Bayesian networks for discrete multivariate data: an algebraic approach to inference

In this paper we demonstrate how Gröbner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Gröbner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.     

Co-variation for sensitivity analysis in Bayesian networks: Properties,consequences and alternatives

Upon varying parameters in a sensitivity analysis of a Bayesian network, the standard approach is to co-vary the parameters from the same conditional distribution such that their proportions remain the same. Alternative co-variation schemes are, however, possible. In this paper we investigate the properties of the standard proportional co-variation and introduce two alternative schemes: uniform and order-preserving co-variation. We theoretically investigate the effects of using alternative co-variation schemes on the so-called sensitivity function, and conclude that its general form remains the same under any linear co-variation scheme. In addition, we generalise the CD-distance for bounding global belief change to explicitly include the co-variation scheme under consideration. We prove a tight lower bound on this distance for parameter changes in single conditional probability tables.     

A methodology for developing Bayesian networks: An application to information technology (IT) implementation

Bayesian Networks (BNs) are probabilistic inference engines that support reasoning under uncertainty. This article presents a methodology for building an information technology (IT) implementation BN from client–server survey data. The article also demonstrates how to use the BN to predict the attainment of IT benefits, given specific implementation characteristics (e.g., application complexity) and activities (e.g., reengineering). The BN is an outcome of a machine learning process that finds the network’s structure and its associated parameters, which best fit the data. The article will be of interest to academicians who want to learn more about building BNs from real data and practitioners who are interested in IT implementation models that make probabilistic statements about certain implementation decisions.     

Independence for full conditional probabilities: Structure,factorization, non-uniqueness,and Bayesian networks

This paper examines concepts of independence for full conditional probabilities; that is, for set-functions that encode conditional probabilities as primary objects, and that allow conditioning on events of probability zero. Full conditional probabilities have been used in economics, in philosophy, in statistics, in artificial intelligence. This paper characterizes the structure of full conditional probabilities under various concepts of independence; limitations of existing concepts are examined with respect to the theory of Bayesian networks. The concept of layer independence (factorization across layers) is introduced; this seems to be the first concept of independence for full conditional probabilities that satisfies the graphoid properties of Symmetry, Redundancy, Decomposition, Weak Union, and Contraction. A theory of Bayesian networks is proposed where full conditional probabilities are encoded using infinitesimals, with a brief discussion of hyperreal full conditional probabilities.     

Linking structural equation modeling to Bayesian networks: Decision support for customer retention in virtual communities

Bayesian networks are limited in differentiating between causal and spurious relationships among decision factors. Decision making without differentiating the two relationships cannot be effective. To overcome this limitation of Bayesian networks, this study proposes linking Bayesian networks to structural equation modeling (SEM), which has an advantage in testing causal relationships between factors. The capability of SEM in empirical validation combined with the prediction and diagnosis capabilities of Bayesian modeling facilitates effective decision making from identification of causal relationships to decision support. This study applies the proposed integrated approach to decision support for customer retention in a virtual community. The application results provide insights for practitioners on how to retain their customers. This research benefits Bayesian researchers by providing the application of modeling causal relationships at latent variable level, and helps SEM researchers in extending their models for managerial prediction and diagnosis.     

Variable selection in high‐dimensional regression: a nonparametric procedure for business failure prediction

Business failure prediction models are important in providing warning for preventing financial distress and giving stakeholders time to react in a timely manner to a crisis. The empirical approach to corporate distress analysis and forecasting has recently attracted new attention from financial institutions, academics, and practitioners. In fact, this field is as interesting today as it was in the 1930s, and over the last 80 years, a remarkable body of both theoretical and empirical studies on this topic has been published. Nevertheless, some issues are still under investigation, such as the selection of financial ratios to define business failure and the identification of an optimal subset of predictors. For this purpose, there exist a large number of methods that can be used, although their drawbacks are usually neglected in this context. Moreover, most variable selection procedures are based on some very strict assumptions (linearity and additivity) that make their application difficult in business failure prediction. This paper proposes to overcome these limits by selecting relevant variables using a nonparametric method named Rodeo that is consistent even when the aforementioned assumptions are not satisfied. We also compare Rodeo with two other variable selection methods (Lasso and Adaptive Lasso), and the empirical results demonstrate that our proposed procedure outperforms the others in terms of positive/negative predictive value and is able to capture the nonlinear effects of the selected variables. Copyright © 2017 John Wiley & Sons, Ltd.