Estimating and Choosing - Matheron, Georges

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Résumé :
Ever since the beginning of modern probability theory in the seventeenth century there has been a continuous debate over the meaning and applicability of the concept of probability. This book presents a coherent and well thoughtout framework for the use of probabilistic models to describe unique phenomena in a purely objective way. Although Estimating and Choosing was written with geostatistical applications in mind, the approach is of general applicability across the whole spectrum of probabilistic modelling. The only full-fledged treatment of the foundations of practical probability modelling ever written, this book fills an important gap in the literature of probability and statistics.

Sommaire:
I A Quest for Objectivity.- 0 Introduction.- 1 Monod and the Concept of Chance or How to Overstep the Limits of Objectivity.- Chance is a Metaphysical Concept.- The Parable of the Plumber and the Physician.- Polypeptide Chains.- An Apparent Paradox.- The Threshold of Realism or Objectivity.- 2 Why we do not Agree with the Etruscans or On the Objectivity of Probabilistic Models.- The Problem.- Some Anthropomorphic Illusions.- The Popperian Criterion of Objectivity.- Operational Concepts.- Subjectivity.- There is no Probability in Itself. There are Only Probabilistic Models.- Probabilistic Models.- The Model of Repeated Trials.- A Quest for a Criterion of Objectivity.- Operational Reconstruction of Probabilistic Concepts.- The Anticipatory Hypothesis and the Risk of Radical Error.- Panscopic and Monoscopic Models.- External Criteria and the Objectivity of a Methodology.- Criteria of Internal Objectivity Linked to the Concrete Character of the Space.- II Criteria of Internal Objectivity in the Case of Unique Phenomena.- 3 The Poisson Forest.- The Parameter ?: Does it Exist and is it Useful?.- Three Steps in the Choice of a Model.- Some Basic Guidelines.- A Criterion of Objectivity: Regional Magnitudes.- From the Vantage Point of the Practitioner.- 4 Choice and Hierarchy of Models.- A First Criterion: Decidability Through Regionals.- The Constitutive Model.- The Generic Model: Type and Specification.- Preliminary Remarks on the Criteria of Choice.- The Primary Model.- Threshold of Robustness and Threshold of Realism.- An Example of Control of Type Robustness.- Robustness in Relation to Data.- 5 Sorting Out.- Fluctuations of Regionals.- Ergodicity.- Range.- Microergodicity.- Estimation in Praxi of Regional Magnitudes.- The Example of Conditional Expectation.- The Example of Kriging.- III Operational Reconstruction.- 6 Global Models.- Representations: Strictly Objective Probabilistic Models.- Transitive Representations.- Estimation of the Transitive Covariogram.- The Approximation Formulae.- The Case of an Irregular Mesh.- Changeover to the Usual Probabilistic Models.- Global Non-Stationary Models.- 7 Local Models.- Sliding Representations.- Priority of the Method.- Locally Stationary Random Functions of Order 2.- Locally Intrinsic Random Functions of Order 0.- Locally Intrinsic Random Functions of Order k.- 8 Is Conditional Expectation Operational?.- After the Fact Objectivity of Conditional Laws.- Some Orders of Magnitude.- In Praxi: Estimation of Conditional Laws.- Disjunctive Estimators.