Fast algorithms for computing statistics under interval uncertainty, with applications to computer science and to electrical and computer engineering
In many engineering applications, we have to combine probabilistic and interval uncertainty. 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 measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data. In this dissertation, we will provide a survey of known algorithms for computing various statistics under interval uncertainty and their computational complexity, a description of new algorithms, and the applications of the new algorithms, including applications to the seismic inverse problem in geosciences, to chip design in computer engineering, and to radar data processing.
Xiang, Gang, "Fast algorithms for computing statistics under interval uncertainty, with applications to computer science and to electrical and computer engineering" (2007). ETD Collection for University of Texas, El Paso. AAI3304645.