Computer Engineering Commons^™

Monte-Carlo-Type Techniques For Processing Interval Uncertainty, And Their Geophysical And Engineering Applications, Matthew G. Averill, Kate C. Miller, George R. Keller, Vladik Kreinovich, Jan Beck, Roberto Araiza, Roberto Torres, Scott A. Starks

Departmental Technical Reports (CS)

To determine the geophysical structure of a region, we measure seismic travel times and reconstruct velocities at different depths from this data. There are several algorithms for solving this inverse problem, but these algorithms do not tell us how accurate these reconstructions are.

Traditional approach to accuracy estimation assumes that the measurement errors are independently normally distributed. Problem: the resulting accuracies are not in line with geophysical intuition. Reason: a typical error is when we miss the first arrival of the seismic wave; it is not normal (bounded by the wave period T) and not independent.

Typically, all we know …

Towards Combining Probabilistic And Interval Uncertainty In Engineering Calculations, Scott A. Starks, Vladik Kreinovich, Luc Longpre, Martine Ceberio, Gang Xiang, Roberto Araiza, J. Beck, R. Kandathi, A. Nayak, R. Torres

Departmental Technical Reports (CS)

In many engineering applications, we have to combine probabilistic and interval errors. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only know the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data. Such modification are described in this paper.