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Suppose we have some real-valued function f(x) and several data points for certain values of x:

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What would be the best way to estimate the value of f(x) for some arbitrary x (for example, x = 3.5) without assuming any prior knowledge of f internals? Is it possible to derive a probability distribution for f(x) for given x?

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    Which one is best depends on your application. You could do trapezoids, parabolas, Fourier, polynomial, and probably dozens of others, all with their different advantages. – 2017-02-03
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    @Arthur - my understanding is that I would be able to select from those methods if I had some domain-specific knowledge about `f(x)`. But is there some generalized way, that while non-optimal will still converge to real distribution for any function, given enough data points? – 2017-02-03

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