This paper by David J. C. MacKay explores the Bayesian approach to regularization and model comparison, focusing on the problem of interpolating noisy data. The Bayesian framework is demonstrated through the inference problem of fitting noisy data, where the concepts and methods are general and can be applied to various data modeling problems. The paper emphasizes that Bayesian methods automatically embody Occam's razor, penalizing over-complex models without the need for ad hoc penalty terms. The key concept is the evaluation of the evidence, which quantifies the preference for different models based on their ability to predict the data. The evidence is derived from the posterior probability distribution, which is influenced by the prior distribution and the likelihood of the data given the parameters. The paper also discusses the evaluation of the evidence for different parameters, such as the regularizing constant and the noise level, and how these evaluations help in choosing the most appropriate model. The Bayesian approach is shown to be particularly useful in handling complex models and noisy data, providing a robust method for model selection and regularization.This paper by David J. C. MacKay explores the Bayesian approach to regularization and model comparison, focusing on the problem of interpolating noisy data. The Bayesian framework is demonstrated through the inference problem of fitting noisy data, where the concepts and methods are general and can be applied to various data modeling problems. The paper emphasizes that Bayesian methods automatically embody Occam's razor, penalizing over-complex models without the need for ad hoc penalty terms. The key concept is the evaluation of the evidence, which quantifies the preference for different models based on their ability to predict the data. The evidence is derived from the posterior probability distribution, which is influenced by the prior distribution and the likelihood of the data given the parameters. The paper also discusses the evaluation of the evidence for different parameters, such as the regularizing constant and the noise level, and how these evaluations help in choosing the most appropriate model. The Bayesian approach is shown to be particularly useful in handling complex models and noisy data, providing a robust method for model selection and regularization.