Characterization of Parameter Uncertainty in Global Analysis for Ultrafast Spectroscopy Using Markov Chain Monte Carlo Sampling

Ultrafast spectroscopy has advanced our understanding of chemical reaction mechanisms on molecular time scales, guiding the rational design of molecular systems and processes with spatial (atomic, nuclear) and temporal (electronic, vibrational) precisions. Kinetic analysis of ultrafast spectroscopic measurements yields valuable insights into the physical mechanisms that determine the behavior of a wide range of important chemical systems from chromophores and fluorescent proteins to nanosystems. One powerful and widely used method is global analysis, which uses a unified kinetic description of the entire spectrum. Importantly, interpretation of fit parameters to build a mechanistic understanding relies on an accurate estimate of the uncertainty. Software and numerical techniques using global analysis to fit data are well-developed; however, there is much less work on uncertainty analysis of the resulting kinetic parameters. Due to the nonlinear nature of modeling, traditional methods tend to underestimate the uncertainty. Building on previous work, we implement Markov chain Monte Carlo (MCMC) sampling to estimate the parameter uncertainty. We develop a procedure that can be readily included in the existing analysis software and demonstrate it on a series of generated and experimental femtosecond transient absorption data sets. Our results suggest that global analysis, using the simultaneously collected spectral data at many wavelengths, is crucial for accurate parameter estimation. The retrieved parameter uncertainty is well within 10% for a typical spectral data set with reasonable signal-to-noise ratios.