Description
Book SynopsisThe 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 boo
Table of ContentsNon-Precise Data and Their Formal DescriptionNon-Precise DataNon-Precise Numbers and Characterizing FunctionsConstruction of Characterizing FunctionsNon-Precise VectorsFunctions of Non-Precise Quantities and Non-Precise FunctionsDescriptive Statistics with Non-Precise DataNon-Precise SamplesHistograms for Non-Precise DataCumulative Sums for Non-Precise DataEmpirical Distribution Function for Non-Precise DataEmpirical Fractiles for Non-Precise DataFoundations for Statistical Inference with Non-Precise DataCombination of Non-Precise ObservationsSample Moment for Non-Precise ObservationsSequences of Non-Precise ObservationsClassical Statistical Inference for Non-Precise DataPoint Estimators for ParametersConfidence Regions for ParametersNonparametric EstimationStatistical Tests and Non-Precise DataBayesian Inference for Non-Precise DataBayes' Theorem for Non-Precise DataBayesian Confidence Regions Based on Non-Precise DataNon-Precise Predictive DistributionsNon-Precise a priori DistributionsBayes Theorem for Non-Precise a priori Distribution and Non-Precise DataBayesian Decisions Based on Non-Precise InformationOutlookReferencesList of SymbolsIndex
