56 Result(s)
within
Chapter
**lin Wu
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
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Chapter
Computing under Fuzzy Uncertainty Can Be Reduced to Computing under Interval Uncertainty: Reminder
In this part, we present algorithms for computing the values of different statistical characteristics C(x1,...,x n ) under interval and fuzzy uncertainty.
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Computing Mean under Interval Uncertainty
We have already mentioned that for the interval data x1 = [ \(\underline{x}_{1}\) ,
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Computing Mean, Variance, Higher Moments, and Their Linear Combinations under Interval Uncertainty: A Brief Summary
In the previous chapters, we described several results and algorithms for computing:
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Computing Statistics under Probabilistic and Interval Uncertainty: A Brief Description
Computing statistics under probabilistic uncertainty. In the case of probabilistic uncertainty, we know the probability distributions for measurement errors corresponding to all the inputs x1,..., x ...
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Computing under Interval Uncertainty: When Measurement Errors Are Small
Linearization: main idea. When the measurement errors Δx i are relatively small, we can use a simplification called linearization. The main idea of linearization is as follows.
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Beyond Traditional Fuzzy Uncertainty: Interval-Valued Fuzzy Techniques
For fuzzy information, we assumed that we have exact numerical degrees describing expert uncertainty. This is, of course, a simplifying assumption. In practice, an expert can, at best, provide bounds (i.e., an in...
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Computing Median (and Quantiles) under Interval Uncertainty
Need to go beyond arithmetic average. We have mentioned, in the Formulation of the Problem chapter, that an important source of interval uncertainty is the existence of the lower detection limits for sensors: if ...
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Computing under Interval Uncertainty: Computational Complexity
In this chapter, we will briefly describe the computational complexity of the range estimation problem under interval uncertainty.
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Types of Interval Data Sets: Towards Feasible Algorithms
Need to consider specific types of interval data sets. The main objective of this book is to compute statistics under interval uncertainty. The simplest and most widely used statistical characteristics are mean a...
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Computing Variance under Hierarchical Privacy-Related Interval Uncertainty
Need for hierarchical statistical analysis. In the above text, we assumed that we have all the data in one large database, and we process this large statistical database to estimate the desired statistical charac...
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Computing Covariance under Interval Uncertainty
When we have two sets of data x1,..., x n and y1,..., y n , we normally compute finite population covariance
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Computing Higher Moments under Interval Uncertainty
Higher central moments M h = \(\frac{1}{n}\) ·
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Computing Expected Value under Interval Uncertainty
In statistics, the values of the statistical characteristics are estimated either directly from the sample x1,...,x n , or indirectly: based on the values of other statistical ch...
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Computing Entropy under Interval Uncertainty. II
Formulation of the problem. In most practical situations, our knowledge is incomplete: there are several (n) different states which are consistent with our knowledge. How can we gauge this uncertainty? A natural ...
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Computing Statistics under Interval Uncertainty: Possibility of Parallelization
In this chapter, we show how the algorithms for estimating variance under interval and fuzzy uncertainty can be parallelized. The results of this chapter first appeared in [336].
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From Computing Statistics under Interval and Fuzzy Uncertainty to Practical Applications: Need to Propagate the Statistics through Data Processing
Need for data processing. In many areas of science and engineering, we are interested in a quantity y which is difficult (or even impossible) to measure directly. For example, it is difficult to directly measure ...
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How Reliable Is the Input Data?
In traditional interval computations, we assume that the interval data corresponds to guaranteed interval bounds, and that fuzzy estimates provided by experts are correct. In practice, measuring instruments ar...
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Applications to Computer Science: Optimal Scheduling for Global Computing
In many practical situations, in particular in many bioinformatics problems, the amount of computations is so huge that the only way to perform these computations in reasonable time is to distribute them betwe...
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Applications to Information Management: How to Measure Loss of Privacy
In this chapter, we use the experience of measuring a degree of mismatch between probability models, p-boxes, etc., described in Chapter 30, to measure loss of privacy. Some of our privacy-related results firs...
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Applications to Computer Engineering: Timing Analysis of Computer Chips
In chip design, one of the main objectives is to decrease its clock cycle. On the design stage, this time is usually estimated by using worst-case (interval) techniques, in which we only use the bounds on the ...
