The problem: Find the estimated lifetime of an object (e.g. the time it is written next) or the corresponding PDF. This is known as a renewal process.
Constraint: it is infeasible to track metadata for every single object
Assumptions: Prediction inaccuracies for low-volume objects are permissible but inaccuracy should decrease with increasing popularity of an object
Do you have any ideas how these predictions could be achieved, possibly through the use of sketch data structures (Bloom filters, Count-min sketches, etc.) or forms of sampling (e.g. exponentially-biased reservoir sampling)? Would assuming a specific stochastic process (e.g. a Poisson process) make the problem easier to solve?
A colorful example of this problem would be: estimate when a user will next visit your site / click something, without being able to track the history of every user.
