Applied Stochastic Models in Business and Industry最新文献

We investigate two asymmetric loss functions, namely linear exponential (LINEX) loss and power divergence loss for optimal spatial prediction with area-level data. With our motivation arising from the real estate industry, namely in real estate valuation, we use the Zillow Home Value Index (ZHVI) for county-level values to show the change in prediction when the loss is different (asymmetric) from a traditional squared error loss (symmetric) function. Additionally, we discuss the importance of choosing the asymmetry parameter and propose a solution to this choice for a general asymmetric loss function. Since the focus is on area-level data predictions, we propose the methodology in the context of conditionally autoregressive (CAR) models. We conclude that the choice of the loss functions for spatial area-level predictions can play a crucial role and is heavily driven by the choice of parameters in the respective loss.

This study delves into the comparison of two parallel systems, each composed of multiple component types following the scale models with a shared baseline distribution. Under some assumptions imposed on the baseline distribution, it is shown that a restricted version of the $��p�$-larger order between the scale parameter vectors implies the hazard rate order between the system lifetimes, provided that the allocation vectors of the two systems are the same. Additionally, we explore scenarios where one system embodies heterogeneous scale parameters, whereas the other adopts homogeneous ones, examining the hazard rate order between their lifetimes. For the case when the scale vectors of the two systems are the same, it is shown under some assumptions on the baseline distribution that the weak supermajorization order between the allocation vectors results in the reversed hazard rate order between the system lifetimes. Under more restrictions on the allocation vectors, an extension of this result to the likelihood ratio order is also established. Our discussion also highlights the fulfillment of these assumptions by well-known lifetime distributions such as Feller-Pareto, generalized gamma, power-generalized Weibull, exponentiated Weibull, and half-normal distributions. The findings of this work contribute to addressing gaps in the understanding of stochastic orderings between parallel systems and further refine prior research in this domain. Furthermore, the results provide a foundation for practical applications, such as optimizing resource allocation and reliability assessment in engineering and operational contexts.

North star metrics and online experimentation play a central role in how technology companies improve their products. In many practical settings, however, evaluating experiments based on the north star metric directly can be difficult. The two most significant issues are (1) low sensitivity of the north star metric and (2) differences between the short-term and long-term impact on it. A common solution is to rely on proxy metrics rather than the north star in experiment evaluation and launch decisions. Existing literature on proxy metrics concentrates mainly on the estimation of the long-term impact from short-term experimental data. In this article, instead, we focus on the trade-off between the estimation of the long-term impact and the sensitivity in the short term. In particular, we propose the Pareto optimal proxy metrics method, which simultaneously optimizes prediction accuracy and sensitivity. We also give a multi-objective optimization algorithm to solve our specific problem. We apply our methodology to experiments from a large industrial recommendation system, and found proxy metrics that are eight times more sensitive than the north star and consistently moved in the same direction, increasing the velocity and the quality of the decisions to launch new features.

The paper arises from the experience of Applied Stochastic Models in Business and Industry which has seen, over the years, more and more contributions related to Machine Learning rather than to what was intended as a stochastic model. The very notion of a stochastic model (e.g., a Gaussian process or a Dynamic Linear Model) can be subject to change: What is a Deep Neural Network if not a stochastic model? The paper presents the views, supported by examples, of distinguished researchers in the field of business and industrial statistics. They are discussing not only whether there is a future for traditional stochastic models in the era of Machine Learning and Artificial Intelligence, but also how these fields can interact and gain new life for their development.

The aim of this paper is to investigate the problem of one and two active redundant components allocation in a k-out-of-n system with dependent components. Here, some necessary and sufficient conditions are presented under which the redundancies are optimally allocated to the system components based on the usual stochastic order criterion. In addition, it is shown that, unlike the independence mode, a redundant component is not necessarily allocated to the weakest component. Further, in the case of the two redundant components, the weak (strong) redundant component is not necessarily allocated to the stronger (weaker) component of the system. Some algorithms are also presented for calculating the reliability of the considered system under the assumption of dependency between the main and redundant components. Using different copula functions for describing the dependencies between components, various examples are given to illustrate the optimal allocation of redundant components.