The roles of inductive modelling and coherence in Bayesian statistics.

Tom Leonard

Trabajos de Estadística e Investigación Operativa (1980)

  • Volume: 31, Issue: 1, page 537-555
  • ISSN: 0041-0241

Abstract

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The role of the inductive modelling process (IMP) seems to be of practical importance in Bayesian statistics; it is recommended that the statistician should emphasize meaningful real-life considerations rather than more formal aspects such as the axioms of coherence. It is argued that whilst axiomatics provide some motivation for the Bayesian philosophy, the real strength of Bayesianism lies in its practical advantages and its plausible representation of real-life processes. A number of standard procedures, e.g. validation of results, choosing between different models, predictive distributions, the linear model, sufficiency, tail area behaviour of sampling distributions, and hierarchical models are reconsidered in the light of the IMP philosophy, with a variety of conclusions. For example, whilst mathematical theory and Bayesian methodology are thought to prove invaluable techniques at many local points in a statistician's IMP, a global theoretical solution might restrict the statistician's inductive thought processes. The linear statistical model is open to improvement in a number of medical and socio-economic situations; a simple Bayesian alternative related to logistic discrimination analysis often leads to better conclusions for the inductive modeller.

How to cite

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Leonard, Tom. "The roles of inductive modelling and coherence in Bayesian statistics.." Trabajos de Estadística e Investigación Operativa 31.1 (1980): 537-555. <http://eudml.org/doc/40847>.

@article{Leonard1980,
abstract = {The role of the inductive modelling process (IMP) seems to be of practical importance in Bayesian statistics; it is recommended that the statistician should emphasize meaningful real-life considerations rather than more formal aspects such as the axioms of coherence. It is argued that whilst axiomatics provide some motivation for the Bayesian philosophy, the real strength of Bayesianism lies in its practical advantages and its plausible representation of real-life processes. A number of standard procedures, e.g. validation of results, choosing between different models, predictive distributions, the linear model, sufficiency, tail area behaviour of sampling distributions, and hierarchical models are reconsidered in the light of the IMP philosophy, with a variety of conclusions. For example, whilst mathematical theory and Bayesian methodology are thought to prove invaluable techniques at many local points in a statistician's IMP, a global theoretical solution might restrict the statistician's inductive thought processes. The linear statistical model is open to improvement in a number of medical and socio-economic situations; a simple Bayesian alternative related to logistic discrimination analysis often leads to better conclusions for the inductive modeller.},
author = {Leonard, Tom},
journal = {Trabajos de Estadística e Investigación Operativa},
keywords = {Inferencia bayesiana; Modelos estadísticos; Coherencia},
language = {eng},
number = {1},
pages = {537-555},
title = {The roles of inductive modelling and coherence in Bayesian statistics.},
url = {http://eudml.org/doc/40847},
volume = {31},
year = {1980},
}

TY - JOUR
AU - Leonard, Tom
TI - The roles of inductive modelling and coherence in Bayesian statistics.
JO - Trabajos de Estadística e Investigación Operativa
PY - 1980
VL - 31
IS - 1
SP - 537
EP - 555
AB - The role of the inductive modelling process (IMP) seems to be of practical importance in Bayesian statistics; it is recommended that the statistician should emphasize meaningful real-life considerations rather than more formal aspects such as the axioms of coherence. It is argued that whilst axiomatics provide some motivation for the Bayesian philosophy, the real strength of Bayesianism lies in its practical advantages and its plausible representation of real-life processes. A number of standard procedures, e.g. validation of results, choosing between different models, predictive distributions, the linear model, sufficiency, tail area behaviour of sampling distributions, and hierarchical models are reconsidered in the light of the IMP philosophy, with a variety of conclusions. For example, whilst mathematical theory and Bayesian methodology are thought to prove invaluable techniques at many local points in a statistician's IMP, a global theoretical solution might restrict the statistician's inductive thought processes. The linear statistical model is open to improvement in a number of medical and socio-economic situations; a simple Bayesian alternative related to logistic discrimination analysis often leads to better conclusions for the inductive modeller.
LA - eng
KW - Inferencia bayesiana; Modelos estadísticos; Coherencia
UR - http://eudml.org/doc/40847
ER -

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