Originally posted by jamesbrown
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It's true some deterministic predictions may use of historical data. Typically not the case with myself, I would not depend on the results nor would my clients. In my industry accuracy is a prerequisite or I'll be sent packing back to Blighty. Probabilistic predictions offer far more utility using historical data than deterministic ever will.

All sorts of deterministic models make use of historical data to estimate their parameters without introducing any stochastic terms. As I said, it's a modelling choice. No idea what you're on about with regard to "similar event" or the time invariance of a stochastic process or "likelihood" w/r to a deterministic prediction. I think you're getting confused by stationarity or, perhaps, just in general.
An event is simply a subset of a sample space. You don't need a "similar" event to make a prediction, you need a model, which may or may not have parameters to estimate from data.
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