The paper presents a practical Bayesian framework for learning mappings in feedforward networks, addressing several key issues such as objective comparisons between network architectures, stopping rules for pruning or growing procedures, and the selection of weight decay terms. The Bayesian approach embodies "Occam's razor" by penalizing overcomplex models and helps detect poor underlying assumptions in learning models. The framework is based on the Bayesian evidence, which automatically penalizes overflexible and overcomplex models. The paper also discusses the limitations of traditional methods like cross-validation and test set evaluation, and proposes objective criteria for setting parameters and comparing solutions. The Bayesian framework is applied to a small interpolation problem, demonstrating its effectiveness in selecting optimal network structures and regularizers. The paper concludes with a discussion on the theoretical and practical aspects of the Bayesian method, including its scalability and potential applications to larger problems and classification tasks.The paper presents a practical Bayesian framework for learning mappings in feedforward networks, addressing several key issues such as objective comparisons between network architectures, stopping rules for pruning or growing procedures, and the selection of weight decay terms. The Bayesian approach embodies "Occam's razor" by penalizing overcomplex models and helps detect poor underlying assumptions in learning models. The framework is based on the Bayesian evidence, which automatically penalizes overflexible and overcomplex models. The paper also discusses the limitations of traditional methods like cross-validation and test set evaluation, and proposes objective criteria for setting parameters and comparing solutions. The Bayesian framework is applied to a small interpolation problem, demonstrating its effectiveness in selecting optimal network structures and regularizers. The paper concludes with a discussion on the theoretical and practical aspects of the Bayesian method, including its scalability and potential applications to larger problems and classification tasks.