Probabilities, Intervals, What Next? Extension of Interval Computations to Situations with Partial Information about Probabilities
نویسندگان
چکیده
In many real-life situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easier-to-measure quantities x1, . . . , xn which are related to y by a known relation y = f(x1, . . . , xn). Measurements are never 100% accurate; hence, the measured values x̃i are different from xi, and the resulting estimate ỹ = f(x̃1, . . . , x̃n) is different from the desired value y = f(x1, . . . , xn). How different? Traditional engineering to error estimation in data processing assumes that we know the probabilities of different measurement error ∆xi def = x̃i − xi. In many practical situations, we only know the upper bound ∆i for this error; hence, after the measurement, the only information that we have about xi is that it belongs to the interval xi def = [x̃i − ∆i, x̃i + ∆i]. In this case, it is important to find the range y of all possible values of y = f(x1, . . . , xn) when xi ∈ xi. We start with a brief overview of the corresponding interval computation problems. We then discuss what to do when, in addition to the upper bounds ∆i, we have some partial information about the probabilities of different values of ∆xi.
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