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The formal description of non-precise data before their statistical analysis is, except for error models and interval arithmetic, a relatively young topic. Fuzziness is described in the theory of fuzzy sets but only a few papers on statistical inference for non-precise data exist. In many cases, for example when very small concentrations are being measured, it is necessary to describe the imprecision of data. Otherwise, the results of statistical analysis can be unrealistic and misleading. Fortunately, there is a straightforward technique for dealing with non-precise data. The technique - the generalized inference method - is explained in Statistical Methods for Non-Precise Data. Anyone who understands elementary statistical methods and simple stochastic models will be able to use this book to understand and work with non-precise data. The book includes explanations of how to cope with non-precise data in different practical situations, and makes an excellent graduate level text book for students, as well as a general reference for scientists and practitioners.
Table of Contents
Non-Precise Data and Their Formal Description Non-Precise Data Non-Precise Numbers and Characterizing Functions Construction of Characterizing Functions Non-Precise Vectors Functions of Non-Precise Quantities and Non-Precise Functions Descriptive Statistics with Non-Precise Data Non-Precise Samples Histograms for Non-Precise Data Cumulative Sums for Non-Precise Data Empirical Distribution Function for Non-Precise Data Empirical Fractiles for Non-Precise Data Foundations for Statistical Inference with Non-Precise Data Combination of Non-Precise Observations Sample Moment for Non-Precise Observations Sequences of Non-Precise Observations Classical Statistical Inference for Non-Precise Data Point Estimators for Parameters Confidence Regions for Parameters Nonparametric Estimation Statistical Tests and Non-Precise Data Bayesian Inference for Non-Precise Data Bayes' Theorem for Non-Precise Data Bayesian Confidence Regions Based on Non-Precise Data Non-Precise Predictive Distributions Non-Precise a priori Distributions Bayes Theorem for Non-Precise a priori Distribution and Non-Precise Data Bayesian Decisions Based on Non-Precise Information Outlook References List of Symbols Index
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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