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We show that the slice sampler generates Markov chains whose variables are mean independent and thus uncorrelated when the target density is centrally symmetric. Skewness instead boosts correlations. Popular implementation algorithms such as stepping-out and multivariate-sampling-with-hyperrectangles add statistical inefficiency, the first in case of multimodality, the second in all circumstances. A new sampler which exploits these structural and algorithmic characteristics to reduce the variance of Monte Carlo estimates is experimented in several sampling problems. An insight into the properties of the product slice sampler is also provided. [ABSTRACT FROM AUTHOR]

3D digital models can facilitate the understanding of micro- and nanoscale pore structures and enhance the permeability prediction accuracy of geological materials. However, the reconstruction of digital models using the conventional Markov chain Monte Carlo (MCMC) algorithm cannot well reflect the microstructure of the heterogenous media and needs to be improved. In this study, referring to the box-counting method (BCM) of fractal theory, the conventional probability distribution function was extended to different scale probability functions, and the concept of value paths was introduced to control the reconstruction quality. Subsequently, a comparison to the conventional MCMC algorithm was conducted based on the statistical function and the pore fractal dimension to verify the effectiveness of the improved algorithm. Finally, the reconstruction model was applied in finite element simulation to predict the permeability of soft soil. The verification results showed that the improved MCMC algorithm can well realize the reconstruction of heterogeneous porous media since the squared correlation coefficients of statistical functions of the 3D reconstruction and the original image are above 0.98, and the pore fractal dimension of reconstructions using the improved MCMC was closer to the original image than that using the conventional MCMC. Furthermore, in permeability prediction, permeability simulations using images reconstructed with an improved MCMC algorithm are closer to the experimental values, with a maximum prediction error of 1.87 times (that of MCMC was 4.21 times) the corresponding experimental value. [ABSTRACT FROM AUTHOR]

In many real-world situations, systems frequently fail in their demanding operational settings. Researchers pay little attention to the fact that systems typically fail to execute their intended activities when it reaches its extreme operating situations as appropriate. In this paper, we try to develop and study inferential aspect of a system reliability having multiple components based on a progressive first failure censoring scheme assuming unit length-bias exponential distribution. Regarding estimation, asymptotic, boot-p, and boot-t approaches under the interval estimation are adopted, while the maximum likelihood method under the point estimation is considered. The MCMC method is used to get the Bayes estimate of the reliability parameter assuming both the symmetric and asymmetric loss functions. The associated confidence intervals are also reported as appropriate. The effectiveness of the various adopted estimation strategies is evaluated and compared using Monte Carlo simulation studies and examples from real-world applications. [ABSTRACT FROM AUTHOR]

This article addresses stress-strength reliability estimation in s-out-of-k systems under progressive type-II censoring. The system consists of components facing common stress, where stress and strength variable follows independent new flexible exponential (NFE) distributions, sharing a common parameter. The estimation procedure is carried out using MLE, Bayesian estimation and uniformly minimum variance unbiased estimation (UMVUE) techniques. MLE is derived for known and unknown common parameters. Bayesian estimates are obtained using Lindley's approximation and Markov chain Monte Carlo techniques due to the complexity of obtaining the exact Bayesian estimates, when the common parameter is unknown. Moreover, UMVUE is derived when the common parameter is known. The 95% asymptotic confidence interval, highest posterior density credible intervals, and Bayesian credible intervals, are constructed. An extensive simulation study is carried out to compare the performance of various censoring schemes and estimation methods. Finally, two progressively censored real datasets are analyzed for illustration. [ABSTRACT FROM AUTHOR]

Recent years witnessed the development of powerful generative models based on flows, diffusion, or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical analysis of the performance and understanding of the limitations of these methods remain, however, challenging. In this paper, we undertake a step in this direction by analyzing the efficiency of sampling by these methods on a class of problems with a known probability distribution and comparing it with the sampling performance of more traditional methods such as the Monte Carlo Markov chain and Langevin dynamics. We focus on a class of probability distribution widely studied in the statistical physics of disordered systems that relate to spin glasses, statistical inference, and constraint satisfaction problems. We leverage the fact that sampling via flow-based, diffusionbased, or autoregressive networks methods can be equivalently mapped to the analysis of a Bayes optimal denoising of a modified probability measure. Our findings demonstrate that these methods encounter difficulties in sampling stemming from the presence of a first-order phase transition along the algorithm's denoising path. Our conclusions go both ways: We identify regions of parameters where these methods are unable to sample efficiently, while that is possible using standard Monte Carlo or Langevin approaches. We also identify regions where the opposite happens: standard approaches are inefficient while the discussed generative methods work well. [ABSTRACT FROM AUTHOR]

Limited test data hinder the accurate prediction of mechanical strength and permeability of permeable cement-stabilized base materials (PCBM). Here we show a kriging-based surrogate model assisted artificial neural network (KS-ANN) framework that integrates laboratory testing, mathematical modeling, and machine learning. A statistical distribution model was established from limited test data to enrich the dataset through the combination of markov chain monte carlo simulation and kriging-based surrogate modeling. Subsequently, an artificial neural network (ANN) model was trained using the enriched dataset. The results demonstrate that the well-trained KS-ANN model effectively captures the actual data distribution characteristics. The accurate prediction of the mechanical strength and permeability of PCBM under the constraint of limited data validates the effectiveness of the proposed framework. As compared to traditional ANN models, the KS-ANN model improves the prediction accuracy of PCBM's mechanical strength by 21%. Based on the accurate prediction of PCBM's mechanical strength and permeability by the KS-ANN model, an optimization function was developed to determine the optimal cement content and compaction force range of PCBM, enabling it to concurrently satisfy the requirements of mechanical strength and permeability. This study provides a cost-effective and rapid solution for evaluating the performance and optimizing the design of PCBM and similar materials. Limited data hinders accurate predictions of strength and permeability of permeable cement-stabilized base materials. Here, the authors propose a kriging-based surrogate model assisted neural networks, which improves accuracy by 21% over traditional models. [ABSTRACT FROM AUTHOR]

Effective monitoring of the control charts requires the establishment of appropriate control limits. Various methods have been proposed to determine the fixed control limits (FCLs) based on a specified in‐control average run‐length value, such as Markov chains, integral equations, and Monte Carlo simulations.With the FCLs, the conditional false alarm rate (CFAR) of a control chart varies over time in an unexpected and undesirable way, where the CFAR refers to the probability of a false alarm at a particular time given no previous false alarm. To address this issue, dynamic probability control limits (DPCLs) can be employed to keep the CFAR constant over time. In this study, we determine the DPCLs using fixed and time‐varying sample sizes for the adaptive multivariate EWMA chart when the underlying process is assumed to follow a multivariate normal distribution. The DPCLs are designed to automatically adjust to changes in the probability distribution of the sample size, while maintaining a consistent CFAR. This results in a closely matched run‐length performance for an in‐control process compared to that of the geometric distribution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This article examines the new inverse unit exponential distribution, utilizing both classical and Bayesian methodologies; it begins by presenting the general properties of the proposed model, highlighting characteristic features, such as the presence of a reverse-J or increasing and inverted bathtub-shaped hazard rate function. Furthermore, it explores various statistical properties of the suggested distribution. It employs 12 methods to estimate the associated parameters. A Monte Carlo simulation is conducted to evaluate the accuracy of the estimation procedure. Even for small samples, the results indicate that biases and mean square errors decrease as the sample size increases, demonstrating the robustness of the estimation method. The application of the suggested distribution to real datasets is then discussed. Empirical evidence, using model selection criteria and goodness-of-fit test statistics, supports the assertion that the suggested model outperforms several existing models considered in the study. This article extends its analysis to the Bayesian framework. Using the Hamiltonian Monte Carlo with the no U-turn sampling algorithm, 8000 real samples are generated. The convergence assessment reveals that the chains are convergent and the samples are independent. Subsequently, using the posterior samples, the parameters of the proposed model are estimated, and credible intervals and highest posterior density intervals are computed to quantify uncertainty. The applicability of the suggested model to real data under both classical and Bayesian methodologies provides insights into its statistical properties and performance compared to existing models. [ABSTRACT FROM AUTHOR]

This article constructs an approximate Bayes estimator for the parameter vector consisted of regression coefficients and variance parameter in the linear model in which the error terms follow multivariate t distribution. Its superiorities over the classical estimators are strictly proved in terms of the mean squared error matrix (MSEM) criterion. Compared with the Bayes estimator computed via the MCMC method, the proposed Bayes estimator is simple and easy to interpret and compute, which only requires relatively little prior designation. The numerical computations further verify that the approximate Bayes estimator performs well. Also, the proposed procedure can be easily extended to other multivariate distribution cases. [ABSTRACT FROM AUTHOR]

Context. Analysis of data uncertainties in modeling and forecasting of actuarial processes is very important issue because it allows actuaries to efficiently construct mathematical models and minimize insurance risks considering different situations. Objective. The goal of the following research is to develop an approach that allows for predicting future insurance payments with prior minimization of possible statistical data uncertainty. Method. The proposed method allows for the implementation of algorithms for estimating the parameters of generalized linear models with the preliminary application to data of the optimal Kalman filter. The results demonstrated better forecast results and more adequate model structures. This approach was applied successfully to the simulation procedure of insurance data. For generating insurance dataset the next features of clients were used: age; sex; body mass index (applying normal distribution); number of children (between 0 and 5); smoker status; region (north, east, south, west, center); charges. For creating the last feature normal distribution with known variance and a logarithmic function, exponential distribution with the identity link function and Pareto distribution with a known scale parameter and a negative linear function were used. Results. The proposed approach was implemented in the form of information processing system for solving the problem of predicting insurance payments based on insurance data and with taking into account the noise of the data. Conclusions. The conducted experiments confirmed that the proposed approach allows for more adequate model constructing and accurate forecasting of insurance payments, which is important point in the analysis of actuarial risks. The prospects for further research may include the use of this approach proposed in other fields of insurance related to availability of actuarial risk. A specialized intellectual decision support system should be designed and implemented to solve the problem by using actual insurance data from real world in online mode as well as modern information technologies and intellectual data analysis. [ABSTRACT FROM AUTHOR]

Using a unified hybrid censoring scheme, this study explores statistical inferences for products with lifetimes following the generalized inverted exponential distribution. The model's parameters are estimated using the maximum likelihood approach. In addition, likelihood functions and asymptotic theories are employed to generate approximate confidence intervals. Moreover, Bayesian estimates based on classical likelihood functions are investigated, considering both asymmetric and symmetric loss functions with prior information. It is recommended to approximate the Bayes estimates using Gibbs sampling, which utilizes the Markov chain Monte Carlo technique to establish credible intervals for the parameters. A numerical example is provided to demonstrate the effectiveness of the proposed methods. Furthermore, a simulation study is conducted to illustrate the confidence intervals and the statistical characteristics of the parameters. [ABSTRACT FROM AUTHOR]

The class of semiparametric or transformation models has been presented in the literature as a promising alternative for the analysis of lifetime data in the presence of covariates and censored data. This class of models generalizes the popular class of proportional hazards models proposed by Cox (J R Stat Soc: Ser B (Methodol) 34(2):187–202, 1972) where it is not needed to assume a parametric probability distribution for the survival times. In addition to our focus on semipametric models, we also explore the situation where the population of interest is a mixture of susceptible individuals, who experience the event of interest and non-susceptible individuals that will never experience the event of interest. These individuals are not at risk with respect to the event of interest and are considered immune, non-susceptible, or cured. In this study, we present a simple method to obtain inferences for the parameters of semiparametric or transformation models in the presence of censoring, covariates and cure fraction under a Bayesian approach assuming the unknown hazard rates as latent variables with a given probability distribution. The posterior summaries of interest are obtained using existing Markov Chain Monte Carlo (MCMC) simulation methods. Some applications with real medical survival data illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Allocating patients to treatment arms during a trial based on the observed responses accumulated up to the decision point, and sequential adaptation of this allocation, could minimize the expected number of failures or maximize total benefits to patients. In this study, we developed a Bayesian response‐adaptive randomization (RAR) design targeting the endpoint of organ support‐free days (OSFD) for patients admitted to the intensive care units. The OSFD is a mixture of mortality and morbidity assessed by the number of days of free of organ support within a predetermined post‐randomization time‐window. In the past, researchers treated OSFD as an ordinal outcome variable where the lowest category is death. We propose a novel RAR design for a composite endpoint of mortality and morbidity, for example, OSFD, by using a Bayesian mixture model with a Markov chain Monte Carlo sampling to estimate the posterior probability distribution of OSFD and determine treatment allocation ratios at each interim. Simulations were conducted to compare the performance of our proposed design under various randomization rules and different alpha spending functions. The results show that our RAR design using Bayesian inference allocated more patients to the better performing arm(s) compared to other existing adaptive rules while assuring adequate power and type I error rate control across a range of plausible clinical scenarios. [ABSTRACT FROM AUTHOR]

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set. [ABSTRACT FROM AUTHOR]

Combined sewer overflow (CSO) posed a great threat to the urban aquatic environment of many Chinese cities during the wet weather. For CSO from the specific interceptor well, the drainage capacity of the adjacent downstream interceptor sewer can be viewed as one of the critical thresholds. In this study, the generalized Pareto distribution (GPD) combined with peak over threshold (POT) sampling was used to characterize the excess rainfall intensity (ERI) of CSO events, which is significant for evaluating the severity and intensity of CSO events. First, the 10-year rainfall series were divided into different rainfall events, and the maximum rainfall intensity for the specific rainfall duration (30 min used in this study) over the drainage capacity of interceptor sewers (i.e., ERI) was calculated and sampled from each rainfall event, and its statistic characteristics were analyzed. Moreover, the empirical frequency of excess rainfall intensity (ERI) was calculated by the Weibull formula. Finally, GPD was used for fitting the empirical frequency distribution and its shape, scale parameters were optimized based on the Markov chain Monte Carlo (MCMC) algorithm. It was concluded that: (1) POT sampling combining rainfall event division was appropriate for ERI estimation of CSO events; (2) The Coefficient of skewness (Cs) of ERI was greater than zero for the studied scenarios, which showed that its distribution was right-skewed; (3) The kurtosis of the ERI was greater than three for the studied scenarios, which indicated that its distribution was thick-tailed; (4) GPD was suitable for modeling the theoretical frequency distribution of ERI. [ABSTRACT FROM AUTHOR]

Context. Devising fast and accurate methods of predicting the Lyman-α forest at the field level, avoiding the computational burden of running large-volume cosmological hydrodynamic simulations, is of fundamental importance to quickly generate the massive set of simulations needed by the state-of-the-art galaxy and Lyα forest spectroscopic surveys. Aims. We present an improved analytical model to predict the Lyα forest at the field level in redshift space from the dark matter field, expanding upon the widely used Fluctuating Gunn-Peterson Approximation (FGPA). Instead of assuming a unique universal relation over the whole considered cosmic volume, we introduce a dependence on the cosmic web environment (knots, filaments, sheets, and voids) in the model, thereby effectively accounting for nonlocal bias. Furthermore, we include a detailed treatment of velocity bias in the redshift space distortion modeling, allowing the velocity bias to be cosmic-web-dependent. Methods. We first mapped the dark matter field from real to redshift space through a particle-based relation including velocity bias, depending on the cosmic web classification of the dark matter field in real space. We then formalized an appropriate functional form for our model, building upon the traditional FGPA and including a cutoff and a boosting factor mimicking a threshold and inverse-threshold bias effect, respectively, with model parameters depending on the cosmic web classification in redshift space. Eventually, we fit the coefficients of the model via an efficient Markov chain Monte Carlo scheme. Results. We find evidence for a significant difference between the same model parameters in different environments, suggesting that for the investigated setup the simple standard FGPA is not able to adequately predict the Lyα forest in the different cosmic web regimes. We reproduce the summary statistics of the reference cosmological hydrodynamic simulation that we use for comparison, yielding an accurate mean transmitted flux, probability distribution function, 3D power spectrum, and bispectrum. In particular, we achieve maximum deviation and average deviation accuracy in the Lyα forest 3D power spectrum of ∼3% and ∼0.1% up to k ∼ 0.4 h Mpc−1, and ∼5% and ∼1.8% up to k ∼ 1.4 h Mpc−1. Conclusions. Our new model outperforms previous analytical efforts to predict the Lyα forest at the field level in all the probed summary statistics, and has the potential to become instrumental in the generation of fast accurate mocks for covariance matrices estimation in the context of current and forthcoming Lyα forest surveys. [ABSTRACT FROM AUTHOR]

Background Hypoxia-inducible factor prolyl hydroxylase inhibitors (HIF-PHIs) are oral alternatives to current standard-of-care treatments for anaemia in chronic kidney disease (CKD). We conducted network meta-analyses to indirectly compare clinical outcomes for three HIF-PHIs in dialysis and non-dialysis populations with anaemia in CKD. Methods The evidence base comprised phase III, randomised, controlled trials evaluating daprodustat, roxadustat, or vadadustat. Three outcomes were evaluated: efficacy [change from baseline in haemoglobin (Hgb)], cardiovascular safety [time to first major adverse cardiovascular event (MACE)] and quality of life [change from baseline in 36-Item Short Form Health Survey (SF-36) Vitality score]. Analyses were performed separately for all patients and for erythropoiesis-stimulating agent (ESA) non-users at baseline (non-dialysis population) or prevalent dialysis patients (dialysis population). Bayesian Markov Chain Monte Carlo methods with non-informative priors were used to estimate the posterior probability distribution and generate pairwise treatment comparisons. Point estimates (medians of posterior distributions) and 95% credible intervals (CrI) were calculated. Results Seventeen trials were included. In non-dialysis patients, there were no clinically meaningful differences between the three HIF-PHIs with respect to Hgb change from baseline [all patients analysis (total n  = 7907): daprodustat vs. roxadustat, 0.09 g/dL (95% CrI −0.14, 0.31); daprodustat vs. vadadustat, 0.09 g/dL (−0.04, 0.21); roxadustat vs. vadadustat, 0.00 g/dL (−0.22, 0.22)] or risk of MACE [all patients analysis (total n  = 7959): daprodustat vs. roxadustat, hazard ratio (HR) 1.16 (95% CrI 0.76, 1.77); daprodustat vs. vadadustat, 0.88 (0.71, 1.09); roxadustat vs. vadadustat, 0.76 (0.50, 1.16)]. Daprodustat showed a greater increase in SF-36 Vitality compared with roxadustat [total n  = 4880; treatment difference 4.70 points (95% CrI 0.08, 9.31)]. In dialysis patients, Hgb change from baseline was higher with daprodustat and roxadustat compared with vadadustat [all patients analysis (total n  = 11 124): daprodustat, 0.34 g/dL (0.22, 0.45); roxadustat, 0.38 g/dL (0.27, 0.49)], while there were no clinically meaningful differences in the risk of MACE between the HIF-PHIs [all patients analysis (total n  = 12 320): daprodustat vs. roxadustat, HR 0.89 (0.73, 1.08); daprodustat vs. vadadustat, HR 0.99 (0.82, 1.21); roxadustat vs. vadadustat, HR 1.12 (0.92, 1.37)]. Results were similar in analyses of ESA non-users and prevalent dialysis patients. Conclusions In the setting of anaemia in CKD, indirect treatment comparisons suggest that daprodustat, roxadustat, and vadadustat are broadly clinically comparable in terms of efficacy and cardiovascular safety (precision was low for the latter), while daprodustat may be associated with reduction in fatigue to a greater extent than roxadustat. [ABSTRACT FROM AUTHOR]

This document discusses the importance of specifying prior distributions in reliability analysis, particularly for lifetime probability models. It focuses on the Weibull and log-normal distributions and highlights the challenges of using maximum likelihood estimators when dealing with censored data. The document suggests that Bayesian analysis is a natural choice in such cases and compares Bayes estimators with maximum likelihood estimators. It also discusses the issue of estimating parameters in the three-parameter Weibull distribution and provides examples of informative priors that have been suggested in the literature. The document concludes by proposing a set of priors and an importance sampling technique for implementing Bayesian inference in practice. Additionally, it discusses the use of Bayesian estimation techniques in analyzing data on the strength of carbon fibers, providing an illustrative example and indicating a good fit between the fitted distribution and the empirical data. The document also mentions the availability of the data for further analysis. [Extracted from the article]

This study is anchored in the H2020 SEAMLESS project (https://www.seamlessproject.org , last access: 29 January 2024), which aims to develop ensemble assimilation methods to be implemented in Copernicus Marine Service monitoring and forecasting systems, in order to operationally estimate a set of targeted ecosystem indicators in various regions, including uncertainty estimates. In this paper, a simplified approach is introduced to perform a 4D (space–time) ensemble analysis describing the evolution of the ocean ecosystem. An example application is provided, which covers a limited time period in a limited subregion of the North Atlantic (between 31 and 21 ∘ W, between 44 and 50.5 ∘ N, between 15 March and 15 June 2019, at a 1/4 ∘ and a 1 d resolution). The ensemble analysis is based on prior ensemble statistics from a stochastic NEMO (Nucleus for European Modelling of the Ocean)–PISCES simulator. Ocean colour observations are used as constraints to condition the 4D prior probability distribution. As compared to classic data assimilation, the simplification comes from the decoupling between the forward simulation using the complex modelling system and the update of the 4D ensemble to account for the observation constraint. The shortcomings and possible advantages of this approach for biogeochemical applications are discussed in the paper. The results show that it is possible to produce a multivariate ensemble analysis continuous in time and consistent with the observations. Furthermore, we study how the method can be used to extrapolate analyses calculated from past observations into the future. The resulting 4D ensemble statistical forecast is shown to contain valuable information about the evolution of the ecosystem for a few days after the last observation. However, as a result of the short decorrelation timescale in the prior ensemble, the spread of the ensemble forecast increases quickly with time. Throughout the paper, a special emphasis is given to discussing the statistical reliability of the solution. Two different methods have been applied to perform this 4D statistical analysis and forecast: the analysis step of the ensemble transform Kalman filter (with domain localization) and a Monte Carlo Markov chain (MCMC) sampler (with covariance localization), both enhanced by the application of anamorphosis to the original variables. Despite being very different, the two algorithms produce very similar results, thus providing support to each other's estimates. As shown in the paper, the decoupling of the statistical analysis from the dynamical model allows us to restrict the analysis to a few selected variables and, at the same time, to produce estimates of additional ecological indicators (in our example: phenology, trophic efficiency, downward flux of particulate organic matter). This approach can easily be appended to existing operational systems to focus on dedicated users' requirements, at a small additional cost, as long as a reliable prior ensemble simulation is available. It can also serve as a baseline to compare with the dynamical ensemble forecast and as a possible substitute whenever useful. [ABSTRACT FROM AUTHOR]

For stochastic models with large numbers of states, analytical techniques are often impractical, and simulations time-consuming and computationally demanding. This limitation can hinder the practical implementation of such models. In this study, we demonstrate how neural networks can be used to develop emulators for two outputs of a stochastic within-host model of Francisella tularensis infection: the dose-dependent probability of illness and the incubation period. Once the emulators are constructed, we employ Markov Chain Monte Carlo sampling methods to parameterize the within-host model using records of human infection. This inference is only possible through the use of a mixture density network to emulate the incubation period, providing accurate approximations of the corresponding probability distribution. Notably, these estimates improve upon previous approaches that relied on bacteria counts from the lungs of macaques. Our findings reveal a 50% infectious dose of approximately 10 colony-forming units and we estimate that the incubation period can last for up to 11 days following low dose exposure. Author summary: Francisella tularensis is a highly infectious bacterium that remains in the top category of biothreat agents. Release of aerosolized bacteria could lead to many cases of acute and severe pneumonia over the days following. Mathematical modelling can contribute to the response to such an outbreak, combining dispersion models and disease models to identify the source of release and predict where cases are most likely to occur. However, these models can be computationally demanding and time consuming to run. In this article, we use neural networks to emulate the likelihood of disease and the duration of the incubation period from a stochastic within-host model. This enables rapid predictions to be made across a wide range of doses, thereby improving the practical applications of the model. [ABSTRACT FROM AUTHOR]

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built Eryn , a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the Laser Interferometer Space Antenna Global Fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases. [ABSTRACT FROM AUTHOR]

We explore models of massive (>1010 M⊙) satellite quenching in massive clusters at z ≳ 1 using an MCMC framework, focusing on two primary parameters: R quench (the host-centric radius at which quenching begins) and τquench (the time-scale upon which a satellite quenches after crossing R quench). Our MCMC analysis shows two local maxima in the 1D posterior probability distribution of R quench at approximately 0.25 and 1.0  R 200. Analysing four distinct solutions in the τquench– R quench parameter space, nearly all of which yield quiescent fractions consistent with observational data from the GOGREEN survey, we investigate whether these solutions represent distinct quenching pathways and find that they can be separated between 'starvation' and 'core quenching' scenarios. The starvation pathway is characterized by quenching time-scales that are roughly consistent with the total cold gas (H2 + H  i) depletion time-scale at intermediate z , while core quenching is characterized by satellites with relatively high line-of-sight velocities that quench on short time-scales (∼0.25 Gyr) after reaching the inner region of the cluster (<0.30  R 200). Lastly, we break the degeneracy between these solutions by comparing the observed properties of transition galaxies from the GOGREEN survey. We conclude that only the 'starvation' pathway is consistent with the projected phase-space distribution and relative abundance of transition galaxies at z ∼ 1. However, we acknowledge that ram pressure might contribute as a secondary quenching mechanism. [ABSTRACT FROM AUTHOR]

We present the first version release of SESAMME, a public, Python-based full spectrum fitting tool for Simultaneous Estimates of Star-cluster Age, Metallicity, Mass, and Extinction. SESAMME compares an input spectrum of a star cluster to a grid of stellar population models with an added nebular continuum component, using Markov Chain Monte Carlo methods to sample the posterior probability distribution in four dimensions: cluster age, stellar metallicity Z, reddening E (B − V), and a normalization parameter equivalent to a cluster mass. SESAMME is highly flexible in the stellar population models that it can use to model a spectrum; our testing and initial science applications use both BPASS and Starburst99. We illustrate the ability of SESAMME to recover accurate ages and metallicities even at a moderate signal-to-noise ratio (S/N ∼ 3–5 per wavelength bin) using synthetic, noise-added model spectra of young star clusters. Finally, we test the consistency of SESAMME with other age and metallicity estimates from the literature using a sample of Hubble Space Telescope/Cosmic Origins Spectrograph far-UV spectra toward young, massive clusters in M83 and NGC 1313. We find that, on the whole, SESAMME infers star cluster properties that are consistent with the literature in both low- and high-metallicity environments. [ABSTRACT FROM AUTHOR]

Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases the number of variables used to parameterize these coefficients is large, and oobtaining meaningful statistics of their probability distributions is difficult using simple sampling methods such as the basic Metropolis- Hastings algorithm--in particular, if the inverse problem is ill-conditioned or ill-posed. As a consequence, many advanced sampling methods have been described in the literature that converge faster than Metropolis-Hastings, for example, by exploiting hierarchies of statistical models or hierarchies of discretizations of the underlying differential equation. At the same time, it remains difficult for the reader of the literature to quantify the advantages of these algorithms because there is no commonly used benchmark. This paper presents a benchmark Bayesian inverse problem--namely, the determination of a spatially variable coefficient, discretized by 64 values, in a Poisson equation, based on point measurements of the solution--that fills the gap between widely used simple test cases (such as superpositions of Gaussians) and real applications that are difficult to replicate for developers of sampling algorithms. We provide a complete description of the test case and provide an open-source implementation that can serve as the basis for further experiments. We have also computed 2 x 1011 samples, at a cost of some 30 CPU years, of the posterior probability distribution from which we have generated detailed and accurate statistics against which other sampling algorithms can be tested. [ABSTRACT FROM AUTHOR]

Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples. [ABSTRACT FROM AUTHOR]

The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Markov Chain Monte Carlo (MCMC) sampling methods have been adapted to handle different types of constraints on random variables. Among these methods, Hamilton Monte Carlo (HMC) and the related approaches have shown significant advantages in terms of computational efficiency compared with other counterparts. In this article, we first review HMC and some extended sampling methods, and then we concretely explain three constrained HMC‐based sampling methods, reflection, reformulation, and spherical HMC. For illustration, we apply these methods to solve three well‐known constrained sampling problems, truncated multivariate normal distributions, Bayesian regularized regression, and nonparametric density estimation. In this review, we also connect constrained sampling with another similar problem in the statistical design of experiments with constrained design space. This article is categorized under:Applications of Computational Statistics > Computational MathematicsStatistical and Graphical Methods of Data Analysis > Bayesian Methods and TheoryStatistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)Statistical and Graphical Methods of Data Analysis > Sampling [ABSTRACT FROM AUTHOR]

In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturbation theory, its time-dependent probability characteristics can be approximately obtained from another Markov chain, having piecewise constant intensities and the same state space. The approximation error (the taxicab distance between the state probability distributions) is provided. It is shown how the Cauchy operator and the state probability distribution for an arbitrary initial condition can be calculated. The findings are illustrated with the numerical examples. [ABSTRACT FROM AUTHOR]

In life testing and reliability studies, most researchers have used the maximum likelihood estimation method to estimate unknown parameters, even though it has been proven that the maximum product of spacing method has properties as good as the maximum likelihood estimation method and sometimes even better. In this study, we aim to estimate the unknown parameters of the modified Kies exponential distribution along with the reliability and hazard rate functions under progressive type-II censoring scheme. The maximum likelihood and maximum product of spacing methods are considered in order to find the point estimates and approximate confidence intervals of the various parameters. Moreover, Bayesian estimations based on the likelihood function and the product of the spacing function of the unknown parameters are obtained using the squared error loss function with independent gamma priors. It is observed that the joint posterior distributions have complicated forms. Because of this, Lindley's approximation and the Markov chain Monte Carlo technique are used to obtain the Bayesian estimates and highest posterior credible intervals. Monte Carlo simulations are performed in order to evaluate the performance of the proposed estimation methods. Two real datasets are studied to demonstrate the efficacy of the offered methodologies and highlight how simple and applicable it might be to apply them in practical fields. [ABSTRACT FROM AUTHOR]

In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. However, the literature mainly focused on the bivariate case, since the constraints on the multivariate copulas correlation matrices would make the specifications of covariates arduous. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. We present a novel inferential approach for multivariate distributions, which combines the flexibility of vine constructions with the advantages of Bayesian nonparametrics, not requiring the specification of parametric families for each pair copula. Expressing multivariate copulas using vines allows us to easily account for covariate specifications driving the dependence between response variables. We specify the vine copula density as an infinite mixture of Gaussian copulas, defining a Dirichlet process prior on the mixing measure, and performing posterior inference via Markov chain Monte Carlo sampling. Our approach is successful as for clustering as well as for density estimation. We carry out simulation studies and apply the proposed approach to analyze a veterinary dataset and to investigate the impact of natural disasters on financial development. for this article are available online. [ABSTRACT FROM AUTHOR]

In many seismological, environmental and engineering applications a detailed S -wave velocity model of the shallow subsurface is required. This is generally achieved by the inversion of surface wave dispersion curves using various inversion methods. The classical inversion approaches suffer from several shortcomings, such as inaccurate solutions due to local minima or large computation times in case of a wide parameter space. A number of machine learning (ML) approaches have been suggested to tackle these problems, which however do not provide probabilistic solutions and/or constrain layer number and layer thickness to a fixed value. In this study, we develop a novel neural network (NN) approach in order to characterize the shallow velocity structure from Love and Rayleigh wave dispersion curves. The novelty of our method lies in the simultaneous estimation of layer numbers, layer depth and a complete probability distribution of the S -wave velocity structure. This is achieved by a two-step ML approach, where (1) a regular NN classifies the number of layers within the upper 100 m of the subsurface and (2) a mixture density network outputs the depth estimates together with a fully probabilistic solution of the S -wave velocity structure. We show the advantages of our ML approach compared to a conventional neighbourhood inversion and a Markov chain Monte Carlo algorithm. Our ML approach is then applied to dispersion curves extracted from recorded noise data in Munich, Germany. The resulting velocity profile is in accordance with lithologic information at the site, which highlights the potential of our approach. [ABSTRACT FROM AUTHOR]

Creep behavior is susceptible to uncertainty. Replicated creep data for steel can exhibit logarithm decades of uncertainty, which necessitates the development of probabilistic creep models for reliability‐based design. The deterministic Wilshire–Cano–Stewart (WCS) model is transformed into a probabilistic creep deformation, damage, and rupture prediction model via injecting the uncertainty of test conditions, pre‐existing damage, and material constants. The WCS model is calibrated to replicated quintuplicate creep data from a "single heat" of 304 stainless steel. The Markov chain Monte Carlo (MCMC) method with the Metropolis–Hastings (MH) algorithm is employed to introduce the sources of uncertainties into the model via calibrated probability distribution functions (pdfs). The probabilistic predictions encapsulate most of the experimental outliers across isostresses‐isotherms. Interpolative and extrapolative assessments reveal that minimum‐creep‐strain‐rate (MCSR) and stress rupture (SR) predictions are consistent across isotherms. The WCS probabilistic model captures the range of creep behavior of a single heat of material using short‐term data. Highlights: A probabilistic creep‐damage model is developed by introducing uncertainties of creep.Probabilistic creep curves replicate observed uncertainty in creep data.Interpolative and extrapolative prediction by probabilistic model exhibits physical realism.Probabilistic WCS model exhibits expected range of scatter in MCSR, SR, and ductility. [ABSTRACT FROM AUTHOR]

This study is anchored in the H2020 SEAMLESS project (www.seamlessproject.org), which aims to develop ensemble assimilation methods to be implemented in Copernicus Marine Service monitoring and forecasting systems, in order to operationally estimate a set of targeted ecosystem indicators in various regions, including uncertainty estimates. In this paper, a simplified approach is introduced to perform a 4D (space-time) ensemble analysis describing the evolution of the ocean ecosystem. An example application is provided, which covers a limited time period in a limited subregion of the North Atlantic (between 31°W and 21°W, between 44°N and 50.5°N, between March 15 and June 15, 2019, at a 1/4° and a 1 day resolution). The ensemble analysis is based on prior ensemble statistics from a stochastic NEMO/PISCES simulator. Ocean colour observations are used as constraints to condition the 4D prior probability distribution. As compared to classic data assimilation, the simplification comes from the decoupling between the forward simulation using the complex modelling system and the update of the 4D ensemble to account for the observation constraint. The shortcomings and possible advantages of this approach for biogeochemical applications are discussed in the paper. The results show that it is possible to produce a multivariate ensemble analysis continuous in time and consistent with the observations. Furthermore, we study how the method can be used to extrapolate analyses calculated from past observations into the future. The resulting 4D ensemble statistical forecast is shown to contain valuable information about the evolution of the ecosystem for a few days after the last observation. However, as a result of the short decorrelation time scale in the prior ensemble, the spread of the ensemble forecast is increasing quickly with time. Throughout the paper, a special emphasis is given to discussing the statistical reliability of the solution. Two different methods have been applied to perform this 4D statistical analysis and forecast: the analysis step of the Ensemble Transform Kalman Filter (with domain localization) and a Monte Carlo Markov Chain (MCMC) sampler (with covariance localization), both enhanced by the application of anamorphosis to the original variables. Despite being very different, the two algorithms produce very similar results, thus somehow validating each other. As shown in the paper, the decoupling of the statistical analysis from the dynamical model allows us to restrict the analysis to a few selected variables and, at the same time, to produce estimates of additional ecological indicators (in our example: phenology, trophic efficiency, downward flux of particulate organic matter). This approach can easily be appended to existing operational systems to focus on dedicated users' requirements, at small additional cost, as long as a reliable prior ensemble simulation is available. It can also serve as a baseline to compare with the dynamical ensemble forecast, and as a possible substitute whenever useful. [ABSTRACT FROM AUTHOR]

This study is anchored in the H2020 SEAMLESS project (www.seamlessproject.org), which aims to develop ensemble assimilation methods to be implemented in Copernicus Marine Service monitoring and forecasting systems, in order to operationally estimate a set of targeted ecosystem indicators in various regions, including uncertainty estimates. In this paper, a simplified approach is introduced to perform a 4D (space-time) ensemble analysis describing the evolution of the ocean ecosystem. An example application is provided, which covers a limited time period in a limited subregion of the North Atlantic (between 31° W and 21° W, between 44° N and 50.5° N, between March 15 and June 15, 2019, at a 1/4° and a 1 day resolution). The ensemble analysis is based on prior ensemble statistics from a stochastic NEMO/PISCES simulator. Ocean colour observations are used as constraints to condition the 4D prior probability distribution. As compared to classic data assimilation, the simplification comes from the decoupling between the forward simulation using the complex modelling system and the update of the 4D ensemble to account for the observation constraint. The shortcomings and possible advantages of this approach for biogeochemical applications are discussed in the paper. The results show that it is possible to produce a multivariate ensemble analysis continuous in time and consistent with the observations. Furthermore, we study how the method can be used to extrapolate analyses calculated from past observations into the future. The resulting 4D ensemble statistical forecast is shown to contain valuable information about the evolution of the ecosystem for a few days after the last observation. However, as a result of the short decorrelation time scale in the prior ensemble, the spread of the ensemble forecast is increasing quickly with time. Throughout the paper, a special emphasis is given to discussing the statistical reliability of the solution. Two different methods have been applied to perform this 4D statistical analysis and forecast: the analysis step of the Ensemble Transform Kalman Filter (with domain localization) and a Monte Carlo Markov Chain (MCMC) sampler (with covariance localization), both enhanced by the application of anamorphosis to the original variables. Despite being very different, the two algorithms produce very similar results, thus somehow validating each other. As shown in the paper, the decoupling of the statistical analysis from the dynamical model allows us to restrict the analysis to a few selected variables and, at the same time, to produce estimates of additional ecological indicators (in our example: phenology, trophic efficiency, downward flux of particulate organic matter). This approach can easily be appended to existing operational systems to focus on dedicated users' requirements, at small additional cost, as long as a reliable prior ensemble simulation is available. It can also serve as a baseline to compare with the dynamical ensemble forecast, and as a possible substitute whenever useful. [ABSTRACT FROM AUTHOR]

The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by R = P[Y < X < Z], where X is the strength of the system and Y and Z are the stresses. We look at how X, Y and Z fit into a well-known discrete distribution known as the geometric distribution. The stress-strength reliability of this form is not widely studied in the current literature, and research in this area has only considered the scenario when the strength and stress variables follow a continuous distribution, although it is essentially nil in the case of discrete stress and strength. There are numerous applications wherein a system is exposed to external stress, and its functionality depends on whether its intrinsic physical strength falls within specific stress limits. Furthermore, the continuous measurement of stress and strength variables presents inherent diffculties and inconveniences in such scenarios. For the suggested distribution, we obtain the maximum likelihood estimate of the variable R, as well as its asymptotic distribution and confidence interval. Additionally, in the classical setup, we find the boot-p and boot-t confidence intervals for R. In the Bayesian setup, we utilize the widely recognized Markov Chain Monte Carlo technique and the Lindley approximation method to find the Bayes estimate of R under the squared error loss function. A Monte Carlo simulation study and real data analysis are demonstrated to show the applicability of the suggested model in the real world. [ABSTRACT FROM AUTHOR]

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results. [ABSTRACT FROM AUTHOR]

The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall–Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year. [ABSTRACT FROM AUTHOR]

Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure probabilities against stated criteria. As a result, efficient stochastic simulation schemes are central to computational frameworks that aim to estimate failure probabilities associated with multiple limit states using limited sample sets. In this work, a generalized stratified sampling scheme is proposed in which two phases of sampling are involved: the first is devoted to the generation of strata-wise samples and the estimation of strata probabilities, whereas the second phase aims at the estimation of strata-wise failure probabilities. Phase-I sampling enables the selection of a generalized stratification variable (i.e., not necessarily belonging to the input set of random variables) for which the probability distribution is not known a priori. To improve the efficiency, Markov Chain Monte Carlo Phase-I sampling is proposed when Monte Carlo simulation is deemed infeasible, and optimal Phase-II sampling is implemented based on user-specified target coefficients of variation for the limit states of interest. The expressions for these coefficients are derived with due regard to the sample correlations induced by the Markov chains and the uncertainty in the estimated strata probabilities. The proposed stochastic simulation scheme reaps the benefits of near-optimal stratified sampling for a broader choice of stratification variables in high-dimensional reliability problems with a mechanism to approximately control the accuracy of the estimators of multiple failure probabilities. The practicality and efficiency of the scheme are demonstrated using two examples involving the estimation of failure probabilities associated with highly nonlinear responses induced by wind and seismic excitations. [ABSTRACT FROM AUTHOR]

A novel discrete Poisson mixing probability distribution with two parameters has been developed by combining the Poisson distribution with the transmuted moment exponential distribution. It is possible to deduce several mathematical properties, such as the moment-generating function, ordinary moments, moments about the mean, skewness, kurtosis, and the dispersion index. The maximum likelihood estimation method is utilized to estimate the model's parameters. A thorough simulation study is utilized to determine the behavior of the generated estimators. Estimating model parameters using a Bayesian methodology is another primary topic of this research. The behavior of Bayesian estimates is evaluated by first charting the trace, then generating 1,005,000 iterations of the Markov chain Monte Carlo method. In addition to this, we suggest a new count regression model that uses Poisson and negative binomial models in an alternating fashion. In conclusion, asymmetric datasets derived from various research areas are utilized for practical applications. [ABSTRACT FROM AUTHOR]

Modeling the failure times of processors and memories in computers is crucial for ensuring the reliability and robustness of data science workflows. By understanding the failure characteristics of the hardware components, data scientists can develop strategies to mitigate the impact of failures on their computations, and design systems that are more fault-tolerant and resilient. In particular, failure time modeling allows data scientists to predict the likelihood and frequency of hardware failures, which can help inform decisions about system design and resource allocation. In this paper, we aimed to model the failure times of processors and memories of computers; this was performed by formulating a new type of bivariate model using the copula function. The modified extended exponential distribution is the suggested lifetime of the experimental units. It was shown that the new bivariate model has many important properties, which are presented in this work. The inferential statistics for the distribution parameters were obtained under the assumption of a Type-II censored sampling scheme. Therefore, point and interval estimation were observed using the maximum likelihood and the Bayesian estimation methods. Additionally, bootstrap confidence intervals were calculated. Numerical analysis via the Markov Chain Monte Carlo method was performed. Finally, a real data example of processors and memories failure time was examined and the efficiency of the new bivariate distribution of fitting the data sample was observed by comparing it with other bivariate models. [ABSTRACT FROM AUTHOR]

A major limitation of traditional joint shear strength models is the fact that they cannot consider the shear-resistance mechanisms and various uncertainties comprehensively. To overcome this limitation, a hybrid mechanical- and data-driven model for probabilistic shear strength of reinforced concrete (RC) interior beam-column joints was proposed. A simplified deterministic mechanical model for shear strength of RC interior beam-column joints was derived first. Then, a probabilistic shear strength model for RC interior beam-column joints was developed using a data-driven approach considering both aleatory and epistemic uncertainties. Moreover, the posterior distributions of probabilistic model parameters were updated by means of the Bayesian theory and the Markov chain Monte Carlo method. Finally, the proposed probabilistic shear strength model was verified by using available experimental data and seven typical shear strength models. Comparisons show that the proposed model not only provides reasonable prediction accuracy but also describes the probability distribution of RC interior beam-column joints realistically. Furthermore, the proposed model is useful for the calibration of accuracy and applicability of available deterministic shear strength models, which provide probabilistic calibration methods based on the confidence interval and probability density function. [ABSTRACT FROM AUTHOR]

Markov Chain Monte Carlo simulations form an essential tool for exploring high‐dimensional target distributions. Metropolis developed a fundamental random walk algorithm which was improved by Hastings later. The result is known as the Metropolis‐Hastings algorithm, which enables the exploration of multi‐dimensional distributions. The main drawbacks of this algorithm are its high auto‐correlation and slow exploration of the target distribution space. In order to increase efficiency, researchers have proposed various modifications to this algorithm. In particular, the Hamiltonian Monte Carlo simulation enhances the efficient exploration of the target probability density. The algorithm uses mechanisms inspired by Hamiltonian dynamics to propose a new sample for the target distribution. For reliability analysis, the incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results. However, using the Hamiltonian Monte Carlo method to sample is computationally expensive, especially when dealing with high‐dimensional problems and performing several steps to propose a new state. In this contribution, we show the general applicability of Hamiltonian neural networks to speed up the proposal of new samples within the Hamiltonian Monte Carlo method. [ABSTRACT FROM AUTHOR]

The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation methods of the maximum likelihood and Bayesian are utilized to infer the system reliability. For the Bayesian estimation method, informative and non-informative priors combined with three loss functions are considered. Because the computational difficulty on working posteriors, the Markov chain Monte Carlo method is adopted to obtain the approximation of the reliability estimator posterior. In addition, the bootstrap method and highest probability density interval are used to obtain the reliability confidence intervals. The simulation study shows that the Bayes estimator with informative prior is superior to other competitors. Finally, two real examples are given to illustrate the proposed estimation methods. [ABSTRACT FROM AUTHOR]

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering method for both samples and observations, we investigate a nonparametric prior that arises as the composition of two different discrete random structures and derive a closed‐form expression for the induced distribution of the random partition, the fundamental tool regulating the clustering behavior of the model. On the one hand, this allows to gain a deeper insight into the theoretical properties of the model and, on the other hand, it yields an MCMC algorithm for evaluating Bayesian inferences of interest. Moreover, we single out limitations of this algorithm when working with more than two populations and, consequently, devise an alternative more efficient sampling scheme, which as a by‐product, allows testing homogeneity between different populations. Finally, we perform a comparison with the nested Dirichlet process and provide illustrative examples of both synthetic and real data. [ABSTRACT FROM AUTHOR]

Well logs are geophysical measurements of rock properties acquired continuously along a borehole. Because of the physics underlying their operation, borehole logging instruments perform local spatial averages of rock properties in the vicinity of the borehole, yielding well logs that are often affected by tool design, layer boundaries, borehole environmental conditions and mud‐filtrate invasion. Such environmental effects are ubiquitous and can lead to errors in petrophysical–property estimations from well logs if not accounted for in the interpretation. Separate well‐log inversion mitigates environmental effects by matching well logs with their numerical simulations. The latter simulations rely on specific assumptions about the relative geometry of the borehole and the rocks penetrated by the well. For vertical wells penetrating horizontal layers, it is common to assume piecewise‐constant layer properties that we collectively refer to as the earth model; some of these properties have a direct relationship to well logs (e.g. resistivity, gamma ray, density and acoustic slowness). Well‐log inversion is traditionally approached with deterministic methods such as the Levenberg–Marquardt algorithm to minimize the differences between well logs and their numerical simulations, often without accounting for the relationship between measurement noise and model uncertainty. Bayesian inversion, on the other hand, yields the posterior probability distribution of estimated properties and intrinsically quantifies their uncertainty. However, Bayesian Well‐log inversion usually involves the implementation of Markov chain Monte Carlo sampling, which requires a prohibitive number of forward simulations and is therefore not suitable for rapid petrophysical and/or elastic and mechanical evaluations of rocks. We introduce an efficient Bayesian Well‐log inversion method using a gradient‐based Markov chain Monte Carlo method. Gradient‐based Markov chain Monte Carlo is a group of relatively new Markov chain Monte Carlo algorithms that combine gradient updates with Hessian‐based sampling. gradient‐based Markov chain Monte Carlo draws samples efficiently from the posterior probability distribution using the gradient information to guide samples towards high‐probability regions and the Hessian to approximate the posterior probability distribution locally. We verify the gradient‐based Markov chain Monte Carlo inversion method with the inversion of synthetic well logs, including gamma ray, resistivity, density, neutron porosity, photoelectric factor and compressional/shear‐wave slowness. Results show that gradient‐based Markov chain Monte Carlo decreases the computational cost by more than 90% compared to conventional Markov chain Monte Carlo sampling. Next, gradient‐based Markov chain Monte Carlo inversion is applied to a field example from the Central North Sea, where conventional interpretation methods yield shale concentration, sandstone porosity and water saturation with errors up to 19.2%, 14.9% and 48.8%, respectively. Gradient‐based Markov chain Monte Carlo inversion products satisfactorily reproduce the available measurements with only a modest increase in computational cost compared to deterministic inversion approaches. [ABSTRACT FROM AUTHOR]

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the Bayesian framework with the Markov Chain Monte Carlo algorithm is used to determine the posterior distribution of unknown parameters. To handle the computational burden, a lumped one-dimensional model is proposed. The lumped model approximations are considered within the parameter estimation procedure thanks to the Approximation Error Model. The experiments are carried out for several configurations of chamber ventilator speed. Experimental observations are obtained through a complete measurement uncertainty propagation. By solving the inverse problem, accurate probability distributions are determined. Additional investigations are performed to demonstrate the reliability of the lumped model, in terms of accuracy and computational gains. [ABSTRACT FROM AUTHOR]

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and Metropolis – Hastings algorithms. The proposed techniques are applied to simulated data following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method was well performed in all simulation scenarios with respect to different sample sizes. [ABSTRACT FROM AUTHOR]

Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the different uncertainty components involved in SciML model identification. Hence, this work proposes a comprehensive methodology for uncertainty evaluation of the SciML that also considers several possible sources of uncertainties involved in the identification process. The uncertainties considered in the proposed method are the absence of a theory, causal models, sensitivity to data corruption or imperfection, and computational effort. Therefore, it is possible to provide an overall strategy for uncertainty-aware models in the SciML field. The methodology is validated through a case study developing a soft sensor for a polymerization reactor. The first step is to build the nonlinear model parameter probability distribution (PDF) by Bayesian inference. The second step is to obtain the machine learning model uncertainty by Monte Carlo simulations. In the first step, a PDF with 30,000 samples is built. In the second step, the uncertainty of the machine learning model is evaluated by sampling 10,000 values through Monte Carlo simulation. The results demonstrate that the identified soft sensors are robust to uncertainties, corroborating the consistency of the proposed approach. [ABSTRACT FROM AUTHOR]

Examining life-testing experiments on a product or material usually requires a long time of monitoring. To reduce the testing period, units can be tested under more severe than normal conditions, which are called accelerated life tests (ALTs). The objective of this study is to investigate the problem of point and interval estimations of the Lomax distribution under constant stress partially ALTs based on progressive first failure type-II censored samples. The point estimates of unknown parameters and the acceleration factor are obtained by using maximum likelihood and Bayesian approaches. Since reliability data are censored, the maximum likelihood estimates (MLEs) are derived utilizing the general expectation-maximization (EM) algorithm. In the process of Bayesian inference, the Bayes point estimates as well as the highest posterior density credible intervals of the model parameters and acceleration factor, are reported. This is done by using the Markov Chain Monte Carlo (MCMC) technique concerning both symmetric (squared error) and asymmetric (linear-exponential and general entropy) loss functions. Monte Carlo simulation studies are performed under different sizes of samples for comparison purposes. Finally, the proposed methods are applied to oil breakdown times of insulating fluid under two high-test voltage stress level data. [ABSTRACT FROM AUTHOR]