Limitations

There are limitations to the method used to calculate the differentiable uncertain bound. Specifically, the mu parameter can be the difference between appropriate and inaccurate bounds on the uncertainty. To demonstrate this, two instances of executing the beta distribution example with with different mu values will be discussed below.

In the beta verification case for solving the bound on uncertainty with parameter mu = 0.1

The analytical bound is 0.9999999999999958
The interpolated bound is 0.9999999999999958
The solved bound is 1.1456864325112104

Fig. 31 The figure of solving for the confidence interval using the activation function technique for a beta distribution.

This is the same example discussed in the bound on uncertainty of a beta distribution with only the mu parameter changed. In this case, mu=1e-12 was used to acheive an appropriate result. However, choosing an appropriate value is dependent on the values of which you are calculating the uncertain bound (i.e. a smaller mu is not necessarily better for your application).