Question about Eqn. 21 in the paper and its implementation in rmtpp.py

[NataliaVConnolly]

Hi Georg,

I've greatly enjoyed reading your paper and appreciate you making the code available!

Could you please help me understand Eqn. (21) in your paper and its implementation in the code? Eqn. (20) gives the expression for the conditional expected return time E[T|T>t_p] where t_p = start of prediction window. But then in Eqn. (21) t_p gets replaced by t_s, and I am not sure what that is. Looking at the code in rmtpp.py, it looks like this def corresponds to Eqn. (21), correct?

def pred_next_starttime_rec(self, cur_state, t_j):
    absence_time = 365*self.time_scale - t_j
    s_ts = self._pt(absence_time, cur_state)

    ts = np.arange(t_j, 1000*self.time_scale, self.time_scale)
    delta_ts = ts - t_j
    samples = self._pt(delta_ts, cur_state)

    return (1/s_ts) * trapz(samples[ts>(365*self.time_scale)], ts[ts>(365*self.time_scale)]) + trapz(samples[ts<=(365*self.time_scale)], ts[ts<=(365*self.time_scale)])

So then it looks like t_s is 365 days. I am not sure what that means? Doesn't this imply that we are requiring return times to be after a year? If so, why? Why not use predPeriod[start] for t_s?

I would greatly appreciate your help with this!

Thanks so much,
Natalia