Combining Soft Computing and Statistical Methods in Data Analysis / Edition 1

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More About This Textbook

Overview

Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (shastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc.
About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo.

This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.

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Product Details

Table of Contents

Prior Knowledge in the Classification of Biomedical Data Danilo Abbate Roberta De Asmundis Mario Rosario Guarracino 1

Estimation of a Simple Genetic Algorithm Applied to a Laboratory Experiment Simone Alfarano Eva Camacho Josep Domenech 9

A Comparison of Robust Methods for Pareto Tail Modeling in the Case of Laeken Indicators Andreas Alfons Matthias Templ Peter Filzmoser Josef Holzer 17

R Code for Hausdorff and Simplex Dispersion Orderings in the 2D Case Guillermo Ayala 25

On Some Confidence Regions to Estimate a Linear Regression Model for Interval Data Angela Blanco-Fernández Norberto Corral Gil González-Rodríguez Antonio Palacio 33

Possibilistic Coding: Error Detection vs. Error Correction Luca Bortolussi Andrea Sgarro 41

Coherent Correction for Conditional Probability Assessments with R A. Brozzi A. Morelli F. Vattari 49

Inferential Rules for Weak Graphoid Giuseppe Busanello Barbara Vantaggi 57

Fast Factorization of Probability Trees and Its Application to Recursive Trees Learning Andrés Cano Manuel Gómez-Olmedo Cora B. Pérez-Ariza Antonio Salmerón 65

Option Pricing in Incomplete Markets Based on Partial Information Andrea Capotorti Giuliana Regoli Francesca Vattari 73

Lorenz Curves of extrema Ignacio Cascos Miguel Mendes 81

Likelihood in a Possibilistic and Probabilistic Context: A Comparison Giulianella Coletti Davide Petturiti Barbara Vantaggi 89

Nonparametric Predictive Inference for Order Statistics of Future Observations Frank P.A. Coolen Tahani A. Maturi 97

Expected Pair-Wise Comparison of the Outcomes of a Fuzzy Random Variable Inés Couso Laura Garrido Susana Montes Luciano Sánchez 105

The Behavioral Meaning of the Median Inés Couso Luciano Sánchez 115

Functional Classification and the Random Tukey Depth. Practical Issues Juan A. Cuesta-Albertos Alicia Nieto-Reyes 123

On Concordance Measures and Copulas with Fractal Support E. de Amo M. Díaz Carrillo J. Fernández-Sánchez 131

Factorisation Properties of the Strong Product Gert de Cooman Enrique Miranda Marco Zaffalon 139

Hadamard Majorants for the Convex Order and Applications Jesús de la Cal Javier Cárcamo Luis Escauriaza 149

How to Avoid LEM Cycles in Mutual Rank Probability Relations K. De Loof B. De Baets H. De Meyer 155

Functional Inequalities Characterizing the Frank Family of Copulas Hans De Meyer Bernard De Baets 165

Recent Developments in Censored, Non-Markov Multi-State Models Jacobo de Uña-Áluarez 173

Maximum Likelihood from Evidential Data: An Extension of the EM Algorithm Thierry Denœux 181

A Decision Rule for Imprecise Probabilities Based on Pair-Wise Comparison of Expectation Bounds Sébastien Destercke 189

Handling Bipolar Knowledge with Credal Sets Sébastien Destercke 199

Coherent Upper Conditional Previsions and Their Integral Representation with Respect to Hausdorff Outer Measures Serena Doria 209

Statistical Inference with Belief Functions and Possibility Measures: A Discussion of Basic Assumptions Didier Dubois Thierry Denœux 217

Representation of Exchangeable Sequences by Means of Copulas Fabrizio Durante Jan-Frederik Mai 227

Area-Level Time Models for Small Area Estimation of Poverty Indicators M.D. Esteban D. Morales A. Pérez L. Santamaría 233

Flood Analysis: On the Automation of the Geomorphological-Historical Method Elena Fernández Miguel Fernández Soledad Anadón Gil González-Rodríguez Ana Colubi 239

Geometric Sampling: An Approach to Uncertainty in High Dimensional Spaces Juan Luis Fernández-Martínez Michael Tompkins Tapan Mukerji David Alumbaugh 247

Inverse Problems and Model Reduction Techniques Juan Luis Fernández-Martínez Michael Tompkins Zulima Fernández-Muñiz Tapan Mukerji 255

A Linearity Test for a Simple Regression Model with LR Fuzzy Response Maria Brigida Ferraro Ana Colubi Paolo Giordani 263

Soft Methods in Robust Statistics Peter Filzmoser 273

S-Statistics and Their Basic Properties Marek Gagolewski Przemyslaw Grzegorzewski 281

Particle Swarm Optimization and Inverse Problems Esperanza García-Gonzalo Juan Luis Fernández-Martínez 289

Linear Approximations to the Power Function of Robust Tests A. García-Pérez 297

Decision Support for Evolving Clustering Olga Georgieva Sergey Nedev 305

On Jaffray's Decision Model for Belief Functions Phan H. Giang 313

Quasi Conjunction and p-Entailment in Nonmonotonic Reasoning A. Gilio G. Sanfilippo 321

Elements of Robust Regression for Data with Absolute and Relative Information Karel Hron Peter Filzmoser 329

On Testing Fuzzy Independence Application in Quality Control Olgierd Hryniewicz 337

The Fisher's Linear Discriminant Iuliana F. Iatan 345

Testing Archimedeanity Piotr Jaworski 353

An Attempt to Define Graphical Models in Dempster-Shafer Theory of Evidence Radim Jirousek 361

Comparison of Time Series via Classic and Temporal Protoforms of Linguistic Summaries: An Application to Mutual Funds and Their Benchmarks Janusz Kacprzyk Anna Wilbik 369

Mining Gradual Dependencies Based on Fuzzy Rank Correlation Hyung-Won Koh Eyke Hüllermeier 379

From Probabilities to Belief Functions on MV-Algebras Tomás Kroupa 387

Soft Methods in Trend Detection Piotr Ladyzynski Przemystaw Grzegorzewski 395

Linguistic Decision Trees for Fusing Tidal Surge Forecasting Model Jonathan Lawry Hongmei He 403

Set-Valued Square Integrable Martingales and Stochastic Integral Shoumei Li 411

Smooth Transition from Mixed Models to Fixed Models María José Lombardía Stefan Sperlich 419

Mixture Models with a Black-Hole Component Nicholas T. Longford Pierpaolo D'Urso 427

On the Preservations of Contractions: An Application to Stochastic Orders M.C. López-Díaz M. López-Díaz 437

A New Multivariate Stochastic Order, Main Properties Miguel López-Díaz 443

ANOVA for Fuzzy Random Variables Using the R-package SAFD M. Asunción Lubiano Wolfgang Trutschnig 449

Probability Tree Factorisation with Median Free Term Irene Martínez Carmelo Rodríguez Antonio Salmerón 457

Comparison of Random Variables Coupled by Archimedean Copulas I. Montes D. Martinetti S. Díaz S. Montes 467

Two-Way Analysis of Variance for Interval-Valued Data Takehiko Nakama Ana Colubi M. Asunción Lubiano 475

Estimating the Variance of a Kernel Density Estimation Bilal Nehme Olivier Strauss Kevin Loquin 483

Uncertainty Invariance Transformation in Continuous Case María José Pardo David de la Fuente 491

Detection of Outliers Using Robust Principal Component Analysis: A Simulation Study C. Pascoal M.R. Oliveira A. Pacheco R. Valadas 499

Exploiting Sparse Dependence Structure in Model Based Classification Tatjana Pavlenko Anders Björkström 509

Independence Tests for Uncertain Data with a Frequentist Method Simon Petitrenaud 519

Why Imprecise Regression: A Discussion Henri Prade Mathieu Serrurier 527

Power Analysis of the Homoscedasticity Test for Random Fuzzy Sets Ana Belén Ramos-Guajardo Gil González-Rodríguez Manuel Montenegro María Teresa López 537

Periodic Generalized-Differentiable Solutions to Fuzzy Differential Equations Rosana Rodríguez-López 545

The Selection of the Shrinkage Region in Small Area Estimation Cristina Rueda José A. Menéndez 553

Set-Valued Stochastic Processes and Sets of Probability Measures Induced by Stochastic Differential Equations with Random Set Parameters Bernhard Schmelzer 561

Coupled Brownian Motion Carlo Sempi 569

The Median of a Random Interval Beatriz Sinova María Rosa Casals Ana Colubi María Ángeles Gil 575

The Use of Sets of Stochastic Operators to Constructing Imprecise Probabilities Damjan Škulj 585

Prediction of Future Order Statistics from the Uniform Distribution K.S. Sultan S.A. Alshami 593

Balance Sheet Approach to Agent-Based Computational Economics: The EURACE Project Andrea Teglio Marco Raberto Silvano Cincotti 603

Connections between Statistical Depth Functions and Fuzzy Sets Pedro Terán 611

An Alternative Approach to Evidential Network Construction Jirina Vejnarová 619

Large Deviations of Random Sets and Random Upper Semicontinuous Functions Xia Wang Shoumei Li 627

A Note of Proposed Privacy Measures in Randomized Response Models Hong Zhimin Yan Zaizai Wei Lidong 635

Index 643

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