Abstract
Abstract This chapter introduces the Bayesian Belief Network (BBN) experimental protocol. It provides an introduction and a discussion on Bayes’ Research Methodology and the Joint Space and Disjoint Bayesian Belief Network Structure to include a description of the 9-steps to use, in conducting a Bayesian experiment, which include: Step 1: Identify a population of interest, Step 2: Specify a BBN with joint and/or disjoint Nodes, Step 3: Slice through each node, and identify at a minimum, two mutually exclusive or disjoint (unconditional) events, which are the subsets of our population, Step 4: Conduct the random experiment, Step 5: Determine frequency counts, Step 6: Determine prior5 or unconditional probabilities, Step 7: Determine likelihood probabilities, Step 8: Determine joint and marginal probabilities, and Step 9: Determine posterior probabilities.
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Notes
- 1.
This includes joint and disjoint BBN.
- 2.
We use variables (Var) and nodes interchangeably.
- 3.
In this manual, Var A, or Node A will always be the parent node.
- 4.
Since this is an unobservable event, we cannot identify the elements of this set so the conditional identification of the observable element allows for the counting.
- 5.
Our Var A is our proxy for the unobservable event.
- 6.
These priors can be vague, but we will see that they can be “washed them away” across BNN nodes using the chain rule of probability.
- 7.
In theory, we can determine these discrete event probabilities before conducting the experiment, to satisfy the independence requirement of the theorem. This is a common fallacy and researchers should not use priors they obtain from observable events. The concept of prior information and unconditional (see Earman (1992) for a thorough discussion of the problem of priors and other foundational controversies in Bayesian philosophy of science) probabilities is unique and it represents how confident we are in our initial beliefs.
- 8.
In our experiment, we will deviate from this premise only to provide contiguous examples of synthetic BBN and their solutions. We will obtain these priors by counting the experimental data.
- 9.
Of great importance in algorithm development, is that one can compute the joint probabilities directly from the frequency counts. For example, P(A, B) = C(A, B)∕Total.
References
Earman, J. (1992). Bayes or bust: A critical examination of Bayesian confirmation theory. Cambridge: MIT Press.
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Grover, J. (2016). Bayesian Belief Networks Experimental protocol. In: The Manual of Strategic Economic Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-319-48414-3_4
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DOI: https://doi.org/10.1007/978-3-319-48414-3_4
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