*GC*: *n*

CT: A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in causal form) and data. Four, Bayesian statistical methods in conjunction with bayesian networks offer an efficient and principled approach for avoiding the overfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarize Bayesian statistical methods for using data to improve these models. With regard to the latter task, we describe methods for learning both the parameters and structure of a Bayesian network, including techniques for learning with incomplete data. In addition, we relate Bayesian-network methods for learning to techniques for supervised and unsupervised learning. We illustrate the graphical-modeling approach using a real-world case study.

S: http://research.microsoft.com/apps/pubs/?id=69588 (last access: 3 March 2015)

N: 1. bayesian (*adj*): According to David (39; 40; 41), the term “Bayesian” was first used in print by R.A. Fisher in the 1950 introduction to his 1930 paper on fiducial inference entitled “Inverse Probability,” as reprinted in his Contributions to Mathematical Statistics (66).

Eponymous from Thomas Bayes, (born 1702, London, England—died April 17, 1761, Tunbridge Wells, Kent), English Nonconformist theologian and mathematician who was the first to use probability inductively and who established a mathematical basis for probability inference (a means of calculating, from the frequency with which an event has occurred in prior trials, the probability that it will occur in future trials.

network (*n*): “net-like arrangement of threads, wires, etc.,” 1550s, from *net* (*n.*) + *work* (*n.*). Extended sense of “any complex, interlocking system” is from 1839 (originally in reference to transport by rivers, canals, and railways). Meaning “broadcasting system of multiple transmitters” is from 1914; sense of “interconnected group of people” is from 1947.

2. A Bayesian network is a graphical structure that allows us to represent and reason about an uncertain domain. The nodes in a Bayesian network represent a set of random variables, X = X1,..Xi,…Xn, from the domain. A set of directed arcs (or links) connects pairs of nodes, Xi → Xj, representing the direct dependencies between variables. Assuming discrete variables, the strength of the relationship between variables is quantified by conditional probability distributions associated with each node. The only constraint on the arcs allowed in a BN is that there must not be any directed cycles: you cannot return to a node simply by following directed arcs. Such networks are called directed acyclic graphs, or simply dags.

S: 1. http://www.stat.cmu.edu/~fienberg/fienberg-BA-06-Bayesian.pdf. (last access: 3 March 2015); OED – http://www.etymonline.com/index.php?allowed_in_frame=0&search=network&searchmode=none (last access: 3 March 2015); EncBrit – http://global.britannica.com/EBchecked/topic/56807/Thomas-Bayes (last access: 3 March 2015). 2. http://www.csse.monash.edu.au/bai/book/BAI_Chapter2.pdf (last access: 3 March 2015).

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