Bayesian Procedure Research Articles

A multi-fidelity surrogate model for structural health monitoring exploiting model order reduction and artificial neural networks

Stochastic approaches to structural health monitoring (SHM) are often inevitably limited by computational constraints. For instance, for Markov chain Monte Carlo algorithms relying upon computationally expensive finite element models it is almost infeasible to sample the probability distribution of the structural state. To provide instead real-time procedures, this work proposes a non-intrusive surrogate modeling strategy, leveraging model order reduction and artificial neural networks. By relying upon a multi-fidelity (MF) framework, a composition of deep neural networks (DNNs) is devised to map damage and operational parameters onto time-dependent sensor recordings. Such an effective strategy is able to exploit datasets characterized by different fidelity levels without any prior assumption, allowing to blend a small high-fidelity (HF) dataset with a large low-fidelity (LF) dataset, ultimately alleviating the computational burden of supervised training while ensuring the accuracy of the approximated quantities of interest. The resulting surrogate model is made of an LF-DNN, which mimics sensor recordings in the undamaged condition, and of a long short-term memory HF-DNN, which adaptively refines the approximation with the effect of damage. An HF finite element model and an LF reduced order model are adopted offline to generate labeled training data of different fidelity, respectively in the presence or absence of a structural damage. Results relevant to an L-shaped cantilever beam and a portal frame railway bridge prove that the procedure efficiently provides remarkably accurate approximations, outperforming their single-fidelity counterparts. The capability of the MF-DNN to be exploited for SHM purposes is finally shown within an automated Bayesian procedure, aimed at updating the probability distribution of the structural state conditioned on sensor recordings, in the presence of operational variability and measurement noise.

Indicator-based Bayesian variable selection for Gaussian process models in computer experiments

Gaussian process (GP) models are commonly used in the analysis of computer experiments. Variable selection in GP models is of significant scientific interest but existing solutions remain unsatisfactory. For each variable in a GP model, there are two potential effects with different implications: one is on the mean function, and the other is on the covariance function. However, most of the existing research on variable selection for GP models has focused only on one of the effects. To tackle this problem, we propose an indicator-based Bayesian variable selection procedure to take into account the effects from both the mean and covariance functions. A variable is defined to be inactive if both effects are not significant, and an indicator is used to represent the variable being active or not. For active variables, the proposed method adopts different prior assumptions to capture the two effects. The performance of the proposed method is evaluated by both simulations and real applications in computer experiments.

Isolating the Effect of Crosslink Densities on Mechanical Properties of Isotactic Polypropylene Using Dissipative Particle Dynamics

AbstractGiven the importance of preserving the mechanical properties of recycled isotactic polypropylene (iPP) during its processing, this work provides an improved understanding of the contribution of introducing physical or chemical crosslinks using the dissipative particle dynamics (DPD) method, which makes it possible to model iPP structures with a realistic range of crosslink densities. First, the protocol to build a coarse‐grained model of iPP from an all‐atom expression by Bayesian optimization is described. A Bayesian optimization procedure employing two different cutoff distances successfully provides optimal DPD parameters reproducing iPP's properties compared to the all‐atom system. Then, the coarse‐grained iPP model with optimal DPD parameters is applied to study structures containing a realistic range of crosslink densities to evaluate their mechanical properties. These calculations demonstrate that the mechanical properties such as the Young's modulus and ultimate strength increase while the fracture strain decreases with an increase in the crosslink density, which is consistent with experimental observations. The results also show that there is a critical crosslink density above which these properties start to be improved due to the introduction of crosslinks. These findings can help us to obtain targeted properties of recycled iPP by introducing physical or chemical crosslinks.

Joint diagnosis of process mean vector and covariance matrix for multivariate statistical process control

The monitoring methodology in statistical process control is very useful and efficient to detect abnormal changes of a process, however diagnosis ability, accurate fault diagnosis of responsible components for the process change, is limited. Currently, most of work has focused on the diagnosis task of mean shifts. Nevertheless, the shifts of a process also likely occur in the variances/covariances. In this article, we develop a Bayesian procedure to simultaneously diagnose shifts in both mean vector and covariance matrix. Moreover, the proposed method can provide the directions of shifts and corresponding probability. These diagnostic information help decision makers to find quickly root causes of abnormal changes. Compared with existing methods, numerical simulations favor the proposed method. Finally, we use a real dataset from bolt production process to demonstrate the implementation of the proposed Bayesian method.

An Experimental, Computational, and Statistical Strategy for the Bayesian Calibration of Complex Material Models

The study of solids and structures under extreme conditions often relies on simulations that employ complex material models. These, in turn, are formulated using analytical expressions that depend on parameters whose values need to be adjusted for optimally reproducing available experimental results and, especially, out-of-sample predictiveness. In this article we review the process required to calibrate all the parameters of the Johnson-Cook and Zerilli-Armstrong models for a nickel-based superalloy. To this end, we present in an unified fashion the thermomechanical problem, its numerical implementation, a complete experimental campaign that suffices to obtain the material constants, and a Bayesian calibration procedure that can be employed to obtain the optimal values for the model parameters as well as their uncertainty. The advocated methodology is ideally designed to calibrate strain rate-, temperature-, and age-dependent elastoplastic models. The procedure is, however, general enough to be employed as guideline for other complex calibrations.

Reliability-based structural assessment of historical masonry arch bridges: The case study of Cernadela bridge

Nowadays, several historical masonry arch bridges present a deficient state of conservation due to degradation processes induced by natural or human actions. Usually, these constructions have significant economic, cultural, and heritage value. Therefore, they shall be thoroughly assessed to verify their structural integrity and safety condition. For this purpose, reliability-based structural assessments are typically performed. However, the associated outcomes (i.e., reliability index and probability of failure) highly rely on the accuracy of the structural parameters uncertainty quantification. This work presents a study regarding the influence of the scattering of the arches' thickness dimensions in the load-carrying capacity assessment of the Cernadela Bridge, a historical stone bridge located in Galicia, Spain. The study first involved a comprehensive experimental campaign to characterize the outer and inner bridge geometry through geomatic techniques, i.e., terrestrial laser scanning and ground penetrating radar. Subsequently, a limit analysis model was developed, considering only the arches' outer (visible) data. From this initial structural assessment, a reliability index of 2.38 was obtained. The influence of the uncertain structural parameters, both geometric features and material properties, in the collapse load was investigated through a global variance-based sensitivity analysis (i.e., Sobol' indices) complemented by a surrogate modeling strategy based on the Kriging approach. Finally, the measured inner geometry of the arches was introduced in the computational model through Bayesian inference procedures. Thus, two new structural assessments were performed: first, by considering the updated distributions of all arches thicknesses, and second, by considering only the updated distributions of the non-influential ones. Reliability indexes of 1.51 and 2.33 were derived, thus highlighting the importance of a proper uncertainty quantification process and the relevance of the sensitivity analysis outcomes to identify the critical parameters on the bridge mechanical response.

Mechano-biological and bio-mechanical pathways in cutaneous wound healing.

Injuries to the skin heal through coordinated action of fibroblast-mediated extracellular matrix (ECM) deposition, ECM remodeling, and wound contraction. Defects involving the dermis result in fibrotic scars featuring increased stiffness and altered collagen content and organization. Although computational models are crucial to unravel the underlying biochemical and biophysical mechanisms, simulations of the evolving wound biomechanics are seldom benchmarked against measurements. Here, we leverage recent quantifications of local tissue stiffness in murine wounds to refine a previously-proposed systems-mechanobiological finite-element model. Fibroblasts are considered as the main cell type involved in ECM remodeling and wound contraction. Tissue rebuilding is coordinated by the release and diffusion of a cytokine wave, e.g. TGF-β, itself developed in response to an earlier inflammatory signal triggered by platelet aggregation. We calibrate a model of the evolving wound biomechanics through a custom-developed hierarchical Bayesian inverse analysis procedure. Further calibration is based on published biochemical and morphological murine wound healing data over a 21-day healing period. The calibrated model recapitulates the temporal evolution of: inflammatory signal, fibroblast infiltration, collagen buildup, and wound contraction. Moreover, it enables in silico hypothesis testing, which we explore by: (i) quantifying the alteration of wound contraction profiles corresponding to the measured variability in local wound stiffness; (ii) proposing alternative constitutive links connecting the dynamics of the biochemical fields to the evolving mechanical properties; (iii) discussing the plausibility of a stretch- vs. stiffness-mediated mechanobiological coupling. Ultimately, our model challenges the current understanding of wound biomechanics and mechanobiology, beside offering a versatile tool to explore and eventually control scar fibrosis after injury.

Bayesian estimation and testing in random-effects meta-analysis of rare binary events allowing for flexible group variability.

Rare binary events data arise frequently in medical research. Due to lack of statistical power in individual studies involving such data, meta-analysis has become an increasingly important tool for combining results from multiple independent studies. However, traditional meta-analysis methods often report severely biased estimates in such rare-event settings. Moreover, many rely on models assuming a pre-specified direction for variability between control and treatment groups for mathematical convenience, which may be violated in practice. Based on a flexible random-effects model that removes the assumption about the direction, we propose new Bayesian procedures for estimating and testing the overall treatment effect and inter-study heterogeneity. Our Markov chain Monte Carlo algorithm employs Pólya-Gamma augmentation so that all conditionals are known distributions, greatly facilitating computational efficiency. Our simulation shows that the proposed approach generally reports less biased and more stable estimates compared to existing methods. We further illustrate our approach using two real examples, one using rosiglitazone data from 56 studies and the other using stomach ulcers data from 41 studies.

Inverse Bayesian Optimization: Learning Human Acquisition Functions in an Exploration vs Exploitation Search Task

This paper introduces a probabilistic framework to estimate parameters of an acquisition function given observed human behavior that can be modeled as a collection of sample paths from a Bayesian optimization procedure. The methodology involves defining a likelihood on observed human behavior from an optimization task, where the likelihood is parameterized by a Bayesian optimization subroutine governed by an unknown acquisition function. This structure enables us to make inference on a subject's acquisition function while allowing their behavior to deviate around the solution to the Bayesian optimization subroutine. To test our methods, we designed a sequential optimization task which forced subjects to balance exploration and exploitation in search of an invisible target location. Applying our proposed methods to the resulting data, we find that many subjects tend to exhibit exploration preferences beyond that of standard acquisition functions to capture. Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.

Scalable Bayesian High-dimensional Local Dependence Learning

In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities of spatial locations, and so on, with the natural assumption that variables far apart tend to have weak correlations. Applications of such models abound in a variety of fields such as finance, genome associations analysis and spatial modeling. We adopt a flexible framework under which each variable is dependent on its neighbors or predecessors, and the neighborhood size can vary for each variable. It is of great interest to reveal this local dependence structure by estimating the covariance or precision matrix while yielding a consistent estimate of the varying neighborhood size for each variable. The existing literature on banded covariance matrix estimation, which assumes a fixed bandwidth cannot be adapted for this general setup. We employ the modified Cholesky decomposition for the precision matrix and design a flexible prior for this model through appropriate priors on the neighborhood sizes and Cholesky factors. The posterior contraction rates of the Cholesky factor are derived which are nearly or exactly minimax optimal, and our procedure leads to consistent estimates of the neighborhood size for all the variables. Another appealing feature of our procedure is its scalability to models with large numbers of variables due to efficient posterior inference without resorting to MCMC algorithms. Numerical comparisons are carried out with competitive methods, and applications are considered for some real datasets.

Three-way decisions with fuzzy probabilistic covering-based rough sets and their applications in credit evaluation

As a generalization of equivalent class, fuzzy covering makes descriptions of the objective world more realistic, practical and accurate in some cases. In this paper, we establish four kinds of fuzzy probabilistic covering-based rough set, which combine the fuzzy covering-based neighborhood operator and the fuzzy probabilistic rough set, and then obtain the result of their three-way decision. The differences among the above models lie in the selection of thresholds, which further leads to different classification results. In addition, in order to interpret the thresholds rationally under different models, Bayesian decision procedure is adopted to construct the fuzzy probabilistic covering-based upper and lower approximation operators. Finally, a numerical example of the credit evaluation is applied to illustrate the validity of the proposed model.

Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing.

The external noise paradigm and perceptual template model (PTM) have successfully been applied to characterize observer properties and mechanisms of observer state changes (e.g. attention and perceptual learning) in several research domains, focusing on individual level analysis. In this study, we developed a new hierarchical Bayesian perceptual template model (HBPTM) to model the trial-by-trial data from all individuals and conditions in a published spatial cuing study within a single structure and compared its performance to that of a Bayesian Inference Procedure (BIP), which separately infers the posterior distributions of the model parameters for each individual subject without the hierarchical structure. The HBPTM allowed us to compute the joint posterior distribution of the hyperparameters and parameters at the population, observer, and experiment levels and make statistical inferences at all these levels. In addition, we ran a large simulation study that varied the number of observers and number of trials in each condition and demonstrated the advantage of the HBPTM over the BIP across all the simulated datasets. Although it is developed in the context of spatial attention, the HBPTM and its extensions can be used to model data from the external noise paradigm in other domains and enable predictions of human performance at both the population and individual levels.

An efficient Bayesian modelling of extreme winds in the favour​ of energy generation in Pakistan

Daily and annual maximum wind speed quantiles can be estimated using extreme value theory for any metrological site of interest. These estimates are of vast importance for modelling and predicting maximum wind speed. This paper develops an efficient modelling paradigm of extreme winds by analysing daily and annual maximum wind speed data via frequentist and Bayesian methodologies. For this purpose, the generalized extreme value (GEV) model is used for yearly maxima, and the generalized Pareto distribution (GPD) is used for daily exceedance over a high threshold. In frequentist inference, the parameters of both models are estimated using the maximum likelihood and linear moments method. In contrast, the Bayesian Markov Chain Monte Carlo procedure with the Metropolis–Hasting algorithm is used. In addition, the informative priors for both models are constructed empirically using historical records of wind speed data from five other weather stations of Pakistan and one belonging to India. The results show that the Bayesian modelling provides apparent benefits in terms of improved accuracy in the estimation of the parameters as well as return levels of both distributions. Furthermore, the Bayesian analysis expresses that posterior inference might be affected by the choice of priors used to formulate the informative priors. Overall, based on assessment measures, the GPD fitted through Bayesian informative priors provides an efficient estimation strategy in terms of precision than other frameworks when uncertainty in parameters and return levels are taken into account. Our methodology can be implemented easily to other regions by considering the prior information from the border area stations of other countries (e.g., China, Afghanistan, India, and Iran). Moreover, the return level estimates of the GPD based on informative Bayesian priors are very beneficial in policymaking and wind energy generation engineering for the Thatta region of the country.

Cosmicflows-4

With Cosmicflows-4, distances are compiled for 55,877 galaxies gathered into 38,065 groups. Eight methodologies are employed, with the largest numbers coming from the correlations between the photometric and kinematic properties of spiral galaxies (TF) and elliptical galaxies (FP). Supernovae that arise from degenerate progenitors (type Ia SNe) are an important overlapping component. Smaller contributions come from distance estimates from the surface brightness fluctuations of elliptical galaxies and the luminosities and expansion rates of core-collapse supernovae (SNe II). Cepheid period–luminosity relation and tip of the red giant branch observations founded on local stellar parallax measurements along with the geometric maser distance to NGC 4258 provide the absolute scaling of distances. The assembly of galaxies into groups is an important feature of the study in facilitating overlaps between methodologies. Merging between multiple contributions within a methodology and between methodologies is carried out with Bayesian Markov chain Monte Carlo procedures. The final assembly of distances is compatible with a value of the Hubble constant of H 0 = 74.6 km s−1 Mpc−1 with the small statistical error of ±0.8 km s−1 Mpc−1 but a large potential systematic error of ∼3 km s−1 Mpc−1. Peculiar velocities can be inferred from the measured distances. The interpretation of the field of peculiar velocities is complex because of large errors on individual components and invites analyses beyond the scope of this study.

Bayesian modelling of phosphorus content in wheat grain using hyperspectral reflectance data

BackgroundAs a result of the technological progress, the use of sensors for crop survey has substantially increased, generating valuable information for modelling agricultural data. Plant spectroscopy jointly with statistical modeling can potentially help to assess certain chemical components of interest present in plants, which may be laborious and expensive to obtain by direct measurements. In this research, the phosphorus content in wheat grain is modeled using reflectance information measured by a hyperspectral sensor at different wavelengths. A Bayesian procedure for selecting variables was used to identify the set of the most important spectral bands. Additionally, three different models were evaluated: the first model assumes that the observations are independent, the other two models assume that the observations are spatially correlated: one of the proposed models, assumes spatial dependence using a Conditionally Autoregressive Model (CAR), and the other through an exponential correlogram. The goodness of fit of the models was evaluated by means of the Deviance Information Criterion, and the predictive power is evaluated using cross validation.ResultsWe have found that CAR was the model that best fits and predicts the data. Additionally, the selection variable procedure in the CAR model reveals which wavelengths in the range of 500–690 nm are the most important. Comparing the vegetative indices with the CAR model, it was observed that the average correlation of the CAR model exceeded that of the vegetative indices by 23.26%, − 1.2% and 22.78% for the year 2010, 2011 and 2012 respectively; therefore, the use of the proposed methodology outperformed the vegetative indices in prediction.ConclusionsThe proposal to predict the phosphorus content in wheat grain using Bayesian approach, reflect with the results as a good alternative.

Disparities in SARS-CoV-2 Infection by Race, Ethnicity, Language, and Social Vulnerability: Evidence from a Citywide Seroprevalence Study in Massachusetts, USA

ObjectivesUncovering and addressing disparities in infectious disease outbreaks require a rapid, methodical understanding of local epidemiology. We conducted a seroprevalence study of SARS-CoV-2 infection in Holyoke, Massachusetts, a majority Hispanic city with high levels of socio-economic disadvantage to estimate seroprevalence and identify disparities in SARS-CoV-2 infection.MethodsWe invited 2000 randomly sampled households between 11/5/2020 and 12/31/2020 to complete questionnaires and provide dried blood spots for SARS-CoV-2 antibody testing. We calculated seroprevalence based on the presence of IgG antibodies using a weighted Bayesian procedure that incorporated uncertainty in antibody test sensitivity and specificity and accounted for household clustering.ResultsTwo hundred eighty households including 472 individuals were enrolled. Three hundred twenty-eight individuals underwent antibody testing. Citywide seroprevalence of SARS-CoV-2 IgG was 13.1% (95% CI 6.9–22.3) compared to 9.8% of the population infected based on publicly reported cases. Seroprevalence was 16.1% (95% CI 6.2–31.8) among Hispanic individuals compared to 9.4% (95% CI 4.6–16.4) among non-Hispanic white individuals. Seroprevalence was higher among Spanish-speaking households (21.9%; 95% CI 8.3–43.9) compared to English-speaking households (10.2%; 95% CI 5.2–18.0) and among individuals in high social vulnerability index (SVI) areas based on the CDC SVI (14.4%; 95% CI 7.1–25.5) compared to low SVI areas (8.2%; 95% CI 3.1–16.9).ConclusionsThe SARS-CoV-2 IgG seroprevalence in a city with high levels of social vulnerability was 13.1% during the pre-vaccination period of the COVID-19 pandemic. Hispanic individuals and individuals in communities characterized by high SVI were at the highest risk of infection. Public health interventions should be designed to ensure that individuals in high social vulnerability communities have access to the tools to combat COVID-19.

High-dimensional properties for empirical priors in linear regression with unknown error variance

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in Martin et al. (Bernoulli 23(3):1822–1847, 2017). In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper extend their theoretical results to the case of unknown error variance . Under proper sparsity assumption, we achieve model selection consistency, posterior contraction rates as well as Bernstein von-Mises theorem by analyzing multivariate t-distribution.

Improving content validity evaluation of assessment instruments through formal content validity analysis.

Content validity is defined as the degree to which elements of an assessment instrument are relevant to and representative of the target construct. The available methods for content validity evaluation typically focus on the extent to which a set of items are relevant to the target construct, but do not afford precise evaluation of items' behavior, nor their exhaustiveness with respect to the elements of the target construct. Formal content validity analysis (FCVA) is a new procedure combining methods and techniques from various areas of psychological assessment, such as (a) constructing Boolean classification matrices to formalize relationships among an assessment instrument's items and target construct elements, and (b) computing interrater agreement indices. We discuss how FCVA can be extended through the implementation of a Bayesian procedure to improve the interrater agreement indices' accuracy (Bayesian formal content validity analysis [B-FCVA]). With respect to extant methods, FCVA and B-FCVA can provide a great amount of information about content validity while not demanding much more work for authors and experts. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

An adaptive information-theoretic experimental design procedure for high-to-low fidelity calibration of prostate cancer models.

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models requires detailed clinical data. This raises questions about the type and quantity of data that should be collected and when, in order to maximize the information gain about the model behavior while still minimizing the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic procedure, using an adaptive score function to determine the optimal data collection times and measurement types. The novel score function introduced in this work eliminates the need for a penalization parameter used in a previous study, while yielding model predictions that are superior to those obtained using two potential pre-determined data collection protocols for two different prostate cancer model scenarios: one in which we fit a simple ODE system to synthetic data generated from a cellular automaton model using radiotherapy as the imposed treatment, and a second scenario in which a more complex ODE system is fit to clinical patient data for patients undergoing intermittent androgen suppression therapy. We also conduct a robust analysis of the calibration results, using both error and uncertainty metrics in combination to determine when additional data acquisition may be terminated.

Gestational exposure to organophosphate esters and infant anthropometric measures in the first 4 weeks after birth.

Few studies have examined whether gestational exposure to organophosphate esters (OPEs), widely used chemicals with potential endocrine-disrupting potency and developmental toxicity, is associated with impaired infant growth. We analyzed data from 329 mother-infant pairs in the Health Outcomes and Measures of the Environment (HOME) Study (2003-2006, Cincinnati, Ohio, USA). We quantified concentrations of four OPE metabolites in maternal urine collected at 16 and 26 weeks of gestation, and at delivery. We calculated z-scores using 2006 World Health Organization (WHO) child growth standards for the 4-week anthropometric measures (weight, length, and head circumference), the ponderal index, and weekly growth rates. We used multiple informant models to examine window-specific associations between individual OPE metabolites and anthropometric outcomes. We further modeled OPEs as a mixture for window-specific associations with 4-week anthropometric outcomes using mean field variational Bayesian inference procedure for lagged kernel machine regression (MFVB-LKMR). We stratified the models by infant sex. Diphenyl phosphate (DPHP) in mothers at 16 weeks, and bis(2-chloroethyl) phosphate (BCEP) and bis(1,3-dichloro-2-propyl) phosphate (BDCIPP) at delivery were positively associated with z-scores of weight, length, and head circumference in all infants at 4 weeks of age. After stratifying by infant sex, positive associations were only observed in males for DPHP at 16 weeks and BCEP at delivery and in females for BDCIPP at delivery. Negative associations not present in all infants were observed in males for di-n-butyl phosphate (DNBP) at 26 weeks of gestation with weight z-score and DPHP at delivery with head circumference z-score. Results were generally similar using MFVB-LKMR models with more conservative 95 % credible intervals. We did not identify consistent associations of gestational OPE metabolite concentrations with the ponderal index and weekly growth rates. In this cohort, exposure to OPEs during gestation was associated with altered infant anthropometry at 4 weeks after birth.