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I'm currently at a loss. I want to make a model that predicts when content providers aren't going to update anymore, but I'm having trouble finding a model that allows me to capture what I want. To explain, let me introduce my problem as a case of beeping boxes.

Scenario:

Imagine you have a number of red, blue, and green boxes. Every box makes a beeping noise once in a while. Each box beeps at semi-irregular intervals somewhat specific to the box, sometimes with occasionally longer periods of silence.

You notice that some boxes have "died" and no longer beep, and that sometimes their deaths are preceded by the beeping intervals slowing down. The extent to which this is true varies on an individual basis, perhaps correlated with box color. You've logged every beep in many different boxes' lifetimes at this point (and maybe are logging ones that are still "alive"), and you are now presented with a new box.

With data you've collected from the other boxes, and enough data from observing the new box beep, at a given point in time can you predict the probability that the new box will never beep again?

What sort of model can I use that will let me estimate this? Here's what I've considered:

My confusion about what model to use:

  • Survival analysis doesn't quite seem to be the right type of model for this, given that I'm not predicting the survival of population, but of an individual (and that the length of time the box has been alive isn't a factor in its survival).
  • I thought maybe a moving average model would work, but the observations aren't equally spaced in time, and moving averages require stationary data, while I care about trends.
  • The best model I've seen so far probably is a inhomogeneous Poisson point process, but I'm not sure it can account for the types of considerations I want--if, say, a box has a short frequency but occasionally large lags, I'd want the model to "consider" the possibility that the current silence could be a lag as well.

I really like working with stats, but right now I just don't know where to even look. Even if you're not an expert, I'd appreciate any pointers, guesses, or directions you might suggest.

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