Chapter 11 Bayesian Networks

Abstract

A Bayesian network is a tool for modeling and reasoning with uncertain beliefs. A Bayesian network consists of two parts: a qualitative component in the form of a directed acyclic graph (DAG), and a quantitative component in the form conditional probabilities; see Fig. 11.1. Intuitively, the DAG of a Bayesian network explicates variables of interest (DAG nodes) and the direct influences among them (DAG edges). The conditional probabilities of a Bayesian network quantify the dependencies between variables and their parents in the DAG. Formally though, a Bayesian network is interpreted as specifying a unique probability distribution over its variables. Hence, the network can be viewed as a factored (compact) representation of an exponentiallysized probability distribution. The formal syntax and semantics of Bayesian networks will be discussed in Section 11.2.The power of Bayesian networks as a representational tool stems both from this ability to represent large probability distributions compactly, and the availability of inference algorithms that can answer queries about these distributions without necessarily constructing them explicitly. Exact inference algorithms will be discussed in Section 11.3 and approximate inference algorithms will be discussed in Section 11.4.Bayesian networks can be constructed in a variety of ways, depending on the application at hand and the available information. In particular, one can construct Bayesian networks using traditional knowledge engineering sessions with domain experts, by automatically synthesizing them from high level specifications, or by learning them from data. The construction of Bayesian networks will be discussed in Section 11.5.There are two interpretations of a Bayesian network structure, a standard interpretation in terms of probabilistic independence and a stronger interpretation in terms of causality. According to the stronger interpretation, the Bayesian network specifies a family of probability distributions, each resulting from applying an intervention to the situation of interest. These causal Bayesian networks lead to additional types of queries, and require more specialized algorithms for computing them. Causal Bayesian networks will be discussed in Section 11.6.

Bayesian network model to distinguish between intentional attacks and accidental technical failures: a case study of floodgates

“…BNs are used for developing medical decision support systems (Curiac et al 2009;Kahn et al 2001;Kahn Jr et al 1997;Luciani et al 2003;Milho and Fred 2001;Onisko et al 1999). Furthermore, BNs are also used in fault diagnosis (Cai et al 2014;Huang et al 2008;Zhao et al 2013), cyber security (Alile 2018; Apukhtin 2011; Axelrad et al 2013;Elmrabit et al 2020;Greitzer et al 2010;Greitzer et al 2012;Herland et al 2016;Holm et al 2015;Ibrahimović and Bajgorić 2016;Kornecki et al 2013;Kwan et al 2009;Kwan et al 2008;Mo et al 2009;Pappaterra 2021;Pecchia et al 2011;Shin et al 2015;Wang and Guo 2010;Zhou et al 2018).…”

Combining Bayesian Networks and Fishbone Diagrams to Distinguish Between Intentional Attacks and Accidental Technical Failures

“…BNs belong to the family of probabilistic graphical models [9]. BNs consist of a qualitative and a quantitative part [10]. The qualitative part is a directed acyclic graph consisting of nodes and edges.…”

Decision Support Using Belief Network Constructed from Business Process Event Log

“…One of probabilistic methods available for such analysis is Bayesian belief network (Darwiche, 2008). It allows to represent a set of variables and their conditional dependencies via a directed acyclic graph.…”

“…Bayesian inference derives the posterior probability using well known Bayesian inference formula (Darwiche, 2008): P (H |D) = P (D|H ) × P (H ) P (D) .…”