208 Pages
by
CRC Press
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... Read more
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
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
