ok, yes I think we are on the same page now. The only difference is that I don’t really care about the points scored in one “bucket” time interval, but only for the points that are still going to be scored. If S_i = 4 the label/outcome in t=0 would be 4 and in t=99 its 0.
But I think with your definition of R_{i,t} and the cumsum we are talking about the same thing.
Ok so you helped me to understand that I had a big error when modeling the labels / R_{i,t}. I will change that to T \times N. The feature Matrix has the shape T \times k \times N. Which is practically the same as T \cdot N \times k, correct?
So to calculate theta, I take your first advice and calculate
theta = pm.invlogit((at[:, :, None] * xt_theano).sum(axis=1) + beta)
So in the last line:
like = pm.Poisson("like", (100-t)*theta, observed=labels)
Theta is of the size T \times N and with the new/correct modeling of the labels/R_{i,t} is also the size T \times N now for the t part I guess I will also take a T \times N matrix with N times the values from 0 to 99?
And pymc3 “understands” that entry [x][y] of the observed corresponds to entry [x][y] of theta and [x][y] of t? Because then I think I got it 