文献类型： 会议论文

第一作者： Martine Ceberio

作者： Martine Ceberio ¹ ; Vladik Kreinovich ¹ ; Gang Xiang ¹ ; Scott Ferson ² ; Cliff Joslyn ³ ;

作者机构： 1.Dept. of Computer Science, University of Texas at El Paso

2.Applied Biomathematics

3.Distributed Knowl. Syst. Team, Computer Research Group

会议名称： Gamm-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics

主办单位：

页码： 253-261

摘要： In many practical situations, we need to combine probabilistic and interval uncertainty. For example, we need to compute statistics like population mean E = 1/n · ∑ from i=1 to n of x_i or population variance V = 1/n · ∑ from i=1 to n of (x_i - E)~2 in the situations when we only know intervals x_i of possible values of x_i. In this case, it is desirable to compute the range of the corresponding characteristic. Some range computation problems are NP-hard; for these problems, in general, only an enclosure is possible. For other problems, there are efficient algorithms. In many practical situations, we have additional information that can be used as constraints on possible cumulative distribution functions (cdfs). For example, we may know that the actual (unknown) cdf is Gaussian. In this paper, we show that such constraints enable us to drastically narrow down the resulting ranges - and sometimes, transform the originally intractable (NP-hard) computational problem of computing the exact range into an efficiently solvable one. This possibility is illustrated on the simplest example of an NP-problem from interval statistics: the problem of computing the range V of the variance V. We also describe how we can estimate the amount of information under such combined intervals-and-constraints uncertainty.

分类号： TP3-53