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.
Features
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
Biography
Reinhard Viertl
