Search

• Robust functional form contains true parameters far more often than popular models. • Matches/outperforms widely used regression and Neural Network models. • Finds appropriate balance between Model Fit, Inference and Prediction (MIPs). • Introduces new large-sample DGP test; can use to improve A.I. models. • For MIS field finds Popularity Parameter to be important for predicting citations. This article introduces a versatile functional form for Generalized Linear Models (GLMs) through a simple, yet effective, transformation of the current framework. The models are applied through a new hierarchical bayesian estimation procedure for logistic regression to highly-cited papers in the Management Information Systems (MIS) field. The results are uniformly better, in regards to model fit and inference for in-sample and out-of-sample data, for simulation studies and real-world data applications, requiring very little time to convergence to true population parameters. In simulation studies, I show that the method contains the true parameters nearly three times as often as widely used existing GLMs, and does so while having confidence intervals that are 54.50% smaller, while requiring around two-thirds the number of MCMC iterations as existing bayesian methods. In Scientometric applications the methodology is shown to be highly robust with predictive/classification accuracy, either equaling or exceeding existing methods for identifying highly-cited articles including Artificial Neural Networks (ANN). Thus, the method is shown to be robust to the amount of asymmetry (or symmetry) of the probability of success (or failure) and robust to unbalanced samples and varying Data Generating Processes. Further, the methodology is equivalent to current methods if the data support them and is therefore complementary to existing methods, without loss of interpretability of model parameters. For the MIS field it finds that Popularity Parameter (PP) of an article Keywords can predict whether a paper will be highly-cited (top 25% of highly-cited articles) between two to three years after publication and beyond. Furthermore, given the small number of iterations needed for convergence, the methodology can also be used as a baseline method in Big Data (BD) settings for both Artificial Intelligence (AI) and Machine Learning (ML) contexts as well. [ABSTRACT FROM AUTHOR]

Abstract: The Bullionist Controversy in the United Kingdom is one of the first debates about the determination of the price level and the exchange rate under a paper money standard. Despite the importance of the debate in the development of monetary theory, there remains little empirical evidence that uses modern, multivariate time series techniques. The evidence that does exist provides support for the Anti‐Bullionist position. The purpose of this paper is to review the debate and develop a dynamic general equilibrium model that is capable of capturing key features of the nineteenth‐century British financial system. The model is estimated using Bayesian procedures to test the competing hypotheses. The paper provides support for the Bullionist position. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian estimators for the Inverse Weibull Distribution (IWD) scale parameter are derived when the shape parameter of distribution is known. The Bayesian estimators for the parameter are obtained by using the Gamma prior under the different types of loss functions such as square error loss function (Self), Entropy loss function (Elf), Precautionary loss function (Plf), Linear exponential loss function (Linexlf) and nonlinear exponential loss function (Nlinexlf). A classical maximum likelihood estimator (mle) for the parameter is also derived. To compare the efficiency of the parameter estimation methods, a simulation study is carried out. The comparison is based on mean square error. [ABSTRACT FROM AUTHOR]

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. [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]

In quality engineering, process capability indices play a crucial role in assessing the capability of a given process. Among the widely recognized indices are Cp, Cpk, Cpm, and Cpmk, all of which presuppose the normality of the product lifetime. However, Maiti et al. (2010) proposed a more versatile process capability index, denoted as Cpyk, which does not rely on distributional assumptions. The study is currently investigating statistical inferences for the Cpyk index within the context of progressively type-II censored samples, marking the first exploration of this aspect in the research. This paper investigates maximum likelihood and Bayesian inference for the Cpyk when the underlying distribution follows the inverse Rayleigh distribution. Additionally, the study explores Bayesian credible intervals and the highest posterior density intervals using the Markov Chain Monte Carlo procedure. Various types of bootstrap confidence intervals are also taken into consideration. To assess the performance of these intervals, a Monte Carlo simulation is executed, comparing their coverage probabilities and mean lengths. The paper concludes with an illustrative example utilizing real data, providing a practical application of the discussed methodologies. [ABSTRACT FROM AUTHOR]

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry. [ABSTRACT FROM AUTHOR]

In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

Two stage least squares is an approach to fit a mathematical or statistical model to data where there are simultaneous or bidirectional cause and effect relationship between the independent variables and the dependent variable. Two stage least squares method is frequently implemented in the case that there is no prior information. On the other hand, in the existence of some prior information, Bayesian estimation methods may be preferable to the classical ones in the simultaneous equations model. From this point of view, ridge regression approach is adapted to Bayesian approach in this paper. In mathematical sense, ridge regression can be derived as a solution of Tikhonov regularization which is a method to overcome ill-posed problems. Therefore, the proposed Bayes estimators resulted from the adaptation of ridge regression mitigate the multicollinearity. Theoretical comparisons among the estimators are performed by means of matrix mean square error criterion and determination of the biasing parameter is also examined in this paper. While doing these comparisons we utilize the matrix theory and Euclidian norm. Theoretical results are tested by a real life data analysis and an extensive Monte Carlo experiment. Eventually, the researchers relevant to mathematics and statistics may prefer the proposed Bayes estimators to the two stage least squares estimator in the existence of multicollinearity. [ABSTRACT FROM AUTHOR]

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel probability distribution model known as the unit compound Rayleigh distribution, which possesses the distinctive characteristic of defining the range within the bounded interval (0,1). Through an in-depth investigation of this distribution, we analyzed various statistical and structural characteristics including reliability function, risk function, quantile function, moment analysis, order statistics, and entropy measurement. To estimate the unknown parameters of our proposed distribution model, we employed maximum likelihood (ML) estimation and Bayesian estimation. Furthermore, we derived several entropy measures based on ML estimation under the unit compound Rayleigh distribution. To comprehensively evaluate the performance of these entropies, we employed the Monte Carlo simulation method to calculate the average entropy estimate, average entropy bias, corresponding mean square error, and mean relative estimate for assessing the performance of various entropies within the unit compound Rayleigh distribution model. Finally, in order to validate its potential for practical applications, two sets of real data were selected for empirical analysis where fitting and parameter estimation were conducted to demonstrate the advantages of utilizing the unit compound Rayleigh distribution in describing and predicting actual data. This study not only introduces a new probability theory and statistics framework by proposing a novel distribution model but also provides researchers and practitioners in related fields with a powerful analytical tool. [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]

In this paper, Bayesian and non-Bayesian estimations of the shape parameter of the Inverted Topp-Leone distribution are studied under a progressive Type I censoring scheme. The maximum likelihood estimator (MLE) and Bayes estimator (BE) of the unknown parameter under the squared error loss (SEL) function are obtained. Three types of confidence intervals are discussed for the unknown parameter. A simulation study is performed to compare the performances of the proposed methods, and two numerical examples have been analyzed for illustrative purposes. [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]

Most empirical studies evaluating efficiency in the agricultural sector estimate cost efficiency, assuming homogeneity across firms. However, achieving the goal of profit maximisation requires both minimising costs and maximising revenue. Unlike cost efficiency, the concept of profit efficiency considers the errors on both the input side and the output side, and thus, it is more appropriate for evaluating the overall performance of firms. This paper estimates profit efficiency and its determinants in the agricultural sector in Spain using a Bayesian stochastic frontier model with random coefficients. This methodology adequately captures the heterogeneity across firms in the industry. The results reveal, firstly, that agricultural firms in Spain are operating with an average profit inefficiency of 35.78% and, secondly, that this inefficiency is affected, albeit unevenly, by the size and age of the farm. Finally, the implications of these results for managers and public policies are discussed. [ABSTRACT FROM AUTHOR]

This paper considers the statistical inferences of inverse Weibull distribution under progressive type-II censored sample, which is a common distribution in reliability analysis. Two commonly used parameter estimation methods, maximum likelihood estimation and Bayesian estimation, are used in this paper, along with the inverse moment estimation. First, we derive the maximum likelihood estimators of parameters and propose Newtown-Raphson iteration method to solve these estimators. Assuming that shape and rate parameters are independent and follow gamma priors, we further obtain the Bayesian estimators by Lindley approximation. We also derive the inverse moment estimators and construct the generalized confidence intervals using the generalized pivotal quantity. To compare the estimation effects of these methods, we implement Monte Carlo simulation with the help of MATLAB. The simulation results show that the Bayesian estimation method outperforms the other two methods in terms of mean squared error. Finally, we verify the feasibility of these methods by analyzing a set of real data. The results indicate that the Bayesian estimation method provides more accurate estimates than the other two methods. [ABSTRACT FROM AUTHOR]

To achieve high-precision geomagnetic matching navigation, a reliable geomagnetic anomaly basemap is essential. However, the accuracy of the geomagnetic anomaly basemap is often compromised by noise data that are inherent in the process of data acquisition and integration of multiple data sources. In order to address this challenge, a denoising approach utilizing an improved multiscale wavelet transform is proposed. The denoising process involves the iterative multiscale wavelet transform, which leverages the structural characteristics of the geomagnetic anomaly basemap to extract statistical information on model residuals. This information serves as the a priori knowledge for determining the Bayes estimation threshold necessary for obtaining an optimal wavelet threshold. Additionally, the entropy method is employed to integrate three commonly used evaluation indexes—the signal-to-noise ratio, root mean square (RMS), and smoothing degree. A fusion model of soft and hard threshold functions is devised to mitigate the inherent drawbacks of a single threshold function. During denoising, the Elastic Net regular term is introduced to enhance the accuracy and stability of the denoising results. To validate the proposed method, denoising experiments are conducted using simulation data from a sphere magnetic anomaly model and measured data from a Pacific Ocean sea area. The denoising performance of the proposed method is compared with Gaussian filter, mean filter, and soft and hard threshold wavelet transform algorithms. The experimental results, both for the simulated and measured data, demonstrate that the proposed method excels in denoising effectiveness; maintaining high accuracy; preserving image details while effectively removing noise; and optimizing the signal-to-noise ratio, structural similarity, root mean square error, and smoothing degree of the denoised image. [ABSTRACT FROM AUTHOR]

Censoring plays an important role in the reliability and life testing trials due to its cost optimality and time reduction properties. The unified hybrid censoring scheme is the combination of the generalized type-I and type-II hybrid censoring schemes. In this paper, our objective is to study the classical and Bayesian estimation methods of the parameter and reliability characteristics from the inverse Pareto lifetime model under the unified hybrid censoring scheme. In the classical estimation methods, the maximum likelihood and associated asymptotic confidence interval estimators are derived. In Bayesian estimation, the Bayes estimators under squared error loss function and the highest posterior density (HPD) credible intervals based on the informative and non-informative priors are developed. For the Bayesian computations, the Markov chain Monte Carlo techniques are used to compute Bayes and HPD credible interval estimates. A quantitative outcome of the objectives has been shown by a Monte Carlo simulation and with the help of a real-life application. [ABSTRACT FROM AUTHOR]

For operating any new finite capacity (say K) queuing system in which customers arrive according to a Poisson process and are served by a single server under exponential service time (in Kendall's notation M/M/1/K system), the assumption of fixing K and estimating the parameter traffic intensity ρ , is quite practical. But in situation of any pre-existing M/M/1/K queuing system, it is essential to determine an estimator of K to increase system efficiency for fixed value of ρ . This paper therefore considered the problem of estimating the parameter finite buffer (K). A Bayes estimator of K is proposed and compared it with classical estimator based on maximum likelihood principal, under the assumption that ρ is known. A simulation study is carried out to establish the efficacy and effectiveness of the proposed approaches. A real life situation is analyzed to illustrate the applicability of the developed algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information available is in the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function links equal importance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently. [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]

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time–space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal–noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy–Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm. [ABSTRACT FROM AUTHOR]

The aim of this study is twofold: on the one hand, to provide evidence of the positive association between the inflation rate and the labor share in the US; on the other, to show that monetary policy slows inflation by depressing the labor share. With the help of Bayesian econometrics, the paper shows evidence of a conflict Phillips curve. Furthermore, a structural vector autoregressive model reveals the detrimental effects of interest rate hikes on the labor share. Together, these results mean the monetary policy of administered interest rates resolves the class conflict in favor of capital to control inflation. Scrutiny of the US monetary policy development and a model of a controlled predator-prey system prepare the way for the empirical sections. Finally, the paper concludes that controlling the distributive conflict matters for impinging on inflation and that the Fed might follow alternative monetary rules to cease being the third party participating in the distributive conflict. [ABSTRACT FROM AUTHOR]

Considering that the choice of loss function plays a significant role in the derivation of Bayesian estimators, we propose a novel asymmetric loss function named the weighted Q-symmetric entropy loss for computing the estimates of the parameter and reliability function of the Burr XII distribution. This paper covers the classical maximum-likelihood, uniformly minimum-variance unbiased, and Bayesian estimation methods under the squared error loss, general entropy loss, Q-symmetric entropy loss, and new loss functions. Through Monte Carlo simulation, the respective performances of the considered estimators for the reliability function are evaluated, indicating that the Bayesian estimator under the new loss function is more efficient than those under other loss functions. Finally, a real data set is used to demonstrate the practicality of the presented estimators. [ABSTRACT FROM AUTHOR]

The issue of modelling observations generated in matrix form over time is key in economics, finance and many domains of application. While it is common to model vectors of observations through standard vector time series analysis, original matrix-valued data often reflect different types of structures of time series observations which can be further exploited to model interdependencies. In this paper, we propose a novel matrix autoregressive model in a bilinear form which, while leading to a substantial dimensionality reduction and enhanced interpretability: (a) allows responses and potential covariates of interest to have different dimensions; (b) provides a suitable estimation procedure for matrix autoregression with lag structure; (c) facilitates the introduction of Bayesian estimators. We propose maximum likelihood and Bayesian estimation with Independent-Normal prior formulation, and study the theoretical properties of the estimators through simulated and real examples. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Equivalent circuit models that reproduce the current–voltage characteristics of solar cells are useful not only to gain physical insight into the power loss mechanisms that take place in solar cells but also for designing systems that use renewable solar energy as a power source. As mentioned in a previous paper, Bayesian estimation of equivalent circuit parameters avoids the drawbacks of nonlinear least-squares methods, such as the possibility of evaluating estimation errors. However, it requires a long computation time because the estimated values are obtained by sampling using a Markov chain Monte Carlo method. In this paper, a trial to accelerate the calculation by upgrading the Bayesian statistical package PyMC is presented. PyMC ver. 4, the next version of PyMC3 used in the previous paper, started to support the latest sampling libraries using a machine learning framework JAX, in addition to PyMC-specific methods. The acceleration effect of JAX is remarkable, achieving a calculation time of less than 1/20 times that of the case without JAX. Recommended calculation conditions were disclosed based on the results of a number of trials, and a demonstration with testable Python code on Google Colaboratory using the recommended conditions is published on GitHub. [ABSTRACT FROM AUTHOR]