A major difficulty in computing nonadiabatic electron transfer (ET) reaction rate constants is that they, in principle, involve the computation of real-time quantum dynamics. The saddle point approximation and the maximum entropy method are in this paper explored with the goal of circumventing this problem. The real-time correlation function in the ET rate formalism must first be analytically continued into the imaginary time domain before these approaches can be employed. Both methods are then applied to a model problem of a two-state ET system coupled to a dissipative bath. The resulting numerical studies are primarily focused on the effects of the anharmonicity of the intramolecular vibrational modes and the coupling of the motion of these modes to the electronic tunneling in ET reactions. These calculations show how the anharmonicity and the electronic-vibrational coupling can significantly effect the value of an ET rate constant.