Typical reconstruction limit and phase transition of maximum entropy method

The Maximum Entropy Method (MEM) is a widely used analytical technique in various fields of physics and related disciplines, such as astronomy, planetary science, solid-state physics, and polymer chemistry. It is particularly useful for evaluating true results from noisy and limited observational data, as well as from computationally expensive simulations. This evaluation method relies on prior information known as the "default model," and the influence of this prior on the final results can be substantial. Thus, the validity of the default model directly impacts the accuracy of the results.

In this study, we assess the dependency of MEM evaluations on the default model by employing the replica method. Specifically, we have identified the existence of reconstructable and unreconstructable regions for certain models, and have revealed a phase transition phenomenon between these regions. Through numerical simulations and analysis using the replica method, we demonstrate that when the discrepancy between the default model provided as prior information and the true data increases, there comes a point where reconstruction becomes impossible. We report these findings, supported by concrete numerical calculations.