Bayesian Probabilistic Neural Network (BPNN)

  • Walker H. LandJr.
  • J. David Schaffer


The purpose of this chapter is to introduce a different way of implementing Bayes theorem using a distributed, parallel algorithm first introduced by Specht (1990), which he named the probabilistic neural network (PNN). We have discussed in Chap.  6 the difficulties in constructing Bayesian networks using both the data-driven and expert-driven approaches. A significant advantage of the Bayesian PNN (BPNN) is that the node edge architecture is theoretically predetermined by the Parzen (1962)-Cacoullos (1966) theoretical formulation.

Specifically, this chapter covers the following topics.
  • It develops the mathematical formulation for the PNN.

  • It demonstrates that the normal PNN can be configured as an optimal Bayesian classifier (BPNN).

  • It shows how Parzen’s theorem maps into Cacoullos’s theorem.

  • It provides an illustrative toy example, showing a BPNN analysis for two classes and nine samples (four benign and five malignant) for a twofold cross-validation analysis.

  • It shows how to develop the optimal standard or variance sigma value for the Gaussian density function (a significant problem) and discusses PNN training methods.

  • It provides a BPNN application to the Alzheimer’s speech data.


Bayesian probabilistic neural network Kernel probability estimation Alternative kernel functions Alzheimer’s speech data 



Area under the ROC curve


Bayesian probabilistic neural network


Genetic algorithm


Generalized regression neural network


probability density function


Probabilistic neural network


Receiver operator characteristic


Support vector machine


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Walker H. LandJr.
    • 1
  • J. David Schaffer
    • 2
  1. 1.Retired Emeritus Research ProfessorBinghamton UniversityBowieUSA
  2. 2.Binghamton UniversityBinghamtonUSA

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