Optimal and Adaptive Bayesian Sampling for Non-Linear Parameter Estimation under White Noise

The question of optimal experimental design has been addressed in a vast variety of contexts and answered using manifold approaches. Assuming additive white Gaussian noise, this work applies the Bayesian framework for design optimization to the posterior distribution after marginalization over linear parameters and discusses the implications. Examples of exponentially decaying signals with and without oscillations complement the discussion. Application of the examples considered include but are not limited to nuclear magnetic resonance and relaxometry experiments using solid-state spins sensors.