First, we have studied and proved the Tsallis maximum entropy principle and the Tsallis maximum entropy principle under the constraint conditions. Secondly, in view of the inverse problem of the maximum entropy method, the inverse problem of using the Tsallis maximum entropy principle to determine the prior probabilities in the Bayesian parameter estimation theory is discussed. For some specific probability distributions, the Tsallis maximum entropy principle and variation principle are used to solve the constraint conditions that maximize the Tsallis entropy. The solution of this inverse problem is generally not unique, and other distributions can also be obtained by this method.