Limitations of Realistic MonteCarlo Techniques
 Publication Year:
 2016

 Bepress 10

 Bepress 4
 Repository URL:
 https://digitalcommons.utep.edu/cs_techrep/992
 Author(s):
 Tags:
 MonteCarlo techniques; interval uncertainty; Computer Sciences; Mathematics
article description
Because of the measurement errors, the result Y = f(X1, ..., Xn) of processing the measurement results X1, ..., Xn is, in general, different from the value y = f(x1, ..., xn) that we would obtain if we knew the exact values x1, ..., xn of all the inputs. In the linearized case, we can use numerical differentiation to estimate the resulting difference Y  y; however, this requires >n calls to an algorithm computing f, and for complex algorithms and large $n$ this can take too long. In situations when for each input xi, we know the probability distribution of the measurement error, we can use a faster MonteCarlo simulation technique to estimate Y  y. A similar MonteCarlo technique is also possible for the case of interval uncertainty, but the resulting simulation is not realistic: while we know that each measurement error Xi  xi is located within the corresponding interval, the algorithm requires that we use Cauchy distributions which can result in values outside this interval. In this paper, we prove that this nonrealistic character of interval MonteCarlo simulations is inevitable: namely, that no realistic MonteCarlo simulation can provide a correct bound for Y  y.