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Bayes's Theorem

Richard Swinburne (ed.)

Published in print:
2005
Published Online:
January 2012
ISBN:
9780197263419
eISBN:
9780191734175
Item type:
book
Publisher:
British Academy
DOI:
10.5871/bacad/9780197263419.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Bayes' theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this book consider the worth and applicability of the theorem. The book sets out the philosophical ... More


Bayesian Statistics 9

José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West (eds)

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.001.0001
Subject:
Mathematics, Probability / Statistics

The Valencia International Meetings on Bayesian Statistics – established in 1979 and held every four years – have been the forum for a definitive overview of current concerns and activities in ... More


The Balance of Probability

Richard Swinburne

in The Resurrection of God Incarnate

Published in print:
2003
Published Online:
November 2003
ISBN:
9780199257461
eISBN:
9780191598616
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199257469.003.0014
Subject:
Philosophy, Philosophy of Religion

Summarizes the argument of the book. Given only a moderate amount of evidence from natural theology in favour of the existence of God and his having reason to become incarnate among humans, there is ... More


 What Doctors Must Know about Medical Practice

Bernard Gert, Charles M. Culver, and K. Danner Clouser

in Bioethics: A systematic approach

Published in print:
2006
Published Online:
September 2006
ISBN:
9780195159066
eISBN:
9780199786466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195159063.003.0008
Subject:
Philosophy, Moral Philosophy

This chapter shows the importance of recognizing the probabilistic nature of medical diagnosis and treatment. It discusses the possibly serious effects of physicians not understanding Bayes theorem, ... More


Bayesian estimating functions

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0008
Subject:
Mathematics, Probability / Statistics

This chapter demonstrates that the numerical methods of earlier chapters are not constrained by statistical philosophy. The theory of Bayesian estimating functions is developed. It is shown that this ... More


Coda: ‘Of Miracles’

Colin Howson

in Hume's Problem: Induction and the Justification of Belief

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250371
eISBN:
9780191597749
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250371.003.0012
Subject:
Philosophy, Philosophy of Science

The coda discusses Hume's famous account of miracles in the Enquiry, and his criterion for belief in miracles, and shows that it amounts to a simple argument in the probability calculus.


Democracy as a Bayesian Persuader

Robert E. Goodin

in Reflective Democracy

Published in print:
2003
Published Online:
November 2003
ISBN:
9780199256174
eISBN:
9780191599354
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199256179.003.0006
Subject:
Political Science, Political Theory

Shows how Bayesian thinking should make democratic outcomes so rationally compelling. Bayes's formula provides a mathematical expression for specifying exactly how we ought rationally to update our a ... More


Hailfinder: Tools for and Experiences with Bayesian Normative Modeling

Jie W Weiss and David J Weiss

in A Science of Decision Making: The Legacy of Ward Edwards

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195322989
eISBN:
9780199869206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195322989.003.0010
Subject:
Psychology, Cognitive Psychology

Bayes Nets (BNs) and Influence Diagrams (IDs), new tools that use graphic user interfaces to facilitate representation of complex inference and decision structures, it are the core elements of new ... More


Decision Technology

Jie W Weiss and David J Weiss

in A Science of Decision Making: The Legacy of Ward Edwards

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195322989
eISBN:
9780199869206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195322989.003.0032
Subject:
Psychology, Cognitive Psychology

This chapter focuses on decision technology—the rules and tools that help us make wiser decisions. It begins by reviewing the three rules that are at the heart of most traditional decision ... More


 Keeping Up to Date

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0013
Subject:
Economics and Finance, Microeconomics

This chapter is about Bayesian decision theory. It explains why game theorists model players' beliefs using subjective probability distributions, and how these beliefs are updated using Bayes' rule ... More


 Knowing What to Believe

Ken Binmore

in Playing for Real: Game Theory

Published in print:
2007
Published Online:
May 2007
ISBN:
9780195300574
eISBN:
9780199783748
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300574.003.0015
Subject:
Economics and Finance, Microeconomics

This chapter describes John Harsanyi's theory of so-called games of incomplete information using Poker as a motivating example. The chapter begins by analyzing a simplified version of Von Neumann's ... More


The Justification of Explanation

Richard Swinburne

in The Existence of God

Published in print:
2004
Published Online:
September 2007
ISBN:
9780199271672
eISBN:
9780191709357
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199271672.003.0004
Subject:
Philosophy, Philosophy of Religion

An explanatory hypothesis (whether of the personal or scientific kind) is probable in so far as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable ... More


BEGINNING OF THE PRO-SUBJECTIVE APPROACH

Shoutir Kishore Chatterjee

in Statistical Thought: A Perspective and History

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525318
eISBN:
9780191711657
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525318.003.0007
Subject:
Mathematics, Probability / Statistics

Around the middle of the 18th century, Bayes conceived the idea of treating an unknown parameter as a subjective random variable distributed according to a prior, and inferring about it from its ... More


Simple Bayesian Models

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0005
Subject:
Biology, Ecology

This chapter lays out the basic principles of Bayesian inference, building on the concepts of probability developed in Chapter 3. It seeks to use the rules of probability to show how Bayes' theorem ... More


Objective Bayesianism

Jon Williamson

in In Defence of Objective Bayesianism

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199228003
eISBN:
9780191711060
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228003.003.0002
Subject:
Mathematics, Probability / Statistics, Logic / Computer Science / Mathematical Philosophy

This chapter reviews the various interpretations of probability (§2.2), assessing them in the light of certain desiderata for a philosophical theory of probability that are presented in §2.1. It is ... More


Introduction to Probability and Random Variables

M. Vidyasagar

in Hidden Markov Processes: Theory and Applications to Biology

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691133157
eISBN:
9781400850518
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691133157.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter provides an introduction to probability and random variables. Probability theory is an attempt to formalize the notion of uncertainty in the outcome of an experiment. For instance, ... More


Symmetries of Probability Kinematics

Bas C. van Fraassen

in Laws and Symmetry

Published in print:
1989
Published Online:
November 2003
ISBN:
9780198248606
eISBN:
9780191597459
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198248601.003.0013
Subject:
Philosophy, Philosophy of Science

While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new ... More


The Logic of Scientific Discovery

Colin Howson

in Hume's Problem: Induction and the Justification of Belief

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250371
eISBN:
9780191597749
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250371.003.0009
Subject:
Philosophy, Philosophy of Science

Applies the results of Ch. 7 to scientific methodology and shows that they give a logical interpretation of the subjective Bayesian theory of inductive inference. This theory is therefore no more ... More


Moment Priors for Bayesian Model Choice with Applications to Directed Acyclic Graphs *

Guido Consonni and Luca La Rocca

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0004
Subject:
Mathematics, Probability / Statistics

We propose a new method for the objective comparison of two nested models based on non‐local priors. More specifically, starting with a default prior under each of the two models, we construct a ... More


Plausible Reasoning

David Hodgson

in Rationality + Consciousness = Free Will

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199845309
eISBN:
9780199932269
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199845309.003.0004
Subject:
Philosophy, Philosophy of Mind, General

In Chapter 3, I consider one very important aspect of our rationality, namely our ability to engage in plausible reasoning; that is, reasoning in which the premises or data do not entail the ... More


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