Using Pymc3 to do forecasting and numerical integration

Thanks. I have been recently reading about the integrating codes in Custom theano Op to do numerical integration.

I try to embed the codes with the above model where:
func = pm.math.exp(-(beta*(t - t0))**2)
integrate = Integrate(func, t, beta, t0)
integral_results= integrate(start, stop, beta, t0)
mu = alpha/2 *(1 + 2/pm.math.sqrt(math.pi)*integral_results )

But it does not seem to work. The integrating part is essentially the following formula:
image
where the Greek letter alpha corresponds to “beta” in the above code, and the Greek letter beta corresponds to “t0” in the above code. The ‘t’ variable in the picture is just the “predictor”, indicating timepoint from 0 to 92 (a total of 93 time points).

I know this problem is much more specific, but I think with clear integrating formula, we can understand the codes much better.

Thank you in advance!