Distribution Of Model Parameters Research Articles

Effect of loading conditions on short fatigue crack propagation behaviours in cast Al[sbnd]Si alloys

The effect of loading conditions on short crack propagation behaviours in cast AlSi alloys was investigated by a combination of photo-microscopy monitoring and post mortem analysis. The findings suggest that the path of short cracks is minimally influenced by loading conditions, whereas loading conditions significantly affect the fatigue crack growth rate (FCGR) and its statistical characteristics. Crack closure effect is observed under zero and negative stress ratio conditions. Roughness-induced crack closure occurs due to the coarse grain microstructure of cast AlSi alloys and the Stage-I mode growth of cracks within grains in the microstructural short crack regime. The high level of plasticity around the crack tip under negative stress ratio conditions has a significant impact on FCGR, resulting in a negative crack opening stress. When the stress ratio exceeds approximately 0.3, short cracks exhibit no crack closure. The load-level effect is observed only at high load conditions with negative stress ratios. Finally, a probabilistic short crack growth model was established using a Bayesian linear regression model to analyse the effect of stress ratio on the uncertainty of FCGR. After considering the crack closure effect, the difference in distributions of FCGR model parameters decreases significantly among different stress ratio conditions.

Stochastic inversion of fracture networks using the reversible jump Markov chain Monte Carlo algorithm

Characterization of fracture networks is essential in the production optimization or storage calculation for enhanced geothermal systems or geologic carbon storage. A novel inversion approach is proposed for estimating the fracture networks in this research. The discrete fracture network technique is adopted to probabilistically describe various fracture parameters such as trace length, midpoint position or azimuthal angle. The reversible jump Markov chain Monte Carlo algorithm is applied to explore the target posterior distribution of model parameters of differing dimensionality, in which the number of fractures is assumed to be unknown. More specifically, the birth-death strategy is utilized to perturb the fracture number iteratively in the sampling process. The proposed methodology is applied with two different types of observational datasets, namely the head records from steady-state flow simulation and the acoustic impedance obtained from seismic inversion. The sampling results can successfully recover the fracture geometry in the observed domain, and the number of fractures in the system can be retrieved as well. Benchmarked on multiple Markov chain trials, the technique of parallel tempering can greatly improve the convergence efficiency and increase the diversity of sampled posterior models, through the random swapping of model states across the whole temperature ladder.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

An investigation of traffic speed distributions for uninterrupted flow at blackspot locations in a mixed traffic environment

Modelling traffic characteristics is the foundation for resolving various traffic and transportation issues. Among them, traffic speed has a significant impact on roadway crashes at blackspot (BS) locations. Speed is a random variable; several studies have recommended normal distribution to characterize the distribution of traffic speed for uninterrupted flow. However, a mixed-traffic situation causes heterogeneity, and the distribution of speeds deviates from the normal distribution. The present study investigates the distributions of traffic speeds for uninterrupted flow at 18 blackspot locations and individual vehicle types in mixed-traffic environments. Seven distribution models, namely Normal, Lognormal, Gamma, Logistic, Weibull, Burr, and Generalized Extreme Value (GEV), are considered to determine the speed characteristics. Different parametric distribution models are fitted to the vehicular speeds using maximum likelihood estimation (MLE) methods. Kolmogorov-Smirnov (KS), Anderson-Darling (AD), and two penalized criteria, i.e., Akaike and Bayesian Information Criteria (AIC and BIC), are used as goodness-of-fit (GoF) measures to find the best-fitting distribution. The overall suitability of each predicted distribution is also determined using a novel ranking method. The test findings suggest that GEV and Burr are the most suitable empirical speed distributions, with GEV fitting best above 96%. When the heavy vehicle composition (truck, bus, and tractor) is below 10%, 10–14%, 15–20%, and above 20%, it follows the Weibull, Gamma, GEV, and Burr distributions, respectively, in a mixed traffic environment.

Probabilistic risk assessment for reinforced concrete frame structures subject to mainshock‐aftershock sequences

AbstractRecent earthquakes have highlighted that aftershocks can considerably increase the structural demand and seismic risk of engineering structures. This study presents a probabilistic approach to assess the seismic risk of reinforced concrete (RC) frame structures subjected to mainshock‐aftershock sequences. In this approach, a predictive fragility method is used to evaluate the probabilities of structural damage under sequential excitations. The Bayes theorem is employed to generate posterior distributions of unknown model parameters. Then, a practical seismic hazard assessment method is used to conduct mainshock‐aftershock hazard analysis. The Copula technique is employed to develop a joint distribution model of the mainshock and aftershock intensity measures. Finally, the seismic risk is evaluated using the classical risk integration equation with the mainshock‐aftershock fragilities and hazard surfaces. Confidence bounds for fragilities and seismic risks are also obtained to account for the uncertainties of model parameters caused by aftershocks. The proposed approach is demonstrated by considering a seismic‐designed RC frame building. It can be concluded that aftershocks can significantly increase the seismic risk throughout the entire structural service life. The additional uncertainties caused by aftershocks result in wider confidence bounds for seismic risk.

A new test of gravity – I. Introduction to the method

ABSTRACT We introduce a new scheme based on the marked correlation function to probe gravity using the large-scale structure of the Universe. We illustrate our approach by applying it to simulations of the metric-variation f(R) modified gravity theory and general relativity (GR). The modifications to the equations in f(R) gravity lead to changes in the environment of large-scale structures that could, in principle, be used to distinguish this model from GR. Applying the Monte Carlo Markov Chain algorithm, we use the observed number density and two-point clustering to fix the halo occupation distribution (HOD) model parameters and build mock galaxy catalogues from both simulations. To generate a mark for galaxies when computing the marked correlation function we estimate the local density using a Voronoi tessellation. Our approach allows us to isolate the contribution to the uncertainty in the predicted marked correlation function that arises from the range of viable HOD model parameters, in addition to the sample variance error for a single set of HOD parameters. This is critical for assessing the discriminatory power of the method. In a companion paper, we apply our new scheme to a current large-scale structure survey.

A doubly self-exciting Poisson model for describing scoring levels in NBA basketball

Abstract In this article, Poisson time series models are considered to describe the number of field goals made by a basketball team or player at both the game (within-season) and the minute (within-game) level. The model is endowed with a doubly self-exciting structure, following the INGARCH(1,1) specification. To estimate the model at the within-game level, a divide-and-conquer procedure is carried out under a Bayesian framework. Then, we perform a clustering of the players in terms of their similarity according to the corresponding posterior distributions of key model parameters. The model is tested with National Basketball Association (NBA) teams and players from the 2018–2019 season.

Identification of aquifer heterogeneity through inverse methods

The paper underlines the contributions of Ghislain de Marsily (GdM) to the identification of aquifers heterogeneity using inverse methods mainly for modeling subsurface flow. Inverse methods require an objective function to express the goodness of fit of the chosen model, a parameterization to describe the spatial distribution of model parameters, and a minimization algorithm. The resulting inverse problem, which consists in seeking model parameters’ values that render model outputs close to the observations, is usually unstable. GdM developed seminal ideas for the two key inversion issues that are: to stabilize the inverse problem through regularization, and to parameterize it to reproduce the natural heterogeneity of the subsurface with a limited number of parameters. GdM conducted pioneering works that are the basis of current parameterization methods relying upon adaptive zonation and/or interpolation based on pilot points. We take here the opportunity to highlight the GdM’s contributions inspiring currently used techniques.

Age and sex-dependent sensitivity analysis of a common carotid artery model

The common carotid artery (CCA) is an accessible and informative site for assessing cardiovascular function which makes it a prime candidate for clinically relevant computational modelling. The interpretation of supplemental information possible through modelling is encumbered by measurement uncertainty and population variability in model parameters. The distribution of model parameters likely depends on the specific sub-population of interest and delineation based on sex, age or health status may correspond to distinct ranges of typical parameter values. To assess this impact in a 1D-CCA-model, we delineated specific sub-populations based on age, sex and health status and carried out uncertainty quantification and sensitivity analysis for each sub-population. We performed a structured literature review to characterize sub-population-specific variabilities for eight model parameters without consideration of health status; variations for a healthy sub-populations were based on previously established references values. The variabilities of diameter and distensibility found in the literature review differed from those previously established in a healthy population. Model diameter change and pulse pressure were most sensitive to variations in distensibility, while pressure was most sensitive to resistance in the Windkessel model for all groups. Uncertainties were lower when variabilities were based on a healthy sub-population; however, the qualitative distribution of sensitivity indices was largely similar between the healthy and general population. Average sensitivity of the pressure waveform showed a moderate dependence on age with decreasing sensitivity to distal resistance and increasing sensitivity to distensibility and diameter. The female population was less sensitive to variations in diameter but more sensitive to distensibility coefficient than the male population. Overall, as hypothesized input variabilities differed between sub-populations and resulted in distinct uncertainties and sensitivities of the 1D-CCA-model outputs, particularly over age for the pressure waveform and between males and females for pulse pressure.

A Software Tool for Estimating Uncertainty of Bayesian Posterior Probability for Disease.

The role of medical diagnosis is essential in patient care and healthcare. Established diagnostic practices typically rely on predetermined clinical criteria and numerical thresholds. In contrast, Bayesian inference provides an advanced framework that supports diagnosis via in-depth probabilistic analysis. This study's aim is to introduce a software tool dedicated to the quantification of uncertainty in Bayesian diagnosis, a field that has seen minimal exploration to date. The presented tool, a freely available specialized software program, utilizes uncertainty propagation techniques to estimate the sampling, measurement, and combined uncertainty of the posterior probability for disease. It features two primary modules and fifteen submodules, all designed to facilitate the estimation and graphical representation of the standard uncertainty of the posterior probability estimates for diseased and non-diseased population samples, incorporating parameters such as the mean and standard deviation of the test measurand, the size of the samples, and the standard measurement uncertainty inherent in screening and diagnostic tests. Our study showcases the practical application of the program by examining the fasting plasma glucose data sourced from the National Health and Nutrition Examination Survey. Parametric distribution models are explored to assess the uncertainty of Bayesian posterior probability for diabetes mellitus, using the oral glucose tolerance test as the reference diagnostic method.

Differentiable stochastic halo occupation distribution

ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.

Rare Event Probability Estimation for Groundwater Inverse Problems With a Two‐Stage Sequential Monte Carlo Approach

AbstractBayesian inversions followed by estimations of rare event probabilities are often needed to analyze groundwater hazards. Instead of focusing on the posterior distribution of model parameters, the main interest lies then in the distribution of a specific quantity of interest contingent upon these parameters. To address the associated methodological challenges, we introduce a two‐stage Sequential Monte Carlo approach. In the first stage, it generates particles that approximate the posterior distribution; in the second stage, it employs subset sampling techniques to assess the probability of the rare event of interest. By considering two hydrogeological problems of increasing complexity, we showcase the efficiency and accuracy of the resulting PostRisk‐SMC method for rare event probability estimation related to groundwater hazards. We compare the performance of the PostRisk‐SMC method with a traditional Monte Carlo approach that relies on Markov chain Monte Carlo samples. We showcase that our estimates align with those of the traditional method, but the coefficients of variation are notably lower for the same computational budget when targeting more rare events. Furthermore, we highlight that the PostRisk‐SMC method allows estimating rare event probabilities approaching one in a billion using less than one hundred thousand forward simulations. Even if the presented examples are related to groundwater hazards, the methodology is well‐suited for addressing a wide range of topics in the geosciences and beyond.

An Efficient and Robust Estimation of Spatio‐Temporally Distributed Parameters in Dynamic Models by an Ensemble Kalman Filter

AbstractThe accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change spatio‐temporally, shows promise in quantifying and mitigating systematic model errors, the estimation of the spatio‐temporally distributed model parameters has been practically challenging. Here we present an efficient and practical method to estimate time‐varying parameters in high‐dimensional spaces. In our proposed method, Hybrid Offline and Online Parameter Estimation with ensemble Kalman filtering (HOOPE‐EnKF), model parameters estimated by EnKF are constrained by results of offline batch optimization, in which the posterior distribution of model parameters is obtained by comparing simulated and observed climatological variables. HOOPE‐EnKF outperforms the original EnKF in synthetic experiments using a two‐scale Lorenz96 model and a simple global general circulation model. One advantage of HOOPE‐EnKF over traditional EnKFs is that its performance is not greatly affected by inflation factors for model parameters, thus eliminating the need for extensive tuning of inflation factors. We thoroughly discuss the potential of HOOPE‐EnKF as a practical method for improving parameterizations of process‐based models and prediction in real‐world applications such as numerical weather prediction.

Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.

Population-based estimation for PDE system – Applications in electroporation of tumor spheroids

The estimation of partial differential systems (PDE) – in particular, the identification of their parameters – is fundamental in many applications to combine modeling and available measurements. However, it is well known that parameter prior values must be chosen appropriately to balance our distrust of measurements, especially when data are sparse or corrupted by noise. A classic strategy to compensate for this weakness is to use repeated measurements collected in configurations with common priors, such as multiple subjects in a clinical trial. In the mixed-effects approach, all subjects are pooled and a global distribution of model parameters in the population is estimated. However, due to the high computational cost, this strategy is often not applicable in practice for PDE. In this paper, we propose an estimation strategy to overcome this challenge. This sophisticated method is based on two important existing methodological strategies: (1) a population-based Kalman filter and, (2) a joint state-parameter estimation. More precisely, the errors coming from the initial conditions are controlled by a Luenberger observer and the parameters are estimated using a population-based reduced-order Kalman filter restricted to the parameter space. The performance of the algorithm is evaluated using synthetic and real data for tumor spheroid electroporation.

针对玉米叶片病斑图像的人工智能识别方法研究

Maize eyespot and maize curvularia leaf spot are two diseases that often occur on maize leaves. Because of the similarity of the shape and structure, it is difficult to identify the two diseases just relying on the observation of the growers. For the harmfulness and prevention methods are different, it would cause great loss if the disease can't be identified accurately. To address this issue, this paper first employs a connected region feature recognition method to design an automated lesion cropping process after acquiring leaf images with several lesions. Subsequently, a lesion recognition model based on the AlexNet architecture is built and subjected to five-fold cross-validation experiments. The results indicate that the model achieves a comprehensive recognition accuracy exceeding 99%. To further comprehend model characteristics, an analysis of the recognition accuracy and its fluctuations is conducted, revealing that the fractal growth and biological characteristics of the lesions may influence the recognition results. Moreover, the distribution of model parameters could be a potential reason for fluctuations in recognition accuracy rates with increasing number of iterations. This paper could offer valuable reference and support for the intelligent identification and diagnosis of maize and other plant diseases.

Fixed and random effect selections in generalized linear mixed models.

Generalized linear mixed models are commonly used to describe relationships between correlated responses and covariates in medical research. In this paper, we propose a simple and easily implementable regularized estimation approach to select both fixed and random effects in generalized linear mixed model. Specifically, we propose to construct and optimize the objective functions using the confidence distributions of model parameters, as opposed to using the observed data likelihood functions, to perform effect selections. Two estimation methods are developed. The first one is to use the joint confidence distribution of model parameters to perform simultaneous fixed and random effect selections. The second method is to use the marginal confidence distributions of model parameters to perform the selections of fixed and random effects separately. With a proper choice of regularization parameters in the adaptive LASSO framework, we show the consistency and oracle properties of the proposed regularized estimators. Simulation studies have been conducted to assess the performance of the proposed estimators and demonstrate computational efficiency. Our method has also been applied to two longitudinal cancer studies to identify demographic and clinical factors associated with patient health outcomes after cancer therapies.

Approximate Bayesian computation with semiparametric density ratio model

Approximate Bayesian computation (ABC) is a likelihood-free inference method commonly employed for statistical inference in models with unknown or complex likelihood functions. ABC estimates the posterior distributions of model parameters by comparing summary statistics of the simulated and observed data. However, the selection of informative summary statistics can be challenging in practice. In this study, we propose a summary-statistic-free method called ABC with semiparametric empirical likelihood ratio (ABC-SELR). This method utilises the empirical likelihood within the framework of the semiparametric density ratio model to assess the simulated parameters via testing whether the simulated and observed data conform to the same distribution. By eliminating the need for choosing summary statistics, our approach avoids potential information loss. Furthermore, the proposed method captures the shared characteristics between the simulated and observed data, leading to improved efficiency. We demonstrate the accuracy and efficiency of ABC-SELR by comparing with existing ABC methods through numerical simulations.

Bayesian Risk Assessment Technique for Economic Stress-Strength Models

This paper explores two areas of risk assessment modelling in economics and business: the Stress-Strength model and Bayesian techniques. The model assumes that the probability of stress exceeding strength is a measure of risk. The interpretation of stress and strength largely depends on the particular event or phenomenon being modelled. The use of the Stress-Strength model is demonstrated through the Gaussian assumption of probability distributions for random model parameters, particularly in assessing the risk of not achieving a required margin value. The concept of the capability function, representing the difference between strength and stress, is introduced in the modelling process. The probability distribution for the capability function is initially determined based on the Gaussian distribution of the random variables used in the model, allowing for evaluating the risk metric. The Bayesian approach is then applied to generalise the problem statement when dealing with unknown parameters of probability distributions for the Stress and Strength models. The uncertainty of these parameters is modelled through uniform probability distributions, and equations for calculating prior and posterior estimates are consistently obtained. Since multidimensional integrals are involved in these calculations, and solutions cannot be obtained in closed analytical form, Monte Carlo simulation is used to solve this computation problem.

Learned Lossless Image Compression Through Interpolation With Low Complexity

With the increasing popularity of deep learning in image processing, many learned lossless image compression methods have been proposed recently. One group of algorithms are based on scale-based auto-regressive models and can provide competitive compression performance while also allowing easily parallelized computations and short encoding/decoding times. However, they use large neural networks and have high computational requirements. This paper presents an interpolation based learned lossless image compression method which falls in the scale-based auto-regressive models group. The method achieves compression performance better than or on par with the recent scale-based auto-regressive models, yet requires more than 10x less neural network parameters (0.19M) and encoding/decoding computation complexity. These achievements are due to the contributions/findings in the overall system and neural network architecture design, such as sharing interpolator neural networks across different scales, using separate neural networks for different parameters of the probability distribution model and performing the processing in the YCoCg-R color space instead of the RGB color space.