Parameter Estimation of the Normal Ratio Distribution with Variational Inference

In this paper, we propose a new method for parameter estimation of the probability density function of the photosystem II (PSII) index in chlorophyll fluorescence imaging. The PSII index is modeled as the ratio of two normal distributions. The proposed method is based on hierarchical Bayesian modeling, and the mean field variational Bayes is performed to approximate the hierarchical Bayesian inference. The approach is evaluated using data acquired on Arabidopsis thaliana. The optimal variational Bayes posterior distributions are computed and then used to estimate the parameters. The preliminary results on the parameter estimation are satisfactory and meet our expectations.