The theoretical analysis can be generalized to settings where the statistics T do not necessarily have a maximum entropy distribution or where the statistics are not independent by considering alternative coding schemes that can handle more complex distributions. Instead of relying solely on maximum entropy distributions, the method can incorporate other probabilistic models that better capture the characteristics of the data.
In cases where the statistics T do not have a maximum entropy distribution, the method can utilize alternative coding frameworks that are tailored to the specific characteristics of the data. This may involve using different types of generative models or coding schemes that are better suited for the given statistics. Additionally, the theoretical analysis can be extended to consider dependencies between statistics and how they impact the overall detection performance. By incorporating more advanced modeling techniques and coding strategies, the method can be adapted to a wider range of statistical scenarios.