Measuring Distribution Differences: Kullback-Leibler Divergence for Improved Transfer Matrix Methods

Previous sections highlighted the limitations of traditional transfer matrix methods when dealing with samples influenced by noise, particularly when the posterior estimate of noise probability is inaccurate. This challenge arises from the gap between the distributions of probabilities A and B. To address this, we propose a metric to quantify this gap. Specifically, we introduce Kullback-Leibler divergence (KL divergence), a measure of the difference between probability distributions. KL divergence can be used to compare the similarity of two probability distributions by multiplying the ratio of each element in one distribution to its corresponding element in the other distribution, taking the logarithm of the result, and then summing the multiplied results. Calculating KL divergence allows us to quantify the difference between probability distributions, enabling the design of more accurate transfer matrix methods to handle situations involving noisy samples and unreliable noise probability posterior estimates.