The paper discusses the use of information-based objective functions for active data selection in a Bayesian learning framework. The author proposes three criteria for selecting data points that maximize the expected informativeness of the measurements, each based on different assumptions about the information to be gained. These criteria are: 1. Maximizing information about the parameters of the interpolant. 2. Maximizing information about the interpolant in a specific region of interest. 3. Maximizing the discrimination between two models. The criteria are derived using a quadratic approximation and assume that the probability distributions defined by the interpolation model are correct. The paper also addresses the potential weakness of these methods, which is that they assume the model is correct, and discusses the computational complexity of the objective functions. The results are demonstrated through a neural network example, showing the expected total and marginal information gains. The paper concludes by highlighting the potential benefits and limitations of information-based approaches for active data selection.The paper discusses the use of information-based objective functions for active data selection in a Bayesian learning framework. The author proposes three criteria for selecting data points that maximize the expected informativeness of the measurements, each based on different assumptions about the information to be gained. These criteria are: 1. Maximizing information about the parameters of the interpolant. 2. Maximizing information about the interpolant in a specific region of interest. 3. Maximizing the discrimination between two models. The criteria are derived using a quadratic approximation and assume that the probability distributions defined by the interpolation model are correct. The paper also addresses the potential weakness of these methods, which is that they assume the model is correct, and discusses the computational complexity of the objective functions. The results are demonstrated through a neural network example, showing the expected total and marginal information gains. The paper concludes by highlighting the potential benefits and limitations of information-based approaches for active data selection.