Abstract
The previous chapters have laid a foundation for building probability models and embedding them in a graphical structure. Once we have expressed all of the interrelationships in terms of a joint probability distribution, it is possible to calculate the effect of new information about any subset of the variables on our beliefs about the remaining variables (i.e., to propagate the evidence). This chapter addresses efficient calculation in networks of discrete variables. The objective is to ground intuition with a simplified version of a basic junction-tree algorithm, illustrated in detail with a numerical example.
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Notes
- 1.
Weiss (2000) attempts to characterize situations in which the algorithm will converge and produce proper marginal distributions. This seems to depend on both the network and the evidence (Murphy et al. 1999). Weiss (2000) does note that the loopy-propagation algorithm will always produce the proper Maximum A Posteriori (MAP) estimate, even if the margins are incorrect.
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Almond, R., Mislevy, R., Steinberg, L., Yan, D., Williamson, D. (2015). Efficient Calculations. In: Bayesian Networks in Educational Assessment. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2125-6_5
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DOI: https://doi.org/10.1007/978-1-4939-2125-6_5
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2124-9
Online ISBN: 978-1-4939-2125-6
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