Tryfos, Peter

The Measurement of Economic Relationships

Series: Advanced Studies in Theoretical and Applied Econometrics, Vol. 41

2004, XIII, 148 p., Hardcover
ISBN: 1-4020-2838-5

About this book

The Measurement of Economic Relationships presents a critical review of the established approach to measuring relationships in business and economics and of the one that preceded it. The first approach is based on the notion of a process "generating" the observations in a certain "random" manner, the second on the concept of approximating the observations of the variable of interest as closely as possible. It is shown that both approaches offer measures of the contribution of the determining variables, interval estimates and tests concerning the effects of the variables, and interval forecasts; in general, however, their solutions are different. In reviewing the two approaches since their first appearance at the end of the 18th century, little justification is found for the manner in which the established approach perceives the economic world. Doubts are raised that substantial real progress has been made since the advent of the so-called "probabilistic revolution." It is suggested that the simplicity and transparency of the approximating approach should be preferred

Table of contents

Preface Chapter 1 Introduction 1.1 The Status Quo 1.2 The CLM in Academic Studies 1.3 The CLM in Practice 1.4 Extensions of the CLM 1.5 The Road Ahead Chapter 2 The Fitting Method: An Introduction 2.1 Introduction 2.2 The Problem 2.3 The Available Information 2.4 One Solution 2.5 Least Squares and Spreadsheets 2.6 Constrained Least Squares 2.7 Tolerance Intervals 2.8 Joint Tests and Tolerance Regions 2.9 Interval Forecasts 2.10 Computer Output 2.11 In Summary Chapter 3 The Fitting Method: A formal Treatment 3.1 Introduction 3.2 Relationships 3.3 Unrestricted Least Squares 3.4 Restricted Least Squares 3.5 Ordinary Tolerance Intervals and Regions 3.6 A Tolerance Region for All Parameters 3.7 Tolerance Interval Forecasts 3.8 Possible Extensions Chapter 4 The Classical Linear Model 4.1 Introduction 4.2 The Assumptions of the CLM 4.3 Estimates and Their Properties 4.4 Statistical Inference 4.5 Specification Error 4.6 On Confidence Interval Estimates 4.7 The Many Problems of Significance 4.8 On Confidence Interval Forecasts 4.9 The Art and Practice of Statistical Inference 4.10 Bad Practice or Bad Theory? Chapter 5 The Central Assumptions 5.1 Introduction 5.2 True Parameters? 5.3 The Randomness of Error 5.4 Probability 5.5 The Central Limit Theorem and Normality 5.6 Are the Unknown Factors Random Variables? 5.7 Serial Correlation 5.8 The eAs Iff Argument 5.9 A Probably Deviation 5.10 On the Distribution of Residuals 5.11 In Summary Chapter 6 Random Processes 6.1 Introduction 6.2 The Coin Toss 6.3 Of Birth and Deaths 6.4 Stock market Prices 6.5 Some Perils of Time Series Analysis 6.6 In Conclusion Chapter 7 The eProbabilistic Revolutionf 7.1 Introduction 7.2 Before Haavelmo 7.3 Haavelmo on Relationships 7.4 Haavelmo in Contemporary Reviews 7.5 The Probability Approach Reconsidered 7.6 Random Sampling 7.7 The Assumptions Reconsidered, Continuation 7.8 In Summary Chapter 8 Assessment 8.1 The Fitting Method in Perspective 8.2 The Tolerance Level 8.3 The Technical Pursuit of Fit 8.4 The Success Rate of Tolerance Interval Forecasts 8.5 The Poverty of Properties 8.6 Does it Matter 8.7 Subjective Probability 8.8 Determinism and Probabilism 8.9 The eAs Iff Assumption Revisited 8.10 Why the Status Quo 8.11 A Pragmatic Approach References Index

S.D. Iliadis , University of Patras, Patras, Greece.

Universal Spaces and Mapping

North-Holland Mathematics Studies, vol.198.

Description

The book is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on.

Audience

Researchers in Topology, postgraduate students.

Contents

Preface. Introductory remarks. Chapter 1. The construction of Containing Spaces. Chapter 2. Saturated classes. Chapter 3. Dimension-like functions. Chapter 4. Saturated classes of spaces with structure. Chapter 5. Completely regular and compact spaces. Chapter 6. Saturated classes of mappings. Chapter 7. Actions of groups. Chapter 8. Containing Spaces and factorizing T-spectra. Chapter 9. Isometries and universality. Chapter 10. Concluding remarks and open problems. Bibliography. Index of symbols. Subject index.

Bibliographic & ordering Information
Hardbound, ISBN: 0-444-51586-0, 575 pages, publication date: 2005

Mordechai Feingold

The Newtonian Moment
Isaac Newton and the Making of Modern Culture

0-19-517735-5, hardback, 240 pages Also In Stock paper Dec 2004,

Description

Isaac Newton is a legendary figure whose mythical dimension threatens to overshadow the actual man. The story of the apple falling from the tree may or may not be true, but Isaac Newton's revolutionary discoveries and their importance to the Enlightenment era and beyond are undeniable. The Newtonian Moment, a companion volume to a forthcoming exhibition by the New York Public Library, investigates the effect that Newton's theories and discoveries had, not only on the growth of science, but also on the very shape of modern culture and thought.

Newton's scientific work at Cambridge was groundbreaking. From his optical experiments with prisms during the 1660s to the publication of both Principia (1687) and Opticks (1704), Newton's achievements were widely disseminated, inciting tremendous interest and excitement. Newtonianism developed into a worldview marked by many tensions: between modernity and the old guard, between the humanities and science, and the public battles between great minds. The Newtonian Moment illuminates the many facets of his colossal accomplishments, as well as the debates over the kind of knowledge that his accomplishments engendered. The book contributes to a greater understanding of the world today by offering a panoramic view of the profound impact of Newtonianism on the science, literature, art, and religion of the Enlightenment.

Copiously illustrated with items drawn from the collections of the New York Public Library as well as numerous other libraries and museums, The Newtonian Moment enlightens its audience with a guided and in-depth look at the man, his world, and his enduring legacy.

Reviews

"Lavish, lively...educates us in the manifold, particular, and paradoxical ways of genius. In the presence of these extraordinary documents, the work of Newton's skilled hands and speeding, inspired intellect, it would be easy to do what so many writers did in the eighteenth century: to treat Newton himself as more than human, as someone who stood above the conflicts of his own time, one who simply saw farther and worked on a higher level than his contemporaries, and achieved what he did unaided by ordinary mortals. One of the great virtues of The Newtonian Moment is that it refuses to do this."--New York Review of Books

Product Details

240 pages; 230 color halftones; 8 x 10; 0-19-517735-5

About the Author(s)
Mordechai Feingold, Professor of History, California Institute of Technology

Dario A. Bini, Professor of Numerical Analysis, Department of Mathematics, University of Pisa, Guy Latouche, Professor of Applied Probability, Department of Informatics at the Universite Libre de Bruxelles, and Beatrice Meini, Associate Professor of Numerical Analysis, Department of Mathematics, University of Pisa

Numerical Methods for Structured Markov Chains

0-19-852768-3
Publication date: January 2005
352 pages, 234mm x 156mm
Series: Numerical Mathematics and Scientific Computation

First text to cover the interplay between applied probability and numerical analysis--an emerging and important field for applied mathematicians and engineers
Each important concept is presented and analyzed with from a probabilistic and numerical analysis viewpoint
A source of efficient algorithms for solving queueing problems, advanced algorithms are simply described allowing easy translation into code in a high level language
Bibliographic notes at end of each chapter allow for further development of each topic
Appendix section provides a useful reference list of the main annotations and algorithms used in the book, and highlights the general concepts and results

Description

Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic modeling. Aimed at graduates and researchers in numerical analysis, applied mathematics, probability, engineering and computer science it provides a thorough overview of the current literature.

Readership: Graduates and researchers in numerical analysis, applied mathematics, probability, engineering and computer science

Contents

TOOLS
Introduction to Markov chains
Structured matrix analysis
Matrix equations and canonical factorization
STRUCTURED MARKOV CHAINS
M/G/1-type Markov chains
Phase-type queues
ALGORITHMS
Functional iterations
Logarithmic reduction and cyclic reduction
Alternative approaches
Specialized structures
Appendix
Notations
List of Algorithms
Bibliography


Cristoforo Bertuglia, Retired; formerly Professor of Urban and Regional Planning, Politecnico di Torino and Franco Vaio, Professor of Mathematics, Politecnico di Torino

Nonlinearity, Chaos, and Complexity
The Dynamics of Natural and Social Systems

(Hardback (laminated boards)) 0-19-856790-1
(Paperback) 0-19-856791-X
Publication date: May 2005
320 pages, 64 line figures, 234mm x 156mm

Emerging and important field

A broad cross-disciplinary text aimed at economics, sociology, physics/applied mathematics, engineering and philosophy students
Excellent clarity of reasoning takes non-specialists by the hand through technical details


Readership: Undergraduates, graduates and researchers in the social and natural sciences seeking a comprehensive survey of the modelling of chaotic dynamics and complexity in their fields.

Contents

Preface

Part I: Linear and nonlinear processes

1.1 Introduction
1.2 Modelling
1.3 The Origins of System Dynamics: Mechanics
1.4 Linearity in Models
1.5 One of The Most Basic Natural Systems: The Pendulum
1.6 Linearity as a First, Often Insufficient Approximation
1.7 The Nonlinearity of Natural Processes: The Case of The Pendulum
1.8 Dynamical Systems and The Phase Space
1.9 Extension of The Concepts and Models Used in Physics to Economics
1.10 The Chaotic Pendulum
1.11 Linear Models in Social Processes: The Case of Two Interacting Populations
1.12 Nonlinear Models in Social Processes: The Model of Volterra-Lotka and Some of Its Variants in Ecology
1.13 Nonlinear Models in Social Processes: The Volterra-Lotka Model Applied to Urban and Regional Science

Part II: From nonlinearity to chaos

2.1 Introduction
2.2 Dynamical Systems and Chaos
2.3 Strange and Chaotic Attractors
2.4 Chaos in Real Systems and in Mathematical Models
2.5 Stability in Dynamical Systems
2.6 The Problem of Measuring Chaos in Real Systems
2.7 Logistic Growth as A Population Development Model
2.8 A Nonlinear Discrete Model: The Logistic Map
2.9 The Logistic Map: Some Results of Numerical Simulations and An Application
2.10 Chaos in Systems: The Main Concepts

Part III: Complexity

3.1 Introduction
3.2 Inadequacy of Reductionism
3.3 Some Aspects of The Classical Vision of Science
3.4 From Determinism to Complexity: Self-Organisation, A New Understanding of System Dynamics
3.5 What is Complexity?
3.6 Complexity and Evolution
3.7 Complexity in Economic Processes
3.8 Some Thoughts on The Meaning of 'Doing Mathematics'
3.9 Digression into The Main Interpretations of The Foundations of Mathematics
3.10 The Need for A Mathematics of (or for) Complexity

References
Name Index
Subject Index