I have a series of observations, with an associated probability that an event is occuring at timestep t, something like:
[0.8, 0.8, 0.3, 0.9, 0.2]
Events can last multiple timesteps, and I know the distribution of event durations. So I have a survival function
sf(t) that tells me how likely an event is to last t timesteps.
How do I combine these to determine the probability that the event is occuring in some time window?
In the example above, there may be an event of length 4 lasting from time 0 to time 3. Another interpretation is that an event of length 2 from time 0 to 1, and another event of length 1 at time 3. How do I use the sf to determine which is most likely?