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New York: Springer, 2018. — 897 p.This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including

Mathematics of chance (Probability and Statistics),

Mathematics of communication (Information Theory), and

Mathematics of imprecision (Fuzzy Sets Theory and others).

These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications.

The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.The Mathematics of the UncertainUsing Mathematica to Calculate Shortest Confidence Intervals

An Optimal Transportation Approach for Assessing Almost Stochastic Order

An Alternative to the Variation Coefficient

Nonparametric Mean Estimation for Big-But-Biased Data

Band Depths Based on Multiple Time Instances

On the Combination of Depth-Based Ranks

A Bayesian Network Model for the Probabilistic Safety Assessment of Roads

The Spiking Problem in the Context of the Isotonic Regression

Estimation of the Inter-occurrence Time Between Events from Incomplete Data. Analysis of Periods of Unemployment in Spain

Modelling Dynamic Hotel Pricing with Isotonic Functions

On Multistage Stochastic Mixed 0–1 Optimization with Time-Consistent Stochastic Dominance Risk Averse Management

Bivariate Copula Additive Models for Location, Scale and Shape with Applications in Biomedicine

Domain Mean Estimators Assisted by Nested Error Regression Models

Robust Approaches for Fuzzy Clusterwise Regression Based on Trimming and Constraints

Robust Morphometric Analysis Based on Landmarks

Smoothing-Based Tests with Directional Random Variables

Asymptotic Behavior of Fractional Blending Systems

Multiple Hypothesis Tests: A Bayesian Approach

\(\delta \)-Records Observations in Models with Random Trend

Recent Developments and Advances in Joint Modelling of Longitudinal and Survival Data

Long-Term Survival After Abdominal Aortic Aneurysm Repair

Some Comments on Stochastic Orders and Posets

Optimal Experimental Design for Model Selection: A Partial Review

A Statistical Analysis of the Treatment of Type 2 Diabetes in the Presence of Chronic Kidney Disease in Patients Hospitalized for Heart Failure

A Diagnostic Test Approach for Multitesting Problems

The Length-Time Bias in Tourism Surveys

Detecting Change-Points in the Time Series of Surfaces Occupied by Pre-defined NDVI Categories in Continental Spain from 1981 to 2015

Choice Functions and Rejection Sets

Mathematical Modeling in Biological Populations with Reproduction in a Non-predictable Environment

Field Substitution and Sequential Sampling Method

Working with (too) Few Samples

Estimation of the Owen Value Based on Sampling

The \(\beta \)-Gradient for Testing Probability Profiles

Mixtures of Gaussians as a Proxy in Hybrid Bayesian Networks

Sublinear Expectations: On Large Sample Behaviours, Monte Carlo Method, and Coherent Upper Previsions

A Non-iterative Estimator for Interval Sampling and Doubly Truncated Data

The Mathematics of the Uncertain: Factors Related to Survival of Spanish Firms Along Recent Crisis

A Functional Stochastic Model for the Evolution of Spanish Stock Market

Limit Behavior of Polya Urn Schemes

A Simple Step-Stress Model for Coherent Systems and Associated Inference Based on System SignaturesAsymptotic Developments for the \(\phi \)-Inequality Indices

A Logistic Regression Analysis Approach for Sample Survey Data Based on Phi-Divergence Measures

Some Multivariate Measures Based on Distances and Their Entropy Versions

Cryptographic Uncertainness: Some Experiments on Finite Semifield Based Substitution Boxes

The Roll of Dices in Cryptology

Tools for Detecting Leverage and Influential Observations in Generalized Linear Models

On Economic Applications of Information Theory

Concept Uncertainty in Adversarial Statistical Decision Theory

On Some Properties of Beta-Generated DistributionsFuzzy Multi-criteria Support for Sustainable and Social Responsible Investments: The Case of Investors with Loss Aversion

Graphical Exploratory Analysis of Fuzzy Data as a Teaching Tool

Some Results and Applications Using Fuzzy Logic in Artificial Intelligence

On Extending Fuzzy Preorders to Sets and Their Corresponding Strict Orders

Resolution of Fuzzy Relation Equations When the Fuzzy Relation is Defined on Fuzzy Subsets

Measuring Dispersion in the Context of Ordered Qualitative Scales

The Kolmogorov–Smirnov Goodness-of-Fit Test for Interval-Valued Data

On New Frameworks for Decision Making and Optimization

The Additively Decomposable Fuzzy Shannon Type Inequality Index for Positive Random Fuzzy Numbers

An Incipient Fuzzy Logic-Based Analysis of the Medical Specialty Influence on the Perception About Mental Patients

Some Results About the Vertices of k-Additive Dominating Measures

Divergence Measures: From Uncertainty to Imprecision

Discounting Imprecise Probabilities

On Some Concepts Related to Star-Shaped Sets

A Case Study-Based Analysis of the Influence of the Fuzzy Data Shape in Quantifying Their Fréchet’s Variance

A Note on Generalized Convexity for Fuzzy Mappings Through a Linear Ordering

Scale Equivariant Alternative for Fuzzy M-Estimators of Location

Measures and Vagueness

A Short Reflection on the Word ‘Probable’ in Language

Measuring Uncertainty in the Portfolio Selection ProblemQuantities Characterizing Lower Semi-Fredholm Linear Relations

Some Examples of First Exit Times

Jordan Systems: A Search for the Exceptional

The Cyclic Universe: From the Cyclical Night to the Latest Cosmological Data

Phasors, Always in the Real World

Indexation Strategies and Calmness Constants for Uncertain Linear Inequality Systems

The LFM Data Qualification in Convex Multiobjective Semi-infinite Programming

Complexity and Dynamical Uncertainty

Finite Orthogonal Laurent Polynomials

From Semi-infinite Programming to Efficiency Analysis: Forty Years of Research Experiences

Coupling of a Mixed-FEM and a Spectral BEM for the Approximation of an Exterior Elliptic ProblemPedro Gil, Colleague and Friend: Experiences Shared in the Department of Statistics and Operations Research at the Complutense University of Madrid

Pedro Gil at the Complutense University

Pedro Gil: Teacher, Researcher, Mentor, Leader and Colleague at the University of Oviedo

BSc Mathematics at the University of Oviedo. On the Launching and Two First Bachellor’s Programmes in Mathematics

Mathematics of chance (Probability and Statistics),

Mathematics of communication (Information Theory), and

Mathematics of imprecision (Fuzzy Sets Theory and others).

These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications.

The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.The Mathematics of the UncertainUsing Mathematica to Calculate Shortest Confidence Intervals

An Optimal Transportation Approach for Assessing Almost Stochastic Order

An Alternative to the Variation Coefficient

Nonparametric Mean Estimation for Big-But-Biased Data

Band Depths Based on Multiple Time Instances

On the Combination of Depth-Based Ranks

A Bayesian Network Model for the Probabilistic Safety Assessment of Roads

The Spiking Problem in the Context of the Isotonic Regression

Estimation of the Inter-occurrence Time Between Events from Incomplete Data. Analysis of Periods of Unemployment in Spain

Modelling Dynamic Hotel Pricing with Isotonic Functions

On Multistage Stochastic Mixed 0–1 Optimization with Time-Consistent Stochastic Dominance Risk Averse Management

Bivariate Copula Additive Models for Location, Scale and Shape with Applications in Biomedicine

Domain Mean Estimators Assisted by Nested Error Regression Models

Robust Approaches for Fuzzy Clusterwise Regression Based on Trimming and Constraints

Robust Morphometric Analysis Based on Landmarks

Smoothing-Based Tests with Directional Random Variables

Asymptotic Behavior of Fractional Blending Systems

Multiple Hypothesis Tests: A Bayesian Approach

\(\delta \)-Records Observations in Models with Random Trend

Recent Developments and Advances in Joint Modelling of Longitudinal and Survival Data

Long-Term Survival After Abdominal Aortic Aneurysm Repair

Some Comments on Stochastic Orders and Posets

Optimal Experimental Design for Model Selection: A Partial Review

A Statistical Analysis of the Treatment of Type 2 Diabetes in the Presence of Chronic Kidney Disease in Patients Hospitalized for Heart Failure

A Diagnostic Test Approach for Multitesting Problems

The Length-Time Bias in Tourism Surveys

Detecting Change-Points in the Time Series of Surfaces Occupied by Pre-defined NDVI Categories in Continental Spain from 1981 to 2015

Choice Functions and Rejection Sets

Mathematical Modeling in Biological Populations with Reproduction in a Non-predictable Environment

Field Substitution and Sequential Sampling Method

Working with (too) Few Samples

Estimation of the Owen Value Based on Sampling

The \(\beta \)-Gradient for Testing Probability Profiles

Mixtures of Gaussians as a Proxy in Hybrid Bayesian Networks

Sublinear Expectations: On Large Sample Behaviours, Monte Carlo Method, and Coherent Upper Previsions

A Non-iterative Estimator for Interval Sampling and Doubly Truncated Data

The Mathematics of the Uncertain: Factors Related to Survival of Spanish Firms Along Recent Crisis

A Functional Stochastic Model for the Evolution of Spanish Stock Market

Limit Behavior of Polya Urn Schemes

A Simple Step-Stress Model for Coherent Systems and Associated Inference Based on System SignaturesAsymptotic Developments for the \(\phi \)-Inequality Indices

A Logistic Regression Analysis Approach for Sample Survey Data Based on Phi-Divergence Measures

Some Multivariate Measures Based on Distances and Their Entropy Versions

Cryptographic Uncertainness: Some Experiments on Finite Semifield Based Substitution Boxes

The Roll of Dices in Cryptology

Tools for Detecting Leverage and Influential Observations in Generalized Linear Models

On Economic Applications of Information Theory

Concept Uncertainty in Adversarial Statistical Decision Theory

On Some Properties of Beta-Generated DistributionsFuzzy Multi-criteria Support for Sustainable and Social Responsible Investments: The Case of Investors with Loss Aversion

Graphical Exploratory Analysis of Fuzzy Data as a Teaching Tool

Some Results and Applications Using Fuzzy Logic in Artificial Intelligence

On Extending Fuzzy Preorders to Sets and Their Corresponding Strict Orders

Resolution of Fuzzy Relation Equations When the Fuzzy Relation is Defined on Fuzzy Subsets

Measuring Dispersion in the Context of Ordered Qualitative Scales

The Kolmogorov–Smirnov Goodness-of-Fit Test for Interval-Valued Data

On New Frameworks for Decision Making and Optimization

The Additively Decomposable Fuzzy Shannon Type Inequality Index for Positive Random Fuzzy Numbers

An Incipient Fuzzy Logic-Based Analysis of the Medical Specialty Influence on the Perception About Mental Patients

Some Results About the Vertices of k-Additive Dominating Measures

Divergence Measures: From Uncertainty to Imprecision

Discounting Imprecise Probabilities

On Some Concepts Related to Star-Shaped Sets

A Case Study-Based Analysis of the Influence of the Fuzzy Data Shape in Quantifying Their Fréchet’s Variance

A Note on Generalized Convexity for Fuzzy Mappings Through a Linear Ordering

Scale Equivariant Alternative for Fuzzy M-Estimators of Location

Measures and Vagueness

A Short Reflection on the Word ‘Probable’ in Language

Measuring Uncertainty in the Portfolio Selection ProblemQuantities Characterizing Lower Semi-Fredholm Linear Relations

Some Examples of First Exit Times

Jordan Systems: A Search for the Exceptional

The Cyclic Universe: From the Cyclical Night to the Latest Cosmological Data

Phasors, Always in the Real World

Indexation Strategies and Calmness Constants for Uncertain Linear Inequality Systems

The LFM Data Qualification in Convex Multiobjective Semi-infinite Programming

Complexity and Dynamical Uncertainty

Finite Orthogonal Laurent Polynomials

From Semi-infinite Programming to Efficiency Analysis: Forty Years of Research Experiences

Coupling of a Mixed-FEM and a Spectral BEM for the Approximation of an Exterior Elliptic ProblemPedro Gil, Colleague and Friend: Experiences Shared in the Department of Statistics and Operations Research at the Complutense University of Madrid

Pedro Gil at the Complutense University

Pedro Gil: Teacher, Researcher, Mentor, Leader and Colleague at the University of Oviedo

BSc Mathematics at the University of Oviedo. On the Launching and Two First Bachellor’s Programmes in Mathematics

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