Classical neural networks use maximum likelihood to determine network parameters (weights and biases) and hence make predictions. Bayesian neural networks marginalize over the distribution of parameters in order to make predictions. So the Bayesian approach allows different models to be compared (e.g. no of hidden units).
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. The model takes prior knowledge and data, and lets you estimate posterior probabilities of outcomes.
Bayesian neural network can employ Bayesian prior to regularize the neural network. This can find the optimum complexity for the model I.e. optimum sparsity that minimizes overfitting, provides an objective stopping criterion for training, and maximizes the predictive power of models
Article Robust QSAR Models from Novel Descriptors and Bayesian Regul...
As i know, Bayesian Networks are graphical models that present the probabilistic relationships between continus/ discret, qualitative/ quantitative variables using the bayesian inference . So with this tool you can estimate a probability of having an event given some observations or prior knowledge. her the concept of causality is explicitly treated.
As far as Bayesian Neural Networks, they are mathematical models that use the bayesian inference to maximise the posterior probability distribution of the parameters( weights and biases) of the network in the training phase to avoid the problem of overfiting and generalization. Two posibilities were develloped for this purpose : optimization and integration. see http://wol.ra.phy.cam.ac.uk/mackay/Bayes_FAQ.html
they are different side utility and building. BN are often for pilotage and risk management issues and BNN are often used in simulation and approximation of non-linear function without explicitly describe the interaction between input variables
Bayesian networks and Bayesian neural networks are two different types of models in machine learning.
A Bayesian network is a probabilistic graphical model representing the relationships between variables and their conditional dependencies. In a Bayesian network, the nodes represent variables and the edges represent the relationships between variables. The model can perform probabilistic inference and make predictions based on uncertain data.
On the other hand, a Bayesian neural network is a type of artificial neural network that incorporates Bayesian principles into the training process. In a Bayesian neural network, the weights and biases of the network are treated as random variables, and their distribution is estimated during the training process. This allows for a probabilistic model interpretation and provides a measure of uncertainty in the predictions.