For a classification problem, consider two steps: training and testing.
Assume that the Bayesian network classifier is required to be designed based on data.
At first, uniform distribution is assigned to each node because there is no prior information. Then in training step, the parameters of each node is determined based on Maximum Likelihood estimation.
Is it correct to say learned parameters define posterior distribution?
In addition, the next step is testing. P(Class | evidence) is calculated for each feature vectors and the posterior distribution is evaluated for each class node. I would assign the feature vector to any class that have the highest probability.
Is it called the maximum a-posteriori?
http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation can help you
In statistical terms,a-posteriori probability occurs whenever you try to learn how to optimize a model by comparing a theoretical distribution with your output, by guessing your data follow an a-priori not known distribution and adjusting a weighted function to make your result much closer to the theoretical distribution.
See for instance the concept of cross-entropy
Have a nice time
http://en.wikipedia.org/wiki/Maximum_a_posteriori_estimation can help you
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