[13] Maximum entropy method of data analysis in time-resolved spectroscopy

The maximum entropy method (MEM) has become a standard method for data analysis in many fields such as image analysis, radio astronomy, nuclear magnetic resonance (NMR) spectroscopy, X-ray crystallography, electrospray mass spectroscopy, and electron spectroscopy. In time-resolved spectroscopy, MEM can successfully handle the Laplace transform without suffering from instabilities even with a limited number of data points. The latest developments of the maximum entropy method benefit from a full quantification. In this chapter, the quantified version is referred to as “classic” maximum entropy (MaxEnt) because of its fully Bayesian derivation. In practice, the most probable lifetime distribution is estimated along with extra information about the accuracy of surface, position, and width of the spectral peaks. This chapter describes the principle of the maximum entropy method and gives practical examples of simple use for biophysicists and biologists.