Gil E., Gil E., Gil J., Gil M.A. (eds.) The Mathematics of the Uncertain: A Tribute to Pedro Gil

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
Modeling 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 Modeling 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