56 Result(s)
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Chapter
**lin Wu
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
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Chapter
Formulation of the Problem
Need for statistical analysis. In many areas of science and engineering, we have a class (“population”) of objects, and we are interested in the values of one or several quantities characterizing objects from thi...
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Chapter
Beyond Interval Uncertainty: Taking Constraints into Account
For set information, in addition to the interval bounds on each variables x1,..., x n , we may have additional information: e.g., we may know that the actual values should satisf...
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Applications to Geophysics: Inverse Problem
In many real-life situations, we have several types of uncertainty: measurement uncertainty can lead to probabilistic and/or interval uncertainty, expert estimates come with interval and/or fuzzy uncertainty, ...
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Computing Statistics under Fuzzy Uncertainty: Formulation of the Problem
Need to process fuzzy uncertainty. In many practical situations, we only have expert estimates for the inputs x i . Sometimes, experts provide guaranteed bounds on the x ...
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Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Smooth Distributions and Info-Gap Decision Theory
In the traditional statistical approach, we assume that we know the exact cumulative distribution function (CDF) F(x). In practice, we often only know the envelopes [
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Chapter
How to Select Appropriate Statistical Characteristics
Which is the best way to describe the corresponding probabilistic uncertainty? One of the main objectives of data processing is to make decisions. As we have seen in the previous chapter, a standard way of making...
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Computing under Interval Uncertainty: Traditional Approach Based on Uniform Distributions
Traditional statistical approach: main idea. In the case of interval uncertainty, we only know the intervals, we do not know the probability distributions on these intervals. The traditional statistical approach ...
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Beyond Interval Uncertainty in Describing Statistical Characteristics: Case of Normal Distributions
In the previous two chapters, we considered the case when, in addition to the bounds on the cumulative distribution function F(x), we also have additional information about F(x) – e.g., we know that F(x) is smoot...
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Chapter
Computing under Interval Uncertainty: General Algorithms
Need for interval computations. In many application areas, it is sufficient to have an approximate estimate of y – e.g., an estimate obtained from linearization. However, in some applications, it is important to ...
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Chapter
Beyond Traditional Fuzzy Uncertainty: Type-2 Fuzzy Techniques
For fuzzy information, we assumed that we have exact numerical degrees describing expert uncertainty. As we have mentioned in the previous chapter, in practice, an expert can, at best, provide bounds (i.e., an in...
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Chapter
Computing Variance under Interval Uncertainty: An Example of an NP-Hard Problem
Formulation of the problem: reminder. In many practical applications, we need to estimate the sample variance V = \(\frac{1}{n}\) ...
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Towards Selecting Appropriate Statistical Characteristics: The Basics of Decision Theory and the Notion of Utility
In the previous chapter, we mentioned that in general, the problem of estimating statistical characteristics under interval uncertainty is NP-hard. This means, crudely speaking, that it is not possible to desi...
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Chapter
Computing Correlation under Interval Uncertainty
As we have mentioned in Chapter 21, finite population covariance C between the data sets x1,..., x n and y1,..., y n is often used to compute ...
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Chapter
Computing Entropy under Interval Uncertainty. I
Measurement results (and, more generally, estimates) are never absolutely accurate: there is always an uncertainty, the actual value x is, in general, different from the estimate
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Computing the Range of Convex Symmetric Functions under Interval Uncertainty
In general, a statistical characteristic f can be more complex so that even computing f can take much longer than linear time. For such f, the question is how to compute the range [y,
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Chapter
How Accurate Is the Input Data?
Different models can be used to describe real-life phenomena: deterministic, probabilistic, fuzzy, models in which we have interval-valued or fuzzy-valued probabilities, etc. Models are usually not absolutely ...
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Chapter
Computing Statistics under Interval Uncertainty: Case of Relative Accuracy
Formulation of the problem. In the previous chapters, we have shown that for many statistical characteristics C, computing them with a given absolute accuracy ε – i.e., computing a value
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Chapter
Applications to Bioinformatics
Formulation of the practical problem. In cancer research, it is important to find out the genetic difference between the cancer cells and the healthy cells.
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Chapter
Applications to Information Management: How to Estimate Degree of Trust
In this chapter, we use the probabilistic and interval uncertainty to estimate the degree of trust in an agent. Some of these results first appeared in [56, 141].
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Chapter
Application to Signal Processing: Using 1-D Radar Observations to Detect a Space Explosion Core among the Explosion Fragments
A radar observes the result of a space explosion. Due to radar’s low horizontal resolution, we get a 1-D signal x(t) representing different 2-D slices. Based on these slices, we must distinguish between the body ...
