Applied Stochastic Models in Business and Industry最新文献

Congratulations on this great and comprehensive achievement. Undoubtedly, Bayesian inference plays an increasingly important role in reliability data analysis, dictated on the one hand by the usually small sample sizes per experimental condition, which bring standard frequentist procedures to their limits, and on the other hand by the fact that uncertainty quantification and communication are more straightforward in a Bayesian setup. Reliability data are mostly censored, with many realistic censoring schemes leading to complicated likelihood functions and posterior distributions that can be only approximated numerically with Markov Chain Monte Carlo (MCMC) methods. With the advances in Bayesian computation techniques and algorithms, this is however not a limitation anymore. The authors managed in this enlightening work to embed the reliability perspective view, grounded on the practitioners' needs, in a Bayesian theoretic setup, providing and commenting fundamental literature from both fields. This paper will be a valuable reference for practitioning Bayesian inference in reliability applications and, most importantly, for understanding the effect of the priors' choice. The provided insight on the role of a sensitivity analysis for the prior distribution is very important as well, especially when extrapolating results. Furthermore, the technical details and hints on the implementation in R will be highly appreciated.

It is not surprising, but good to see, that the essential role of the independence Jeffreys (IJ) priors is verified also in this context, for example, in cases of Type-I censoring with few observed failures. A crucial statement of the paper I would like to highlight is that in case of limited observed data, the usually “safe” choice of a noninformative prior can deliver misleading conclusions, since it may consider unlikely or impossible parts of the parameter space with high probability. Therefore, in reliability applications weakly informative priors that reflect the underlying framework or known effect of experimental conditions have to be prioritized. Moreover, along these lines, in case of experiments combining more than one experimental condition, if the level of the experimental condition has a monotone effect on the quantity of interest, say the expected lifetime, the choice of the priors under the different conditions should reflect this ordering. This is a direction of future research on Bayesian procedures for reliability applications with high expected impact.

In a Bayesian inferential framework, the derivation and use of credible intervals (CIs) is more natural and flexible than frequentist confidence intervals. In this work the focus lies on equal tailed CIs. For highly skewed posteriors, it would be of interest to consider in the future highest posterior density (HPD) CIs as well.

Motivated by the reference of the authors to Reference 1 and the priors in the framework of a

Firstly, I want to congratulate the authors in Reference 1 for their practical contextualization in describing the Bayesian method in real-world problems with reliability data. Undoubtedly, one of the main strengths of this article is its highly practical approach, starting from real situations and examples, and showing why Bayesian inference is many times a nice alternative for making estimations. The authors nicely describe how, in reliability applications, there are generally few failure records and, therefore, little information available. For example, this is often the case in the study of the reliability of engineering systems in the army, such as some types of weapons. Since the specific prior is a key aspect of the Bayesian framework, they are primarily concerned with guiding readers on how to make this choice properly.

Once the parameter of interest $��\theta �=�(�\mu �,�\sigma �)�$ has been identified, and without losing sight of real-world applications, the authors develop their exposition based on three essential premises. Firstly, they remind us that the distribution of $��\theta �$ may not always be the main focus of our interest in practical situations. Instead, our key objective might involve estimating cumulative failure probabilities at a specific time or a failure-time distribution $��p�$-quantile, given by the expression $��{�t�}_{�p�}�=�\exp �[�\mu �+�{�\Phi �}^{�-�1�}�(�$

Traditional risk measurements have proven inadequate in capturing tail risk and nonlinear correlation. This study proposes a novel approach to measure financial risk in the Internet finance industry: a new Value-at-Risk (VaR) measurement based on quantile regression neural network (QRNN). Sparrow Search Algorithm (SSA) is utilized to optimize the QRNN model, which improves the model's performance in predicting internet finance risk. By comparing the TGARCH-VaR and QR-VaR approaches, our study demonstrates the effectiveness of the QRNN-VaR approach and its potential to improve the accuracy of risk prediction in the Internet finance industry. This study further examines and compares the risks between the traditional and internet finance industries. It also considers the unique impact of COVID-19 on industry risk based on statistical testing for differences and machine learning models. Our results indicate that the level of risk in the Internet finance industry is higher than in the traditional finance industry. Moreover, COVID-19 has contributed to increased risk within the Internet finance industry. These findings have significant implications for investors and policymakers seeking to better understand and manage risks within the Internet finance industry, particularly in the ongoing COVID-19 pandemic.

A new explicit solution is obtained for a general class of two-dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi-homogeneous problems is presented in a comprehensive framework. Then the general problem—including the unsolved case of inhomogeneous functions—is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi-)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one-dimensional case as well.

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.

Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions, and we show the advantages of utilizing these techniques for bootstrapping. The discrete convolutional approach can provide exact numerical solutions for bootstrap quantities, or at least mathematical error bounds. In contrast, Monte Carlo bootstrap methods can only provide confidence intervals which converge slowly. Additionally, for some problems the computation time of the convolutional approach can be dramatically less than that of Monte Carlo resampling. This article provides several examples of bootstrapping using the proposed convolutional technique and compares the results to those of the Monte Carlo bootstrap, and to those of the competing saddlepoint method.