Limitations of Transition Matrix Method in Noisy Data: A Detailed Analysis

As mentioned in the previous section, although the transition matrix method ensures estimability, it is not applicable to situations with sample-dependent noise. Additionally, the performance of the algorithm is heavily influenced by the accuracy of the noise posterior estimation. The main reason for this result is that the product of the noise posterior probability and the transition matrix probability is not always equal, i.e., the second equation in the formula does not always hold true.