The relation between ANNs and statistics is a topic over which much ink was spilled in the 1990s. This is the most concise discussion I can think of:
Sarle, Warren S. (1994). Neural Networks and Statistical Models. Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994.
If you want an in-depth discussion, these books relate ANNs and statistical methods:
Schürmann, Jürgen. (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches.
Raudys, Sarunas. (2001). Statistical and Neural Classifiers: An Integrated Approach to Design.
Sarle, Warren S. (1994). Neural Networks and Statistical Models. Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994.
If you want an in-depth discussion, these books relate ANNs and statistical methods:
Schürmann, Jürgen. (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches.
Raudys, Sarunas. (2001). Statistical and Neural Classifiers: An Integrated Approach to Design.