Air pollution and children's mental health in rural areas: compositional spatio-temporal model.

Air pollution stands as an environmental risk to child mental health, with proven relationships hitherto observed only in urban areas. Understanding the impact of pollution in rural settings is equally crucial. The novelty of this article lies in the study of the relationship between air pollution and behavioural and developmental disorders, attention deficit hyperactivity disorder (ADHD), anxiety, and eating disorders in children below 15 living in a rural area. The methodology combines spatio-temporal models, Bayesian inference and Compositional Data (CoDa), that make it possible to study areas with few pollution monitoring stations. Exposure to nitrogen dioxide (NO2), ozone (O3), and sulphur dioxide (SO2) is related to behavioural and development disorders, anxiety is related to particulate matter (PM10), O3 and SO2, and overall pollution is associated to ADHD and eating disorders. To sum up, like their urban counterparts, rural children are also subject to mental health risks related to air pollution, and the combination of spatio-temporal models, Bayesian inference and CoDa make it possible to relate mental health problems to pollutant concentrations in rural settings with few monitoring stations. Certain limitations persist related to misclassification of exposure to air pollutants and to the covariables available in the data sources used.

Percutaneous coronary intervention with drug-eluting stents versus coronary bypass surgery for coronary artery disease: a Bayesian perspective.

OBJECTIVES: Coronary revascularization is frequently performed for coronary artery disease (CAD). This study aims to assess the totality of randomized evidence comparing percutaneous coronary intervention with drug-eluting stents (DES-PCI) to coronary artery bypass grafting (CABG) for CAD. METHODS: A systematic search was applied to three electronic databases, including randomized trials comparing DES-PCI to CABG for CAD with 5-year follow-up. A Bayesian hierarchical meta-analytic model was applied. The primary outcome was all-cause mortality at five years; secondary outcomes were stroke, myocardial infarction, and repeat revascularization. Endpoints were reported in median relative risks (RR) and absolute risk differences (ARD), with 95% credible intervals (CrI). Kaplan-Meier curves were used to reconstruct individual patient data. RESULTS: Six studies comprising 8269 patients (DES-PCI n=4134, CABG n=4135) were included. All-cause mortality at 5 years was increased with DES-PCI (median RR 1.23 (95%CrI 1.01-1.45), with a median ARD of +2.3% (95%CrI 0.1-4.5%). For stroke, MI, and repeat revascularization, the median RRs were 0.79 (95%CrI 0.54-1.25), 1.84 (95%CrI 1.23-2.75), and 1.80 (95%CrI 1.51-2.16) for DES-PCI, respectively. In a sample of 1000 patients undergoing DES-PCI instead of CABG for CAD, a median of 23 additional deaths, 46 myocardial infarctions and 85 repeat revascularizations occurred at five years, while 10 strokes were prevented. CONCLUSION: The current data suggests a clinically relevant benefit of CABG over DES-PCI at five years, in terms of mortality, myocardial infarction, and repeat revascularization, despite an increased risk of stroke. These findings may guide the heart-team and the shared decision-making process.

Effects of transcranial direct current stimulation on cognition in MCI with Alzheimer's disease risk factors using Bayesian analysis.

Despite the growing interest in precision medicine-based therapies for Alzheimer's disease (AD), little research has been conducted on how individual AD risk factors influence changes in cognitive function following transcranial direct current stimulation (tDCS). This study evaluates the cognitive effects of sequential tDCS on 63 mild cognitive impairment (MCI) patients, considering AD risk factors such as amyloid-beta deposition, APOE ε4, BDNF polymorphism, and sex. Using both frequentist and Bayesian methods, we assessed the interaction of tDCS with these risk factors on cognitive performance. Notably, we found that amyloid-beta deposition significantly interacted with tDCS in improving executive function, specifically Stroop Word-Color scores, with strong Bayesian support for this finding. Memory enhancements were differentially influenced by BDNF Met carrier status. However, sex and APOE ε4 status did not show significant effects. Our results highlight the importance of individual AD risk factors in modulating cognitive outcomes from tDCS, suggesting that precision medicine may offer more effective tDCS treatments tailored to individual risk profiles in early AD stages.

Association between Combined Metals and PFAS Exposure with Dietary Patterns: A Preliminary Study.

Background: The global burden of chronic diseases has been increasing, with evidence suggesting that diet and exposure to environmental pollutants, such as per- and polyfluoroalkyl substances (PFAS) and heavy metals, may contribute to their development. The Dietary Inflammatory Index (DII) assesses the inflammatory potential of an individual's diet. However, the complex interplay between PFAS, heavy metals, and DII remains largely unexplored. Objective: The goal of this cross-sectional study was to investigate the associations between diet operationalized as the DII with individual and combined lead, cadmium, mercury, perfluorooctanoic acid (PFOA), and perfluorooctanesulfonic acid (PFOS) exposures using data from the National Health and Nutrition Examination Survey (NHANES) 2017-2018. Methods: Descriptive statistics, a correlational analysis, and linear regression were initially used to assess the relationship between the variables of interest. We subsequently employed Bayesian kernel Machine regression (BKMR) to analyze the data to assess the non-linear, non-additive, exposure-response relationships and interactions between PFAS and metals with the DII. Results: The multi-variable linear regression revealed significant associations between the DII and cadmium and mercury. Our BKMR analysis revealed a complex relationship between PFAS, metal exposures, and the DII. In our univariate exposure-response function plot, cadmium and mercury exhibited a positive and negative linear relationship, respectively, which indicated a positive and negative relationship across the spectrum of exposures with the DII. In addition, the bivariate exposure-response function between two exposures in a mixture revealed that cadmium had a robust positive relationship with the DII for different quantiles of lead, mercury, PFOA, and PFOS, indicating that increasing levels of cadmium are associated with the DII. Mercury's bivariate plot demonstrated a negative relationship across all quantiles for all pollutants. Furthermore, the posterior inclusion probability (PIP) results highlighted the consistent importance of cadmium and mercury with the inflammatory potential of an individual's diet, operationalized as the DII in our study, with both showing a PIP of 1.000. This was followed by PFOS with a PIP of 0.8524, PFOA at 0.5924, and lead, which had the lowest impact among the five environmental pollutants, with a PIP of 0.5596. Conclusion: Our study suggests that exposures to environmental metals and PFAS, particularly mercury and cadmium, are associated with DII. These findings also provide evidence of the intricate relationships between PFAS, heavy metals, and the DII. The findings underscore the importance of considering the cumulative effects of multi-pollutant exposures. Future research should focus on elucidating the mechanistic pathways and dose-response relationships underlying these associations in a study that examines causality, which will enable a deeper understanding of the dietary risks associated with environmental pollutants.

A macroevolutionary analysis of European Late Upper Palaeolithic stone tool shape using a Bayesian phylodynamic framework.

Phylogenetic models are commonly used in palaeobiology to study the patterns and processes of organismal evolution. In the human sciences, phylogenetic methods have been deployed for reconstructing ancestor-descendant relationships using linguistic and material culture data. Within evolutionary archaeology specifically, phylogenetic analyses based on maximum parsimony and discrete traits dominate, which sets limitations for the downstream role cultural phylogenies, once derived, can play in more elaborate analytical pipelines. Recent methodological advances in Bayesian phylogenetics, however, now allow us to infer evolutionary dynamics using continuous characters. Capitalizing on these developments, we here present an exploratory analysis of cultural macroevolution of projectile point shape evolution in the European Final Palaeolithic and earliest Mesolithic (approx. 15 000-11 000 BP) using a Bayesian phylodynamic approach and the fossilized birth-death process model. This model-based approach leaps far beyond the application of parsimony, in that it not only produces a tree, but also divergence times, and diversification rates while incorporating uncertainties. This allows us to compare rates to the pronounced climatic changes that occurred during our time frame. While common in cultural evolutionary analyses of language, the extension of Bayesian phylodynamic models to archaeology arguably represents a major methodological breakthrough.

Human reliability analysis in maintenance and repair operations of mining trucks: A Bayesian network approach.

Failures in mining machinery can abruptly halt mineral production and operations, emphasizing the indispensable role of humans in maintenance and repair operations. Addressing human errors is crucial for ensuring a safe and reliable system, particularly during maintenance activities where accidents frequently occur. This paper focuses on evaluating Human Reliability (HR) to enhance activity implementation effectiveness. Given the challenge of limited and uncertain data on human errors, this study aims to estimate the probability of human errors using Bayesian networks (BN) under uncertain parameters. Applying this approach to assess HR in the maintenance and repair operations of mining trucks at Golgohar Iron Ore Mine in Iran, the study identifies critical factors influencing error occurrence in a fuzzy environment. The results highlight key factors impacting human error and offer insights into estimating HR with minimal human intervention.

Effect of combined exposure to phthalates and polycyclic aromatic hydrocarbons during early pregnancy on gestational age and neonatal size: A prospective cohort study.

Many studies have indicated that individual exposure to phthalates (PAEs) or polycyclic aromatic hydrocarbons (PAHs) affects pregnancy outcomes. However, combined exposure to PAEs and PAHs presents a more realistic situation, and research on the combined effects of PAEs and PAHs on gestational age and newborn size is still limited. This study aimed to assess the effects of combined exposure to PAEs and PAHs on neonatal gestational age and birth size. Levels of 9 PAE and 10 PAH metabolites were measured from the urine samples of 1030 women during early pregnancy from the Zunyi Birth Cohort in China. Various statistical models, including linear regression, restricted cubic spline, Bayesian kernel machine regression, and quantile g-computation, were used to study the individual effects, dose-response relationships, and combined effects, respectively. The results of this prospective study revealed that each ten-fold increase in the concentration of monoethyl phthalate (MEP), 2-hydroxynaphthalene (2-OHNap), 2-hydroxyphenanthrene (2-OHPhe), and 1-hydroxypyrene (1-OHPyr) decreased gestational age by 1.033 days (95 % CI: -1.748, -0.319), 0.647 days (95 % CI: -1.076, -0.219), 0.845 days (95 % CI: -1.430, -0.260), and 0.888 days (95 % CI: -1.398, -0.378), respectively. Moreover, when the concentrations of MEP, 2-OHNap, 2-OHPhe, and 1-OHPyr exceeded 0.528, 0.039, 0.012, and 0.002 µg/g Cr, respectively, gestational age decreased in a dose-response manner. Upon analyzing the selected PAE and PAH metabolites as a mixture, we found that they were significantly negatively associated with gestational age, birth weight, and the ponderal index, with 1-OHPyr being the most important contributor. These findings highlight the adverse effects of single and combined exposure to PAEs and PAHs on gestational age. Therefore, future longitudinal cohort studies with larger sample sizes should be conducted across different geographic regions and ethnic groups to confirm the impact of combined exposure to PAEs and PAHs on birth outcomes.

Evaluating the evidence for genotype-informed Bayesian dosing of tacrolimus in children undergoing solid organ transplantation: A systematic literature review.

Tacrolimus, a calcineurin inhibitor, is a highly effective immunosuppressant used in solid organ transplantation (SOT). However, it is characterized by a narrow therapeutic range and high inter-patient variability in pharmacokinetics. Standard weight-based dosing followed by empiric dose titration is suboptimal in controlling drug concentrations, increasing risk of rejection or toxicity, particularly in the initial months post transplantation. This review explores the potential of combined pre-transplant genotyping and pharmacokinetic (PK) modelling to improve tacrolimus dosing in paediatric SOT recipients. A systematic search of Medline, Embase and Cochrane databases identified studies published between March 2013 and March 2023 that investigated genotype- and PK model-informed tacrolimus dosing in children post-SOT. The Newcastle-Ottawa Scale assessed study quality. Seven studies encompassing paediatric kidney, heart, liver and lung transplants reported using genotype and model-informed dosing. A combination of clinical and genetic factors significantly impacts tacrolimus clearance and thus initial dose recommendation. Body size, transplant organ and co-medications were consistently important, while either time post-transplant or haematocrit emerged in some studies. Several models were identified, however, with limitations evident in some and with absence of evidence for their effectiveness in optimizing initial and subsequent dosing. This review highlights the development of PK models in paediatric SOT that integrate genotype and clinical covariates to personalize early tacrolimus dosing. While promising, prospective studies are needed to validate and confirm their effectiveness in improving time to therapeutic concentrations and reducing under- or overexposure. This approach has the potential to optimize tacrolimus therapy in paediatric SOT, thereby improving outcomes.

ROM-based stochastic optimization for a continuous manufacturing process.

This paper proposes a model-based optimization method for the production of automotive seals in an extrusion process. The high production throughput, coupled with quality constraints and the inherent uncertainty of the process, encourages the search for operating conditions that minimize nonconformities. The main uncertainties arise from the process variability and from the raw material itself. The proposed method, which is based on Bayesian optimization, takes these factors into account and obtains a robust set of process parameters. Due to the high computational cost and complexity of performing detailed simulations, a reduced order model is used to address the optimization. The proposal has been evaluated in a virtual environment, where it has been verified that it is able to minimize the impact of process uncertainties. In particular, it would significantly improve the quality of the product without incurring additional costs, achieving a 50% tighter dimensional tolerance compared to a solution obtained by a deterministic optimization algorithm.

Reducing uncertainty in dose-response assessments by incorporating Bayesian benchmark dose modeling and in vitro data on population variability.

There are two primary sources of uncertainty in the interpretability of toxicity values, like the reference dose (RfD): estimates of the point of departure (POD) and the absence of chemical-specific human variability data. We hypothesize two solutions-employing Bayesian benchmark dose (BBMD) modeling to refine POD determination and combining high-throughput toxicokinetic modeling with population-based toxicodynamic in vitro data to characterize chemical-specific variability. These hypotheses were tested by deriving refined probabilistic estimates for human doses corresponding to a specific effect size (M) in the Ith population percentile (HDM I) across 19 Superfund priority chemicals. HDM I values were further converted to biomonitoring equivalents in blood and urine for benchmarking against human data. Compared to deterministic default-based RfDs, HDM I values were generally more protective, particularly influenced by chemical-specific data on interindividual variability. Incorporating chemical-specific in vitro data improved precision in probabilistic RfDs, with a median 1.4-fold reduction in uncertainty variance. Comparison with US Environmental Protection Agency's Exposure Forecasting exposure predictions and biomonitoring data from the National Health and Nutrition Examination Survey identified chemicals with margins of exposure nearing or below one. Overall, to mitigate uncertainty in regulatory toxicity values and guide chemical risk management, BBMD modeling and chemical-specific population-based human in vitro data are essential.

Combined interpretation of objective firearm evidence comparison algorithms using Bayesian networks.

Traditionally, firearm and toolmark examiners manually evaluate the similarity of features on two bullets using comparison microscopy. Advances in microscopy have made it possible to collect 3D topographic data, and several automated comparison algorithms have been introduced for the comparison of bullet striae using these data. In this study, open-source approaches for cross-correlation, congruent matching profile segments, consecutive matching striations, and a random forest model were evaluated. A statistical characterization of these automated approaches was performed using four datasets of consecutively manufactured firearms to provide a challenging comparison scenario. Each automated approach was applied to all samples in a pairwise fashion, and classification performance was compared. Based on these findings, a Bayesian network was empirically learned and constructed to leverage the strengths of each individual approach, model the relationship between the automated results, and combine them into a posterior probability for the given comparison. The network was evaluated similarly to the automated approaches, and the results were compared. The developed Bayesian network classified 99.6% of the samples correctly, and the resultant probability distributions were significantly separated more so than the automated approaches when used in isolation.

Bayesian estimates of genetic parameters for growth traits in Harnali sheep.

The objective of the study was to estimate genetic parameters of the growth traits under Bayesian inference in Harnali sheep. The information of pedigree and targeted traits of 2404 Harnali animals born to 159 sires and 695 dams was collected for the period from 1998 to 2021. The growth traits included weight at birth (BWT), 3 (WWT), 6 (6WT) and 12 (YWT) months of age. The genetic evaluation was carried out using six univariate animal models comprising direct and maternal effects using THRGIBBS1F90 and POSTGIBBSF90 programs. The fixed factors adjusted in the analysis were period of birth, sex of lamb and dam's weight at lambing. Bayesian estimates of direct heritability under best model for BWT, WWT, 6WT and YWT traits were 0.16 ± 0.04, 0.10 ± 0.04, 0.18 ± 0.04, and 0.05 ± 0.03, respectively. The significant maternal influences observed for BWT and WWT traits with 9% and 8% contribution to total phenotypic variances, respectively. Additionally, maternal permanent environmental influences were observed to BWT (4%) and YWT trait (3%). The genetic and phenotypic correlations among studied traits were high and positive. The genetic changes were positive and significant for WWT only. It was concluded that the weight at 6 months of age can be continued as selection criterion for further genetic improvement through selection. Also, maternal effects should be considered in breeding programme for enhancing early growth performance in Harnali sheep.

Hyperparameter optimization: Classics, acceleration, online, multi-objective, and tools.

Hyperparameter optimization (HPO) has been well-developed and evolved into a well-established research topic over the decades. With the success and wide application of deep learning, HPO has garnered increased attention, particularly within the realm of machine learning model training and inference. The primary objective is to mitigate the challenges associated with manual hyperparameter tuning, which can be ad-hoc, reliant on human expertise, and consequently hinders reproducibility while inflating deployment costs. Recognizing the growing significance of HPO, this paper surveyed classical HPO methods, approaches for accelerating the optimization process, HPO in an online setting (dynamic algorithm configuration, DAC), and when there is more than one objective to optimize (multi-objective HPO). Acceleration strategies were categorized into multi-fidelity, bandit-based, and early stopping; DAC algorithms encompassed gradient-based, population-based, and reinforcement learning-based methods; multi-objective HPO can be approached via scalarization, metaheuristics, and model-based algorithms tailored for multi-objective situation. A tabulated overview of popular frameworks and tools for HPO was provided, catering to the interests of practitioners.

Enhancing Periodontal Treatment Through the Integration of Deep Learning-Based Detection with Bayesian Network Models.

This study incorporated deep learning for periodontal disease detection into a Bayesian network (BN) clinical decision support model for comprehensive periodontal care. BN structure and probabilities were based on clinical data and Faster R-CNN-detected radiographic images. Receiver operating characteristic curve analysis confirmed the model's high accuracy in treatment plan recommendations.

Development of a Framework for Establishing 'Gold Standard' Outbreak Data from Submitted SARS-CoV-2 Genome Samples.

Submitted genomic data for respiratory viruses reflect the emergence and spread of new variants. Although delays in submission limit the utility of these data for prospective surveillance, they may be useful for evaluating other surveillance sources. However, few studies have investigated the use of these data for evaluating aberration detection in surveillance systems. Our study used a Bayesian online change point detection algorithm (BOCP) to detect increases in the number of submitted genome samples as a means of establishing 'gold standard' dates of outbreak onset in multiple countries. We compared models using different data transformations and parameter values. BOCP detected change points that were not sensitive to different parameter settings. We also found data transformations were essential prior to change point detection. Our study presents a framework for using global genomic submission data to develop 'gold standard' dates about the onset of outbreaks due to new viral variants.

Neuro-XAI: Explainable deep learning framework based on deeplabV3+ and bayesian optimization for segmentation and classification of brain tumor in MRI scans.

The prevalence of brain tumor disorders is currently a global issue. In general, radiography, which includes a large number of images, is an efficient method for diagnosing these life-threatening disorders. The biggest issue in this area is that it takes a radiologist a long time and is physically strenuous to look at all the images. As a result, research into developing systems based on machine learning to assist radiologists in diagnosis continues to rise daily. Convolutional neural networks (CNNs), one type of deep learning approach, have been pivotal in achieving state-of-the-art results in several medical imaging applications, including the identification of brain tumors. CNN hyperparameters are typically set manually for segmentation and classification, which might take a while and increase the chance of using suboptimal hyperparameters for both tasks. Bayesian optimization is a useful method for updating the deep CNN's optimal hyperparameters. The CNN network, however, can be considered a "black box" model because of how difficult it is to comprehend the information it stores because of its complexity. Therefore, this problem can be solved by using Explainable Artificial Intelligence (XAI) tools, which provide doctors with a realistic explanation of CNN's assessments. Implementation of deep learning-based systems in real-time diagnosis is still rare. One of the causes could be that these methods don't quantify the Uncertainty in the predictions, which could undermine trust in the AI-based diagnosis of diseases. To be used in real-time medical diagnosis, CNN-based models must be realistic and appealing, and uncertainty needs to be evaluated. So, a novel three-phase strategy is proposed for segmenting and classifying brain tumors. Segmentation of brain tumors using the DeeplabV3+ model is first performed with tuning of hyperparameters using Bayesian optimization. For classification, features from state-of-the-art deep learning models Darknet53 and mobilenetv2 are extracted and fed to SVM for classification, and hyperparameters of SVM are also optimized using a Bayesian approach. The second step is to understand whatever portion of the images CNN uses for feature extraction using XAI algorithms. Using confusion entropy, the Uncertainty of the Bayesian optimized classifier is finally quantified. Based on a Bayesian-optimized deep learning framework, the experimental findings demonstrate that the proposed method outperforms earlier techniques, achieving a 97 % classification accuracy and a 0.98 global accuracy.

One Standard for All: Uniform Scale for Comparing Individuals and Groups in Hierarchical Bayesian Evidence Accumulation Modeling.

In recent years, a growing body of research uses Evidence Accumulation Models (EAMs) to study individual differences and group effects. This endeavor is challenging because fitting EAMs requires constraining one of the EAM parameters to be equal for all participants, which makes a strong and possibly unlikely assumption. Moreover, if this assumption is violated, differences or lack thereof may be wrongly found. To overcome this limitation, in this study, we introduce a new method that was originally suggested by van Maanen & Miletic (2021), which employs Bayesian hierarchical estimation. In this new method, we set the scale at the population level, thereby allowing for individual and group differences, which is realized by de facto fixing a population-level hyper-parameter through its priors. As proof of concept, we ran two successful parameter recovery studies using the Linear Ballistic Accumulation model. The results suggest that the new method can be reliably used to study individual and group differences using EAMs. We further show a case in which the new method reveals the true group differences whereas the classic method wrongly detects differences that are truly absent.

Machine learning prediction of the mechanical properties of injection-molded polypropylene through X-ray diffraction analysis.

Predicting the mechanical properties of polymer materials using machine learning is essential for the design of next-generation of polymers. However, the strong relationship between the higher-order structure of polymers and their mechanical properties hinders the mechanical property predictions based on their primary structures. To incorporate information on higher-order structures into the prediction model, X-ray diffraction (XRD) can be used. This study proposes a strategy to generate appropriate descriptors from the XRD analysis of the injection-molded polypropylene samples, which were prepared under almost the same injection molding conditions. To this end, first, Bayesian spectral deconvolution is used to automatically create high-dimensional descriptors. Second, informative descriptors are selected to achieve highly accurate predictions by implementing the black-box optimization method using Ising machine. This approach was applied to custom-built polymer datasets containing data on homo- polypropylene and derived composite polymers with the addition of elastomers. Results show that reasonable accuracy of predictions for seven mechanical properties can be achieved using only XRD.

This study proposes a strategy to generate appropriate descriptors, which realize highly accurate predictions of mechanical properties via machine learning from the XRD analysis of the molded polypropylene samples.

Analysis of Determinants of Stunting and Identifications of Stunting Risk Profiles Among Under 2-Year-Old Children in Ethiopia. A Latent Class Analysis.

Background: Childhood stunting has a long-term impact on cognitive development and overall well-being. Understanding varying stunting profiles is crucial for targeted interventions and effective policy-making. Therefore, our study aimed to identify the determinants and stunting risk profiles among 2-year-old children in Ethiopia. Methods and materials: A cross-sectional study was conducted on 395 mother-child pairs attending selected public health centers for growth monitoring and promotion under 5 outpatient departments and immunization services. The data were collected by face-to-face interviews, with the anthropometric data collected using the procedure stipulated by the World Health Organization. The data were entered using Epi Data version 4.6 and exported to STATA 16 and Jamovi version 2.3.28 for analysis. Bayesian logistic regression analysis was conducted to identify potential factors of stunting. Likewise, lifecycle assessment analysis (LCA) was used to examine the heterogeneity of the magnitude of stunting. Results: The overall prevalence of stunting in children under 24 months was 47.34% (95% confidence interval (CI): 42.44-52.29%). The LCA identified 3 distinct risk profiles. The first profile is Class 1, which is labeled as low-risk, comprised 23.8% of the children, and had the lowest prevalence of stunting (23.4%). This group characterized as having a lower risk to stunting. The second profile is Class 2, which is identified as high-risk, comprised 47.1%, and had a high prevalence of stunting (66.7%), indicating a higher susceptibility to stunting compared to Class 1. The third profile is Class 3, which is categorized as mixed-risk and had a moderate stunting prevalence of 35.7%, indicating a complex interplay of factors contributing to stunting. Conclusion: Our study identified 3 distinct risk profiles for stunting in young children. A substantial amount (almost half) is in the high-risk category, where stunting is far more common. The identification of stunting profiles necessitates considering heterogeneity in risk factors in interventions. Healthcare practitioners should screen, provide nutrition counseling, and promote breastfeeding. Policymakers should strengthen social safety nets and support primary education.

The spike-and-slab lasso and scalable algorithm to accommodate multinomial outcomes in variable selection problems.

Spike-and-slab prior distributions are used to impose variable selection in Bayesian regression-style problems with many possible predictors. These priors are a mixture of two zero-centered distributions with differing variances, resulting in different shrinkage levels on parameter estimates based on whether they are relevant to the outcome. The spike-and-slab lasso assigns mixtures of double exponential distributions as priors for the parameters. This framework was initially developed for linear models, later developed for generalized linear models, and shown to perform well in scenarios requiring sparse solutions. Standard formulations of generalized linear models cannot immediately accommodate categorical outcomes with > 2 categories, i.e. multinomial outcomes, and require modifications to model specification and parameter estimation. Such modifications are relatively straightforward in a Classical setting but require additional theoretical and computational considerations in Bayesian settings, which can depend on the choice of prior distributions for the parameters of interest. While previous developments of the spike-and-slab lasso focused on continuous, count, and/or binary outcomes, we generalize the spike-and-slab lasso to accommodate multinomial outcomes, developing both the theoretical basis for the model and an expectation-maximization algorithm to fit the model. To our knowledge, this is the first generalization of the spike-and-slab lasso to allow for multinomial outcomes.