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In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections with predictions from machine learning models, it is crucial that the uncertainty of the prediction is known. Otherwise, the application of established quality management concepts is not legitimate. Deterministic (machine learning) models lack quantification of their predictive uncertainty and are therefore unsuitable. Probabilistic (machine learning) models provide a predictive uncertainty along with the prediction. However, a concise relationship is missing between the measurement uncertainty of physical inspections and the predictive uncertainty of probabilistic models in their application in quality management. Here, we show how the predictive uncertainty of probabilistic (machine learning) models is related to the measurement uncertainty of physical inspections. This enables the use of probabilistic models for virtual inspections and integrates them into existing quality management concepts. Thus, we can provide a virtual measurement for any quality characteristic based on the process data and achieve a 100 percent inspection rate. In the field of Predictive Quality, the virtual measurement is of great interest. Based on our results, physical inspections with a low sampling rate can be accompanied by virtual measurements that allow an inspection rate of 100 percent. We add substantial value, especially to complex process chains, as faulty products/parts are identified promptly and upcoming process steps can be aborted.

Nguyen et al. [1] introduced altruistic hedonic games in which agents' utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems.

The existence of stylized facts in financial data has been documented in many studies. In the past decade the modeling of financial markets by agent-based computational economic market models has become a frequently used modeling approach. The main purpose of these models is to replicate stylized facts and to identify sufficient conditions for their creations. In this paper we introduce the most prominent examples of stylized facts and especially present stylized facts of financial data. Furthermore, we given an introduction to agent-based modeling. Here, we not only provide an overview of this topic but introduce the idea of universal building blocks for agent-based economic market models., Comment: arXiv admin note: text overlap with arXiv:1812.02726

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy-Levy-Solomon model and the Franke-Westerhoff model. We derive time-continuous formulations of both models, and in particular we discuss the impact of the time-scaling on the model behavior for the Levy-Levy-Solomon model. For the Franke-Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic desciptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy-Levy-Solomon and Franke-Westerhoff model.

We study the qualitative and quantitative appearance of stylized facts in several agent-based computational economic market (ABCEM) models. We perform our simulations with the SABCEMM (Simulator for Agent-Based Computational Economic Market Models) tool recently introduced by the authors (Trimborn et al. 2019). Furthermore, we present novel ABCEM models created by recombining existing models and study them with respect to stylized facts as well. This can be efficiently performed by the SABCEMM tool thanks to its object-oriented software design. The code is available on GitHub (Trimborn et al. 2018), such that all results can be reproduced by the reader., Comment: arXiv admin note: substantial text overlap with arXiv:1801.01811

We introduce the simulation tool SABCEMM (Simulator for Agent-Based Computational Economic Market Models) for agent-based computational economic market (ABCEM) models. Our simulation tool is implemented in C++ and we can easily run ABCEM models with several million agents. The object-oriented software design enables the isolated implementation of building blocks for ABCEM models, such as agent types and market mechanisms. The user can design and compare ABCEM models in a unified environment by recombining existing building blocks using the XML-based SABCEMM configuration file. We introduce an abstract ABCEM model class which our simulation tool is built upon. Furthermore, we present the software architecture as well as computational aspects of SABCEMM. Here, we focus on the efficiency of SABCEMM with respect to the run time of our simulations. We show the great impact of different random number generators on the run time of ABCEM models. The code and documentation is published on GitHub at https://github.com/SABCEMM/SABCEMM, such that all results can be reproduced by the reader.