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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]

In multivariate time series analysis, the Yule-Walker method refers to a system of equations relating the cross-covariances of a stationary vector autoregressive (VAR) model with the matrices of the autoregressive coefficients and the covariance matrix of the noise, both of which are unknown to be estimated. In Bayesian inference of VAR models, one of the key problems is the setting of the prior distributions on these unknown parameters. The Yule-Walker equations are used here to develop a novel prior specification that exploits the reparameterization of the unknowns in terms of the mean, the cross-covariances, and the covariance of the process. Further, the cross-covariance matrices are separated out in terms of the standard deviations and the correlations. All these new quantities are easier to handle because it is more common to have prior information on the mean and the correlation structure of a multiple time series rather than the underlying autoregressive coefficients and the white noise process. The proposed prior specification is suitable for both non informative and informative settings. Through the Yule-Walker based prior, parameter estimation and structure learning of the stationary VAR models are performed via Markov chain Monte Carlo methods. The methodology is illustrated via some synthetic data sets, a benchmark example, and an environmental time series. [ABSTRACT FROM AUTHOR]

The spectroscopic survey of the China's Space Survey Telescope (CSST) is expected to obtain a huge number of slitless spectra, including more than one hundred million galaxy spectra and millions of active galactic nuclei (AGNs) spectra. By making use of these spectra, we can measure the Baryon Acoustic Oscillation (BAO) signals over large redshift ranges with excellent precisions. In this work, we predict the CSST measurements of the post-reconstruction galaxy power spectra at |$0\lt z\lt 1.2$| and pre-reconstruction AGN power spectra at |$0\lt z\lt 4$|⁠ , and derive the BAO signals at different redshift bins by constraining the BAO scaling parameters using the Markov Chain Monte Carlo method. Our result shows that the CSST spectroscopic survey can provide accurate BAO measurements with precisions higher than 1 and 3 per cent for the galaxy and AGN surveys, respectively. By comparing with current measurements in the same range at low redshifts, this can improve the precisions by a factor of |$2\sim 3$|⁠ , and similar precisions can be obtained in the pessimistic case. We also investigate the constraints on the cosmological parameters using the measured BAO data by the CSST , and obtain stringent constraint results for the energy density of dark matter, Hubble constant, and equation of state of dark energy. [ABSTRACT FROM AUTHOR]

In order to constrain the evolutionary history of the Milky Way, we hunt for faint RR Lyrae stars (RRLs) using Dark Energy Camera data from the High cadence Transient Survey and the Halo Outskirts With Variable Stars survey. We report the detection of |$\sim$| 500 RRLs, including previously identified stars and |$\sim$| 90 RRLs not yet reported. We identify nine new RRLs beyond 100 kpc from the Sun, most of which are classified as fundamental-mode pulsators. The periods and amplitudes of the distant RRLs do not place them in either one of the two classical Oosterhoff groups, but in the Oosterhoff intermediate region. We detect two groups of clumped distant RRLs with similar distances and equatorial coordinates, which we interpret as an indication of their association with undiscovered bound or unbound satellites. We study the halo density profile using spheroidal and ellipsoidal (⁠|$q=0.7$|⁠) models, following a Markov chain Monte Carlo methodology. For a spheroidal halo, our derived radial profile is consistent with a broken power law with a break at |$18.1^{+2.1}_{-1.1}$| kpc separating the inner and the outer halo, and an outer slope of |$-4.47^{+0.11}_{-0.18}$|⁠. For an ellipsoidal halo, the break is located at |$24.3^{+2.6}_{-3.2}$| kpc and the outer slope is |$-4.57^{+0.17}_{-0.25}$|⁠. The break in the density profile is a feature visible in different directions of the halo. The similarity of these radial distributions with previous values reported in the literature seems to depend on the regions of the sky surveyed (direction and total area) and halo tracer used. Our findings are compatible with simulations and observations that predict that the outer regions of Milky Way-like galaxies are mainly composed of accreted material. [ABSTRACT FROM AUTHOR]

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results. [ABSTRACT FROM AUTHOR]

When it comes to modelling complex systems using an agent-based approach, there is a problem of choosing the appropriate parameter optimisation technique. This problem is further aggravated by the fact that the parameter space in complex agent-based systems can have a large dimension, and the time required to perform numerical experiments can be large. An alternative approach to traditional optimisation methods are the so-called metaheuristic algorithms, which provide an approximate solution in an acceptable time. The purpose of this study is to compare various metaheuristic algorithms for parameter tuning and to analyse their effectiveness applied to two agent-based models with different complexities. In this study, we considered commonly used metaheuristic algorithms for agent-based model optimisation: the Markov chain Monte Carlo method, the surrogate modelling approach, the particle swarm optimisation algorithm, and the genetic algorithm, as well as the more novel chaos game optimisation algorithm. The proposed algorithms were tested on two agent-based models, one of which was a simple toy model of the spread of contagious disease, and the other was a more complex model of the circulation of respiratory viruses in a city with 10 million agents and 26 calibrated parameters. [ABSTRACT FROM AUTHOR]

AbstractApproximate Bayesian computation (ABC) is a class of Bayesian inference algorithms that targets problems with intractable or unavailable likelihood functions. It uses synthetic data drawn from the simulation model to approximate the posterior distribution. However, ABC is computationally intensive for complex models in which simulating synthetic data is very expensive. In this article, we propose an early rejection Markov chain Monte Carlo (ejMCMC) sampler based on Gaussian processes to accelerate inference speed. We early reject samples in the first stage of the kernel using a discrepancy model, in which the discrepancy between the simulated and observed data is modeled by Gaussian process (GP). Hence, synthetic data is generated only if the parameter space is worth exploring. We demonstrate through theory, simulation experiments, and real data analysis that the new algorithm significantly improves inference efficiency compared to existing early-rejection MCMC algorithms. In addition, we employ our proposed method within an ABC sequential Monte Carlo (SMC) sampler. In our numerical experiments, we use examples of ordinary differential equations, stochastic differential equations, and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We develop an R package that is available at https://github.com/caofff/ejMCMC. [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 this study, we define a series system with n$n$ non‐independent and non‐identical components using a shock model with n+1$n+1$ sources of fatal shocks. Here, it is assumed that the shocks happen randomly and independently, following a Weibull distribution with various scale and shape parameters. A dependability model with 2(n+1)$2(n+1)$ unknown parameters is produced by this process. Making statistical conclusions about the model parameters is the main objective of this research. We apply the maximum likelihood and Bayes approaches to determine the model parameters' point and interval estimates. We shall demonstrate that no analytical solutions to the likelihood equations must be solved to obtain the parameters' maximum likelihood estimates. As a result, we will use the R program to approximate the parameter point and interval estimates. Additionally, we will use the bootstrap‐t and bootstrap‐p methods to approximate the confidence intervals. About the Bayesian approach, we presume that each model parameter is independent and follows a gamma prior distribution with a range of attached hyperparameter values. The model parameters' posterior distribution does not take a practical form. We are unable to derive the Bayes estimates in closed forms as a result. To solve this issue, we use the Gibbs sampler from the Metropolis‐Hasting algorithm based on the Markov chain Monte Carlo method to condense the posterior distribution. To demonstrate the relevance of this research, a real data set application is detailed. [ABSTRACT FROM AUTHOR]

In cognitive neuroscience and psychology, reaction times are an important behavioral measure. However, in instrumental learning and goal-directed decision making experiments, findings often rely only on choice probabilities from a value-based model, instead of reaction times. Recent advancements have shown that it is possible to connect value-based decision models with reaction time models. However, typically these models do not provide an integrated account of both value-based choices and reaction times, but simply link two types of models. Here, we propose a novel integrative joint model of both choices and reaction times by combining a computational account of Bayesian sequential decision making with a sampling procedure. This allows us to describe how internal uncertainty in the planning process shapes reaction time distributions. Specifically, we use a recent context-specific Bayesian forward planning model which we extend by a Markov chain Monte Carlo (MCMC) sampler to obtain both choices and reaction times. As we will show this makes the sampler an integral part of the decision making process and enables us to reproduce, using simulations, well-known experimental findings in value based-decision making as well as classical inhibition and switching tasks. Specifically, we use the proposed model to explain both choice behavior and reaction times in instrumental learning and automatized behavior, in the Eriksen flanker task and in task switching. These findings show that the proposed joint behavioral model may describe common underlying processes in these different decision making paradigms. Author summary: Many influential results in psychology and cognitive neuroscience rest on reaction time effects in behavioral experiments, for example in studies about human decision making. For the particular case of decisions based on the value of options, however, findings often rely on analyses of choices using specific computational models. Until recently, these models did not allow for analysis of reaction times. In this article we introduce a new model of how to explain both choices and reaction times in decision making experiments that involve evaluating expected outcomes over multiple steps. Importantly, the model explains how the brain can make good decisions quickly, even in the face of many potential choices and in complex environments. [ABSTRACT FROM AUTHOR]

Following the apparent final case in an Ebola virus disease (EVD) outbreak, the decision to declare the outbreak over must balance societal benefits of relaxing interventions against the risk of resurgence. Estimates of the end-of-outbreak probability (the probability that no future cases will occur) provide quantitative evidence that can inform the timing of an end-of-outbreak declaration. An existing modeling approach for estimating the end-of-outbreak probability requires comprehensive contact tracing data describing who infected whom to be available, but such data are often unavailable or incomplete during outbreaks. Here, we develop a Markov chain Monte Carlo-based approach that extends the previous method and does not require contact tracing data. Considering data from two EVD outbreaks in the Democratic Republic of the Congo, we find that data describing who infected whom are not required to resolve uncertainty about when to declare an outbreak over. [ABSTRACT FROM AUTHOR]

Path testing is one of the most efficient approaches for covering a program during the test. However, executing a path with a single or limited number of test data does not guarantee that the path is fault-free, specifically in the fault-prone paths. A common solution in these cases is to extract the corresponding domain of the path constraint that covers the path and select the arbitrary numbers of test data from the extracted domain. Many approaches have been proposed to extract and partition the program input domain statically without executing the program under test. However, extracting domain based on the path constraints is inaccurate and time-consuming, specifically in high dimensional inputs. This paper presents a dynamic approach for extracting the input domain of a given path based on the modified Markov chain Monte Carlo method, multi-agent Metropolis algorithm. The algorithm uses sampling and randomly walks around symmetric proposal distribution to find a finite number of points that approximate the target domain. Our approach chooses the highest fault-prone path from the minimum-cost test paths for domain extraction to maximize the fault detection capabilities. Our experiments with ten Python programs reveal a 14% improvement in the accuracy of the extracted domains compared to the state-of-the-art domain extraction approaches. In addition, the mutation score of automatically generated test cases has improved by an average of 17.95% compared to branch and prime-path testing approaches. [ABSTRACT FROM AUTHOR]

Summary Effective collaboration between developers of Bayesian inference methods and users is key to advance our quantitative understanding of biosystems. We here present hopsy , a versatile open-source platform designed to provide convenient access to powerful Markov chain Monte Carlo sampling algorithms tailored to models defined on convex polytopes (CP). Based on the high-performance C++ sampling library HOPS , hopsy inherits its strengths and extends its functionalities with the accessibility of the Python programming language. A versatile plugin-mechanism enables seamless integration with domain-specific models, providing method developers with a framework for testing, benchmarking, and distributing CP samplers to approach real-world inference tasks. We showcase hopsy by solving common and newly composed domain-specific sampling problems, highlighting important design choices. By likening hopsy to a marketplace, we emphasize its role in bringing together users and developers, where users get access to state-of-the-art methods, and developers contribute their own innovative solutions for challenging domain-specific inference problems. Availability and implementation Sources, documentation and a continuously updated list of sampling algorithms are available at https://jugit.fz-juelich.de/IBG-1/ModSim/hopsy , with Linux, Windows and MacOS binaries at https://pypi.org/project/hopsy/. [ABSTRACT FROM AUTHOR]

The blue shark Prionace glauca plays a critical role as a predator in marine ecosystems but is threatened by by‐catch. To obtain more precise biological data, a Bayesian approach was used, and 536 vertebrae samples collected during 1 year at the landing stage called "Playita Mía" Manta, Ecuador, were analysed. The objective was to estimate the age and growth parameters of the species. The size of the specimens varied between 116 and 310 cm in total length (TL). Using a Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method, growth parameters were evaluated. The von Bertalanffy model was the one that best fitted the data and provided more adequate estimates (females: L∞ = 325.50 cm, L0 = 53.23 cm, and k = 0.12 years; males: L∞ = 331.47 cm, L0 = 51.59 cm, k = 0.12 years −1; combined sexes: L∞ = 329.65 cm, L0 = 53.64 cm, k = 0.11 year−1). The results indicated that females and males have a similar growth, and that the species has a slow growth. Further studies using multi‐model Bayesian approaches and covering a broader range of sizes in the Pacific Ocean are suggested. These studies will provide crucial information for the management and conservation of this species. [ABSTRACT FROM AUTHOR]

Genetic diversity is an important biological trait for a successful invasion. During the expansion across a new territory, an invasive species may face unprecedented ecological conditions that will determine its demography and genetic diversity. The first record of the yellow‐legged hornet (Vespa velutina) in Europe dates back to 2004 in France, from where it has successfully spread through a large territory in the continent, including Italy, Spain and Portugal. Integrative approaches offer a powerful strategy to detect and understand patterns of genetic variation in central and marginal populations. Here, we have analysed the relationship between genetic diversity parameters inferred from 15 V. velutina nuclear DNA microsatellite loci, and geographical and environmental drivers, such as the distance to the introduction focus, environmental suitability and distance to native and invasive niche centroids. Our results revealed a central–marginal dynamic, where allelic richness decreased towards the edge of the expansion range. The low environmental suitability of the territories invaded by marginal populations could prevent a diverse population from establishing and reducing the genetic diversity in populations at the expansion edge. Moreover, Markov chain Monte Carlo analysis showed both geographical and environmental distances were influencing population genetic differentiation. This study highlights the importance of combining genetic analysis with geographical and environmental drivers to understand genetic trends of invasive species to new environment. [ABSTRACT FROM AUTHOR]

This paper presents a novel Bayesian method for backcalculation of pavement dynamic modulus, stiffness, thickness, and damping using falling weight deflectometer (FWD) data. The backcalculation procedure yields estimates and uncertainties for each pavement property of interest. As a by‐product of the Bayesian procedure, information about measurement error is recovered. The Bayesian method is tested on simulated FWD backcalculations and compared with a state‐of‐the‐art trust‐region optimization algorithm, and it achieves estimation errors that are nearly an order of magnitude lower than the trust‐region solver. Confidence intervals are computed from thousands of simulated backcalculations and are shown to quantify uncertainty in estimated pavement properties. To cope with the computational expense of backcalculation, a fully parallel transitional Markov chain Monte Carlo procedure is developed. The fully parallel algorithm scales well to computation with many processor cores, and it yields up to a 50% reduction in computation time when compared to existing parallel implementations. [ABSTRACT FROM AUTHOR]

The analysis of multivariate longitudinal data may often encounter a difficult task, particularly in the presence of censored measurements induced by detection limits and intermittently missing values arising when subjects do not respond to a part of outcomes during scheduled visits. The multivariate nonlinear mixed model (MNLMM) has emerged as a promising analytical tool for multi-outcome longitudinal data following arbitrarily nonlinear profiles with random phenomena. This article presents a generalization of the MNLMM, called MNLMM-CM, designed to simultaneously accommodate the effects of censorship and missingness within a Bayesian framework. Specifically, we develop a Markov chain Monte Carlo procedure that combines a Gibbs sampler with the Metropolis–Hastings algorithm. This hybrid approach facilitates Bayesian estimation of essential model parameters and imputation of non-responses under the missing at random mechanism. The issue of posterior predictive inference for the censored and missing outcomes is also addressed. The effectiveness and performance of the proposed methodology are demonstrated through the analysis of simulated data and a real example from an AIDS clinical study. [ABSTRACT FROM AUTHOR]

Degradation modeling serves as a valuable tool for assessing the lifetime information of highly reliable products. One frequently employed approach for describing the degradation phenomenon involves the use of a degradation model that relies on stochastic processes. In a stochastic‐process‐based degradation model, it is assumed that the increments follow a distribution with the additivity property. This property makes the further inferences mathematically and statistically tractable. However, it limits the choices of the distributions. This paper aims to use those distributions without the additivity property to model the increments and explores distributions from the log‐location‐scale family. Under the frame of Bayesian analysis, Markov Chain Monte Carlo algorithms are developed for executing the necessary computations. Given that the proposed degradation models do not adhere to the additivity property, this paper tackles the challenges involved in predicting the lifetime of both on‐line and off‐line products. Two illustrative examples are subsequently analyzed to demonstrate the procedural steps outlined. The suitability of the proposed model is finally validated through a simulation study. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we propose combining the stochastic blockmodel and the smooth graphon model, two of the most prominent modeling approaches in statistical network analysis. Stochastic blockmodels are generally used for clustering networks into groups of actors with homogeneous connectivity behavior. Smooth graphon models, on the other hand, assume that all nodes can be arranged on a one-dimensional scale such that closeness implies a similar behavior in connectivity. Both frameworks belong to the class of node-specific latent variable models, entailing a natural relationship. While these two modeling concepts have developed independently, this paper proposes their generalization towards stochastic block smooth graphon models. This combined approach enables to exploit the advantages of both worlds. Employing concepts of the EM-type algorithm allows to develop an appropriate estimation routine, where MCMC techniques are used to accomplish the E-step. Simulations and real-world applications support the practicability of our novel method and demonstrate its advantages. The paper is accompanied by supplementary material covering details about computation and implementation. [ABSTRACT FROM AUTHOR]

AbstractComputer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme and fine-tuning can prevent being trapped in local optima through a series of intermediate posteriors and weight adjustment. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors. [ABSTRACT FROM AUTHOR]

AbstractPosterior predictive p-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribution is not uniform under the hypothesis that the model did generate the data. Calibrated ppps (cppps) can be obtained via a bootstrap-like procedure, yet remain unavailable in practice due to high computational cost. This article introduces methods to enable efficient approximation of cppps and their uncertainty for fast model assessment. We first investigate the computational tradeoff between the number of calibration replicates and the number of MCMC samples per replicate. Provided that the MCMC chain from the real data has converged, using short MCMC chains per calibration replicate can save significant computation time compared to naive implementations, without significant loss in accuracy. We propose different variance estimators for the cppp approximation, which can be used to confirm quickly the lack of evidence against model misspecification. As variance estimation uses effective sample sizes of many short MCMC chains, we show these can be approximated well from the real-data MCMC chain. The procedure for cppp is implemented in NIMBLE, a flexible framework for hierarchical modeling that supports many models and discrepancy measures. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Exploring the factors influencing Food Security and Nutrition (FSN) and understanding its dynamics is crucial for planning and management. This understanding plays a pivotal role in supporting Africa's food security efforts to achieve various Sustainable Development Goals (SDGs). Utilizing Principal Component Analysis (PCA) on data from the FAO website, spanning from 2000 to 2019, informative components are derived for dynamic spatio-temporal modeling of Africa's FSN Given the dynamic and evolving nature of the factors impacting FSN, despite numerous efforts to understand and mitigate food insecurity, existing models often fail to capture this dynamic nature. This study employs a Bayesian dynamic spatio-temporal approach to explore the interconnected dynamics of food security and its components in Africa. The results reveal a consistent pattern of elevated FSN levels, showcasing notable stability in the initial and middle-to-late stages, followed by a significant acceleration in the late stage of the study period. The Democratic Republic of Congo and Ethiopia exhibited particularly noteworthy high levels of FSN dynamicity. In particular, child care factors and undernourishment factors showed significant dynamicity on FSN. This insight suggests establishing regional task forces or forums for coordinated responses to FSN challenges based on dynamicity patterns to prevent or mitigate the impact of potential food security crises. [ABSTRACT FROM AUTHOR]

Different non-Bayesian and Bayesian techniques were used to estimate the pseudo-Lindley (PsL) distribution's parameters in this study. To derive Bayesian estimators, one must assume appropriate priors on the parameters and use loss functions such as squared error (SE), general entropy (GE), and linear-exponential (LINEX). Since no closed-form solutions are accessible for Bayes estimates under these loss functions, the Markov Chain Monte Carlo (MCMC) approach was used. Simulation studies were conducted to evaluate the estimators' performance under the given loss functions. Furthermore, we exhibited the adaptability and practicality of the PsL distribution through real-world data applications, which is essential for evaluating the various estimation techniques. Also, the acceptance sampling plans were developed in this work for items whose lifespans approximate the PsL distribution. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved Nested Error Regression model in which the random effects for each area are given a prior distribution using the Poisson–Dirichlet Process. Based on this model, we mainly investigate the construction of the parameter estimation using the Empirical Bayesian(EB) estimation method, and we adopt various methods such as the Maximum Likelihood Estimation(MLE) method and the Markov chain Monte Carlo algorithm to solve the model parameter estimation jointly. The viability of the model is verified using numerical simulation, and the proposed model is applied to an actual small area estimation problem. Compared to the conventional normal random effects linear model, the proposed model is more accurate for the estimation of complex real-world application data, which makes it suitable for a broader range of application contexts. [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]

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [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]

Considering the hysteresis effect, the stage-discharge rating curve (SDRC) is challenging to measure at gauge stations. Hysteresis also causes uncertainty in SDRC estimations. Therefore, an accurate method to estimate discharge is essential in such conditions. In steady flow conditions, isovel contours can be used to estimate SDRC. However, this method has not been investigated in unsteady conditions. This study uses the Jones formula and isovel contours-based SDRC to consider the hysteresis in Chattahoochee River, USA. First, this method identifies hydro-geometric parameters, such as velocity parameters extracted from isovel contours, to calculate the steady SDRC (SSDRC). Then, it is combined with the Jones formula to estimate loop SDRC (LSDRC). The SSDRC is calibrated using the Markov chain Monte Carlo (MCMC) method. MCMC calibrates model parameters by iteratively selecting parameters that best fit the observed data from the parameter space. Also, uncertainty in model output can be characterized using the posterior distribution of model parameters. The results show that LSDRC is more accurate than SSDRC based on R2, mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) metrics. Also, the proposed method outperforms the power function rating curve. The proposed model achieved a maximum MAPE of 6.6%, while the power function rating curve reached 24.6%. [ABSTRACT FROM AUTHOR]

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as H 0 = 7 1. 5 4 ± 0. 2 8 , Ω m 0 = 0. 2 6 2 2 ± 0. 0 0 2 1 Ω ϕ 0 = 0. 7 3 3 1 ± 0. 0 0 4 6 and Ω σ 0 = 0. 0 0 0 1 6 2 ± 0. 0 0 0 0 6 3. The model shows a flipping nature and redshift transition occurs at z t = 0. 6 9 6 4 − 0. 0 0 0 6 + 0. 0 1 3 6 , and the present value of decelerated parameter is computed to be q 0 = − 0. 6 9 6 4 ± 0. 0 2 8 for the combined dataset. We have explored characteristics like the universe's age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density ρ ϕ , scalar field pressure p ϕ , and equation of state parameter ω ϕ , are analyzed and presented. We have also described the behavior of the scalar potential V (ϕ) and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field. [ABSTRACT FROM AUTHOR]

Assessing the impact of an intervention by using time-series observational data on multiple units and outcomes is a frequent problem in many fields of scientific research. Here, we propose a novel Bayesian multivariate factor analysis model for estimating intervention effects in such settings and develop an efficient Markov chain Monte Carlo algorithm to sample from the high-dimensional and nontractable posterior of interest. The proposed method is one of the few that can simultaneously deal with outcomes of mixed type (continuous, binomial, count), increase efficiency in the estimates of the causal effects by jointly modeling multiple outcomes affected by the intervention, and easily provide uncertainty quantification for all causal estimands of interest. Using the proposed approach, we evaluate the impact that Local Tracing Partnerships had on the effectiveness of England's Test and Trace programme for COVID-19. [ABSTRACT FROM AUTHOR]

Dialysis patients experience frequent hospitalizations and a higher mortality rate compared to other Medicare populations, in whom hospitalizations are a major contributor to morbidity, mortality, and healthcare costs. Patients also typically remain on dialysis for the duration of their lives or until kidney transplantation. Hence, there is growing interest in studying the spatiotemporal trends in the correlated outcomes of hospitalization and mortality among dialysis patients as a function of time starting from transition to dialysis across the United States Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multivariate spatiotemporal functional principal component analysis model to study the joint spatiotemporal patterns of hospitalization and mortality rates among dialysis patients. The proposal is based on a multivariate Karhunen–Loéve expansion that describes leading directions of variation across time and induces spatial correlations among region-specific scores. An efficient estimation procedure is proposed using only univariate principal components decompositions and a Markov Chain Monte Carlo framework for targeting the spatial correlations. The finite sample performance of the proposed method is studied through simulations. Novel applications to the USRDS data highlight hot spots across the United States with higher hospitalization and/or mortality rates and time periods of elevated risk. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information. [ABSTRACT FROM AUTHOR]

This paper aims to detect anomalous changes in social network structure in real time and to offer early warnings by phase II monitoring social networks. First, the exponential random graph model is used to model social networks. Then, a test and online monitoring technique of the exponential random graph model is developed based on the split likelihood-ratio test after determining the model and its parameters for a specific data set. This proposed approach uses pseudo-maximum likelihood estimation and likelihood ratio to construct the test statistics, avoiding the several steps of discovering Monte Carlo Markov Chain maximum likelihood estimation through an iterative method. A bisection algorithm for the control limit is given. Simulations on three data sets Flobusiness, Kapferer and Faux.mesa.high are presented to study the performance of the procedure. Different change points and shift sizes are compared to see how they affect the average run length. A real application example on the MIT reality mining social proximity network is used to illustrate the proposed modelling and online monitoring methods. [ABSTRACT FROM AUTHOR]

We propose a Markov Chain Monte Carlo Conditional Maximum Likelihood (MCMC-CML) estimator for the two-way fixed-effects logit model for dyadic data, typically used in network analyses. The proposed MCMC approach, based on a Metropolis algorithm, allows us to overcome the computational issues of evaluating the probability of the outcome conditional on nodes in- and out-degrees, which are sufficient statistics for the incidental parameters. Under mild regularity conditions, the MCMC-CML estimator converges to the exact CML one and is asymptotically normal. Moreover, it is more efficient than the existing pairwise CML estimator. We study the finite sample properties of the proposed approach by means of an extensive simulation study and three empirical applications, where we also show that the MCMC-CML estimator can be applied to logit models for binary panel data with both subject and time-fixed effects. Results confirm the expected theoretical advantage of the proposed approach, especially with small, concentrated, and sparse networks or with rare events in panel data. [ABSTRACT FROM AUTHOR]

This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matter accumulation (TDMA) of Allium sativum as a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertz models that use student's t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5. The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertz model fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even for varied error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations. [ABSTRACT FROM AUTHOR]

We propose a novel variational Bayes approach to estimate high-dimensional Vector Autoregressive (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural representation of the parameter space for posterior inference. Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (a) the prior structure maps into posterior inference on the reduced-form transition matrix and (b) posterior estimates are more robust to variables permutation. An extensive simulation study provides evidence that our approach compares favorably against existing linear and nonlinear Markov chain Monte Carlo and variational Bayes methods. We investigate the statistical and economic value of the forecasts from our variational inference approach for a mean-variance investor allocating her wealth to different industry portfolios. The results show that more accurate estimates translate into substantial out-of-sample gains across hierarchical shrinkage priors and model dimensions. [ABSTRACT FROM AUTHOR]

In many applications, modeling based on a normal kernel is preferred because not only does the normal kernel belong to the family of stable distributions, but also it is easy to satisfy the stationary condition in the stochastic process. However, the characteristic of the data, such as count or proportion, is a major obstacle to complete modeling based on a normal distribution. To solve a limited boundary or non-normal distribution problem, we provided a novel transformation method and proposed a nonparametric Bayesian approach based on a normal kernel of the transformed variable. In particular, the provided transformation transforms any probability space into a real space and is free from the constraints of the previous transformation, such as skewness, presence of power, and bounded domains. Another advantage was that it was possible to use the Dirichlet process mixture model with full conditional posterior distributions for all parameters, leading to a fast convergence rate in the Markov chain Monte Carlo. The proposed methodology was illustrated with simulated datasets and two real datasets with non-normal distribution problems. In addition, to demonstrate the superiority of the proposed methodology, the comparison with the transformed Bernstein polynomial model was made in the real data analysis. [ABSTRACT FROM AUTHOR]

An improved adaptive Type-II progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor. [ABSTRACT FROM AUTHOR]

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To accommodate linkage effects of individuals, we develop a new linkage vector autoregressive (LAR) model for dynamic panel data. A main feature of the LAR model is incorporating dynamic network information in autoregressive time series modeling. The dynamic network can be given, or we can formulate the network links as a function of historical data, where unknown parameters of the function can be estimated from the data. We propose a simulation technique to check the stationarity condition of the LAR model and suggest a Bayesian Markov chain Monte Carlo method for estimation. Empirical results for the quarterly growth rates of gross domestic product (GDP) in 45 countries indicate that (i) the autoregressive (AR) coefficient for the aggregated growth rate is hard to distinguish from zero; (ii) a panel AR model with individual effects has a positive autocorrelation; and (iii) the alternative LAR models are preferred to the panel AR model. Depending on the specification of the linkage variables, the sign and size of the linkage effect can differ. The logistic linkage function has a flexible structure to accommodate the size of the linkage of individual GDP growth rates, and it strengthens the dynamics. [ABSTRACT FROM AUTHOR]

Integration of Bayesian parameter estimation (BPE) with model‐based design of experiments (MBDoE) aims to estimate process parameters efficiently and systematically. To achieve more efficient use of resources by iteratively selecting informative experiments based on current knowledge about the parameters, an integrated method with BPE and MBDoE is proposed in this article. A built‐in Markov Chain Monte Carlo is also developed to yield not only the distribution profile of the estimated parameters but also aid in the determination of stopping criteria and the estimation of noise. Two applications of dynamic batch reactor systems are presented. Comparative analysis substantiates the superior performance of this approach in terms of parameter accuracy and the efficiency of experimentation. [ABSTRACT FROM AUTHOR]

For all the nuclear reactor systems, quantitative assessment of the accident management (AM) effects against long-term external hazards became one of the essential issues after the lesson learned from the Fukushima Daiichi Nuclear Power Plant accident. However, the influence from the safety systems' stochastic and dynamic shifting between multiple working states, which is related to the interaction with the adjacent components/systems in general, has not been accounted for yet. Therefore, this research aims to develop a dynamic probability risk assessment tool considering repairable multi-component interdependency for investigating the AM influences on the multi-state safety systems under long-term external hazards. Based on the newly proposed methodology in this research via integrating the Petri net (PN) model with the continuous Markov chain Monte Carlo (CMMC) method, a framework applying PN-CMMC methodology to a severe accident analysis code, SPECTRA, had been originally constructed. Different AM influences on the multi-state decay heat removal systems against long-term volcanic ashfall were also quantitatively confirmed, indicating that halving the repairing time is more influential in suppressing the core damage frequency than doubling the number of adjacent electricity support systems. Therefore, the PN-CMMC-SPECTRA framework can further assess the uncharted dynamic multi-state concerns, leading to a safer AM strategy. [ABSTRACT FROM AUTHOR]

The primary goal of this study is to effectively measure the impact of a severe random shock, such as the COVID-19 pandemic on aggregate economic activity in Greece, seven other euro area economies, three Scandinavian countries, and the United States. The class of linear and quantile predictive regression models is proposed for the analysis of real gross domestic product (GDP) growth, and a Bayesian approach for model selection is developed, by using a computationally flexible Markov chain Monte Carlo stochastic search algorithm that explores the posterior distribution of linear and quantile models, and identifies the relevant predictor variables. Penalized likelihood regression models are also implemented to tackle the issue of model selection. The model confidence set approach is applied and verifies that the selected models identified by the stochastic search algorithm belong to the set of superior models. Our analysis confirms that the outbreak of the pandemic had a profound effect on the economies under study, and reveals that different predictor variables are able to explain different quantiles of the underlying real GDP growth distribution for analyzed countries, suggesting that the quantile modeling approach improves the ability to adequately explain real GDP series compared with the standard conditional mean approach that explains only the average of the relationship between real GDP growth and several predictor variables. [ABSTRACT FROM AUTHOR]

Seawater intrusion (SI) poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into SI predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by integrating various types of observational data with the model to characterize heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ESK) and Markov chain Monte Carlo, face challenges when confronted with the non‐linearity, non‐Gaussianity, and high‐dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ESDL, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ESDL, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models. Our findings reveal that ESDL excels in characterizing heterogeneous aquifers under non‐linear and non‐Gaussian conditions. Comparison between ESDL and ESK under different experimentation settings underscores the robustness of ESDL. Conversely, in certain scenarios, ESK displays noticeable biases in the characterization results, especially when measurement data from non‐linear and discontinuous processes are used. To optimize the efficacy of ESDL, attention must be given to the design of the DL model and the selection of observational data, which are crucial to ensure the universal applicability of this DA method. Key Points: Non‐linearity and non‐Gaussianity in coastal aquifer characterization problems pose challenges to traditional data assimilation (DA) methodsWe propose to address these issues with a deep learning‐based DA method called ESDLVarious factors influencing the performance of ESDL are systematically investigated [ABSTRACT FROM AUTHOR]

We examine the clustering behavior of price and variance jumps using high-frequency data, modeled as a marked Hawkes process (MHP) embedded in a bivariate jump-diffusion model with intraday periodic effects. We find that the jumps of both individual stocks and a broad index exhibit self-exciting behavior. The three dimensions of the model, namely positive price jumps, negative price jumps, and variance jumps, impact one another in an asymmetric fashion. We estimate model parameters using Bayesian inference by Markov Chain Monte Carlo, and find that the inclusion of the jump parameters improves the fit of the model. When we quantify the jump intensity and study the characteristics of jump clusters, we find that in high-frequency settings, jump clustering can last between 2.5 and 6 hours on average. We also find that the MHP generally outperforms other models in terms of reproducing two cluster-related characteristics found in the actual data. [ABSTRACT FROM AUTHOR]

Summary: A finite element model was established using SAP2000 software for the C1 tower, a super high‐rise building in the second phase of the Nanjing Financial City project, and the construction process of the tower was simulated. The C1 tower adopts a frame core tube extension arm and ring truss structure system, with 87 floors above ground and five floors underground. The roof structure has an elevation of 416.6 m. Precise measurements of inter‐story compression deformation were conducted using advanced surveying equipment. Sensitivity analysis, based on the finite difference method, identified the shear wall elastic modulus, frame column elastic modulus, steel beam elastic modulus, and shear wall unit weight as four highly influential parameters. Employing the Bayesian principle, the Markov Chain Monte Carlo (MCMC) method was applied to determine the posterior density probability function of the parameters targeted for modification. Subsequently, the Metropolis–Hastings (MH) sampling algorithm was employed to refine the C1 Tower model. This refinement significantly reduced the root mean square error between the measured and simulated vertical displacements, achieving an error reduction of approximately 10% from 6.082 to around 2.160. The modified material parameters, for the most part, adhered to a normal distribution assumption and exhibited mean values in the posterior probability density functions for the elastic modulus of Q345 steel beams, C70 frame columns, and C60 shear walls. Compared to the initial finite element parameters, the variation range was approximately 13% to 17%. These results serve as a validation of the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The cardinality of this set grows combinatorially with the number of network nodes, which makes this optimisation computationally challenging. For each network, its likelihood is the probability for the observed data to appear during the evolution of the epidemiological process on this network. This probability can be very small, particularly if the network is significantly different from the ground truth network, from which the observed data actually appear. A commonly used stochastic simulation algorithm struggles to recover rare events and hence to estimate small probabilities and likelihoods. In this paper we replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. Since this equation also suffers from the curse of dimensionality, we apply tensor train approximations to overcome it and enable fast and accurate computations. Numerical simulations demonstrate efficient black-box Bayesian inference of the network.

Quantifying volatile concentrations in magmas is critical for understanding magma storage, phase equilibria, and eruption processes. We present PyIRoGlass, an open-source Python package for quantifying concentrations of H2O and CO2 species in the transmission FTIR spectra of basaltic to andesitic glasses. We leverage a dataset of natural melt inclusions and back-arc basin basalts with volatiles below detection to delineate the fundamental shape and variability of the baseline underlying the CO32- and H2Om, 1635 peaks, in the mid-infrared region. All Beer-Lambert Law parameters are examined to quantify associated uncertainties. PyIRoGlass employs Bayesian inference and Markov Chain Monte Carlo sampling to fit all probable baselines and peaks, solving for best-fit parameters and capturing covariance to offer robust uncertainty estimates. Results from PyIRoGlass agree with independent analyses of experimental devolatilized glasses (within 6 %) and interlaboratory standards (10 % for H2O, 6 % for CO2). We determine new molar absorptivities for basalts, εH2Ot,3550 = 63.03 ± 4.47 L/mol · cm and εCO2−3,1515,1430 = 303.44 ± 9.20 L/mol · cm; we additionally update the composition-dependent parameterizations of molar absorptivities, with their uncertainties, for all H2O and CO2 species peaks. The open-source nature of PyIRoGlass ensures its adaptability and evolution as more data become available.