Fitting of nonnegative physical models based on statistical divergence: application to thermally stimulated depolarization currents - Yasunobu Ando; Shusuke Kasamatsu; Suguru Iwasaki; Yumi Tanaka (Science and Technology of Advanced Materials: Methods)
We propose a theoretical formalism for inferring the parameters of non-negative physical models via statistical divergence to generalise the fitting process beyond conventional methods. For example, we show that minimising L2 and Kullback–Leibler divergence is equivalent to least squares and maximum likelihood estimation, respectively, for the parameters of non-negative physical models like a probability distribution. To demonstrate this formalism, parameters were estimated in a theoretical model of the thermally stimulated depolarisation current (TSDC), which has a non-negative but complex exponential form. Some technical aspects were also discussed as key points to enable high-throughput fitting of multimode models of TSDC using the proposed formalism, such as the use of the peak temperature as a fitting parameter, which is easily estimated from measured data, instead of a pre-exponential factor that varies by orders of magnitude, and the use of the generalised exponential integral function to speed up the fitting algorithm.