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Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction



Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction

Frank Lad

ISBN: 978-0-471-14329-1 September 1996 512 Pages


The mathematical implications of personal beliefs and values inscience and commerce

Amid a worldwide resurgence of interest in subjectivist statisticalmethod, this book offers a fresh look at the role of personaljudgments in statistical analysis. Frank Lad demonstrates howphilosophical attention to meaning provides a sensible assessmentof the prospects and procedures of empirical inferentiallearning.

Operational Subjective Statistical Methods offers a systematicinvestigation of Bruno de Finetti's theory of probability and logicof uncertainty, which recognizes probability as the measure ofpersonal uncertainty at the heart of its mathematical presentation.It identifies de Finetti's "fundamental theorem of coherentprovision" as the unifying structure of probabilistic logic, andhighlights the judgment of exchangeability rather than causalindependence as the key probabilistic component of statisticalinference.

Broad in scope, yet firmly grounded in mathematical detail, thistext/reference

Invites readers to address the subjective personalist meaning ofprobability as motivating the mathematical construction
* Contains numerous examples and problems, including computingproblems using Matlab, assuming no background in Matlab
* Explains how to use the material in three distinct sequentialcourses in math and statistics, as well as in courses at thegraduate level in applied fields
* Provides an introductory basis for understanding more complexstructures of statistical analysis

Complete with fifty illustrations, Operational SubjectiveStatistical Methods makes an intriguing discipline accessible toprofessionals, students, and the interested general reader. Itcontains a wealth of teaching and research material, and offersprofound insight into the relationship between philosophy, faith,and scientific method.
Philosophical and Historical Introduction.

Quantities, Prevision, and Coherency.

Coherent Statistical Inference.

Related Forms for Asserting Uncertain Knowledge.

Distribution Functions.

Proper Scoring Rules.

The Multivariate Normal Distribution and Its Mixtures.

Sequential Forecasting Based on Linear Conditional PrevisionStructures: Theory and Practice of Linear Regression.

The Direction of Statistical Research.


"...has a merit for everyone who wonders about the foundations ofinference..." (Australian & New Zealand J Statistics, 2000)