameters. Finite sample properties of the INLA-GMRF approach are assessed through comprehensive Monte Carlo simulations. We also compare its computational efficiency with classic estimation methods. Finally, we demonstrate this approach with an empirical study on renewable energy production in China.

Global, regional, and National levels and trends in burden of dental caries and periodontal disease from 1990 to 2035: result from the global burden of disease study 2021

BackgroundThe global burden of dental caries (DC) and periodontal disease (PD) has evolved significantly from 1990 to 2021, influenced by demographic shifts and socioeconomic factors in oral health interventions. This study aims to analyze historical trends, project future trajectories to 2035, and identify inequalities to inform equitable oral health policy development.MethodsUtilizing data from the Global Burden of Disease Study (GBD), which integrates epidemiological records from systematic reviews, survey data preparation, disease registries, and case notifications, we conducted an observational analysis based on historical population-level data from 1990 to 2021.We analyzed the incidence, prevalence, and their corresponding age-standardized incidence rate (ASIR) and age-standardized prevalence rate (ASPR) for caries of deciduous teeth (CDT), caries of permanent teeth (CPT) and periodontal disease (PD). Bayesian age-period-cohort (BAPC) models with Integrated Nested Laplace Approximation (INLA) were employed to forecast trends through 2035, integrating second-order smoothing effects, overdispersion adjustments, and uncertainty quantification via 1,000 Monte Carlo simulations (95% UI) with future precision expressed as 95% confidence intervals (CI).ResultsFrom 1990 to 2021, CDT prevalence declined regionally, while PD remained prevalent, particularly among middle-aged and elderly populations in high-burden regions like Sub-Saharan Africa and Southeast Asia. Significant gender disparities were noted, with females experiencing comparable deciduous DC in early childhood, whereas males showed dominant PD rates in middle/older ages. Low-income regions still face high burdens despite progress. Projections to 2035 suggest a CDT resurgence and aging-driven PD persistence.ConclusionsDC and PD persist as major public health issues, shaped by gender, age, and regional disparities. The projected resurgence of childhood DC and persistent PD prevalence by 2035 underscore the need for targeted interventions. Tailored public health initiatives are essential to mitigate long-term impacts and improve global oral health outcomes.

Macroecological patterns of planktonic unicellular eukaryotes richness in the Southeast Pacific Ocean

In recent years, studies focusing on microbial biogeography have been developed, but macroecological processes in marine microorganisms remain unclear, especially in seemingly continuous environments such as the Southeast Pacific Ocean (SPO), where information on microbial distribution patterns is limited, and they may vary depending on the habitat and lifestyle. We used unicellular planktonic eukaryotes as model organisms to determine their biogeographic patterns in the SPO, identify the underlying ecological and historical-evolutionary processes and compare with other microorganism groups. Our analyses were based on the Niche Theory to model species diversity distribution using large open-access ecological and physical-biogeochemical databases based on Bayesian approaches, an integrated nested Laplace approximation (INLA), and Generalized Additive Models (GAM). As a result, two richness hotspots were observed, which are associated with coastal and offshore regions in the central southern areas of SPO. The richness hotspots were associated mainly with nutrients (N/Si ratio) and Mixed Layer Depth (MLD), which could be explained by highly productive upwelling events in the SPO. In contrast, the negative correlation of predicted richness with low pH is strongly related to the effect of calcareous shells (tests), as lower pH levels hinder the formation and stability of calcium carbonate shells in protists like foraminifera and radiolaria, thereby affecting overall unicellular planktonic eukaryote diversity. Our results support the role of ecological processes related to productivity, energy dynamics, and ecological limits in shaping broad-scale diversity patterns of unicellular planktonic eukaryotes in the SPO. The results show colonization and extinction dynamics through species replacement (i.e. High Turnover) along the Chilean and Equatorial coasts associated mainly with the Hotspots of their biodiversity, but also a gradual species loss (i.e. High Nestedness) along the Peruvian Coast associated mainly with the Coldspots of their biodiversity; highlighting how local environmental fluctuations can shape these planktonic microorganisms’ behavior, ecology and distribution. The distribution patterns of planktonic unicellular eukaryotes show little evidence of the effects of historical and evolutionary processes. This is because the high dispersal capacity of planktonic microbes probably dilutes the influence of these processes in environments lacking clear barriers to species dispersal. Additionally, the effect of historical events could be highlighted in specific taxonomic groups at the kingdom, phylum level or habitat type and addressing gaps about latitudinal richness in the SPO. This provides insight into the spatial distribution of marine microbes and contributes to conservation efforts, as these organisms are an essential foundation of the upper levels of the food web.