Contributions to Statistics : Contributions to Statistics - P. a. Monney

Instant online reading.
Don't wait for delivery!
Go digital and save!

Contributions to Statistics

By: P. a. Monney, Paul-Andre Monney

Write A Review

Paperback | 23 October 2002

At a Glance

Paperback
174 Pages

Dimensions(cm)
22.86 x 15.24 x 1.27

Paperback

$108.90

or 4 interest-free payments of $27.23 with

Ships in 5 to 7 business days

The subject of this book is the reasoning under uncertainty based on sta tistical evidence, where the word reasoning is taken to mean searching for arguments in favor or against particular hypotheses of interest. The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain spe cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of sta tistical models called functional models. The second aspect deals with the uncertainty under which the formal reasoning takes place. For this aspect, the theory of hints [27] is the appropriate tool. Basically, we assume that some uncertain perturbation takes a specific value and then logically eval uate the consequences of this assumption. The original uncertainty about the perturbation is then transferred to the consequences of the assumption. This kind of reasoning is called assumption-based reasoning. Before going into more details about the content of this book, it might be interesting to look briefly at the roots and origins of assumption-based reasoning in the statistical context. In 1930, R. A. Fisher [17] defined the notion of fiducial distribution as the result of a new form of argument, as opposed to the result of the older Bayesian argument.

Industry Reviews

From the reviews:

"The book, clearly written, is structured in two parts comprising two and six chapters, respectively. ... The overall quality of the book is very good, the material is well organized and notations and terminology are unified. It is a very good presentation of the state of research in the area of modeling reasoning and an insightful reference for the statistician." (Evdokia Xekalaki, Zentralblatt MATH, Vol. 1100 (2), 2007)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Probability & Statistics Philosophy Epistemology & The Theory of Knowledge Optimisation Linear Programming Mathematical Foundation Mathematical Logic Economics

Econometrics Economic Statistics Calculus & Mathematical Analysis Numerical Analysis

The Theory of Generalized Functional Models	p. 1
The Theory of Hints on Finite Frames	p. 1
Definition of a Hint and its Associated Functions	p. 2
Combination of Hints	p. 5
Mass functions and gem-functions	p. 7
Dempster Specialization Matrices	p. 10
A Representation of the Dempster Specialization Matrix	p. 11
Combining Several Hints	p. 12
Application	p. 13
The Combination of Closed Hints	p. 14
The Theories of Bayes and Fisher	p. 18
Jessica's Pregnancy Test	p. 18
The Solution of Bayes	p. 18
The Solution of Fisher	p. 19
The Definition and Analysis of a Generalized Functional Model	p. 21
Generalized Functional Models and Hints	p. 24
Examples of Generalized Functional Models	p. 26
Jessica's Pregnancy Test	p. 26
Policy Identification (I)	p. 28
Policy Identification (II)	p. 31
Prior Information	p. 33
The Plausibility and Likelihood Functions	p. 39
The Likelihood Ratio as a Weight of Evidence	p. 39
The Weight of Evidence for Composite Hypotheses	p. 40
Functional and Distribution Models	p. 43
The Distribution Model of the Problem	p. 43
A GFM Obtained by Conditional Embedding	p. 44
A GFM Inspired by Dempster's Structures of the First Kind	p. 46
Evidence About a Survival Rate	p. 49
Degrees of Support as Weights of Evidence	p. 55
Hints on Continuous Frames and Gaussian Linear Systems	p. 59
Continuous Hints	p. 59
Gaussian Hints	p. 62
Precise Gaussian Hints	p. 64
Gaussian Linear Systems	p. 68
Assumption-Based Reasoning with Classical Regression Models	p. 71
Classical Linear Regression Models as Special Gaussian Linear Systems	p. 71
The Principle of the Inference	p. 72
The Result of the Inference	p. 76
Changing Basis	p. 79
Permissible Bases and Admissible Matrices	p. 82
Different Representations of the Result of the Inference	p. 86
A Representation Derived from Linear Dependencies	p. 86
A Representation Derived from a Special Class of Admissible Matrices	p. 88
Pull Rank Matrices T₂ such that T₂A = 0	p. 90
A Matrix Based on Linear Dependencies	p. 90
A Matrix Based on the Householder Method	p. 91
A Matrix Based on Classical Variable Elimination	p. 91
A Matrix Based on a Generalized Inverse of A	p. 93
Assumption-Based Reasoning with General Gaussian Linear Systems	p. 97
The Principle of the Inference	p. 97
The Gaussian Hint Inferred from a Gaussian Linear System of the First Kind	p. 98
The Gaussian Hint Inferred from a Gaussian Linear System of the Second Kind	p. 99
The Gaussian Hint Inferred from a Gaussian Linear System of the Third Kind	p. 104
The Gaussian Hint Inferred from a Gaussian Linear System of the Fourth Kind	p. 105
Canonical Proper Potentials	p. 106
Gaussian Hints as a Valuation System	p. 109
Shenoy-Shafer's Axiomatic Valuation Systems	p. 109
Marginalization of Gaussian Hints	p. 110
Marginalization of a Precise Gaussian Hint	p. 111
Marginalization of a Non-Precise Gaussian Hint	p. 112
Vacuous Extension of Gaussian Hints	p. 117
Transport of Gaussian Hints	p. 117
Projection and Composition of Potentials	p. 118
Combination of Gaussian Hints Defined on the Same Domain	p. 121
Computation of Combined Gaussian Hints	p. 123
Combination when the Composed Potential is of the Third Kind	p. 123
Combination with a Precise Gaussian Hint	p. 124
Combination of Two Precise Gaussian Hints	p. 125
Combination when the Composed Potential is of the First Kind	p. 126
Combination of Hints Defined on Arbitrary Domains	p. 127
Local Propagation of Gaussian Hints	p. 129
The Axioms of Shenoy and Shafer	p. 130
The Local Propagation Algorithm	p. 133
Application to the Kalman Filter	p. 137
Definition of the Random System	p. 137
Derivation of the Kalman Filter	p. 138
References	p. 149
Index	p. 153
Table of Contents provided by Publisher. All Rights Reserved.

Contributions to Statistics

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Numerical Analysis

Advances in Numerical Methods and Analysis

Introductory Numerical Analysis

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Learning Data Science

Data Wrangling, Exploration, Visualization, and Modeling with Python

Dynamic Characteristics of Layered Structures

Mathematical Modelling and Numerical Simulations

Impact Dynamics

A Numerical Approach

Data-Driven Modeling & Scientific Computation

Methods for Complex Systems & Big Data

Numerical Methods for Modeling Metasurface with GSTC

Introduction to Computational Engineering with MATLAB®

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Stochastic Navier-Stokes Equations on Spheres and Spherical Shells

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Mathematical Methods using Python

Applications in Physics and Engineering

Application of Numerical Methods in Engineering Problems using MATLAB®

Emerging Materials and Technologies

Flight Mechanics Modeling and Analysis

Introduction to Modern Scientific Programming and Numerical Methods

Numerical Solutions for Nanocomposite Structures

Physics-Based and Data-Driven Modeling for Digital Twins

ICIAM2023 Springer Series

Modern Numerical Nonlinear Optimization

Springer Optimization and Its Applications

Applied Mathematics with F#

ELECTRIMACS 2024

Selected Papers - Volume 2

Handbook of Visual, Experimental and Computational Mathematics

Bridges through Data

Optimization, Modeling, Simulation, and Analytics

COMOSA 2025

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Simulation and Hierarchical Optimization, Part II

Modeling with Knowledge and Data

Concepts and Applications for Engineers

Quantum Chaos and Disorder

An Introduction with Sample Programs and Exercises

This product is categorised by