Global fitting without a global model: regularization based on the continuity of the evolution of parameter distributions

We introduce a new approach to global data fitting based on a regularization condition that invokes continuity in the global data coordinate. Stabilization of the data fitting procedure comes from probabilistic constraint of the global solution to physically reasonable behavior rather than to specific models of the system behavior. This method is applicable to the fitting of many types of spectroscopic data including dynamic light scattering, time-correlated single-photon counting (TCSPC), and circular dichroism. We compare our method to traditional approaches to fitting an inverse Laplace transform by examining the evolution of multiple lifetime components in synthetic TCSPC data. The global regularizer recovers features in the data that are not apparent from traditional fitting. We show how our approach allows one to start from an essentially model-free fit and progress to a specific model by moving from probabilistic to deterministic constraints in both Laplace transformed and nontransformed coordinates.