Graham Oppy

Bayes not Bust! Why Simplicity is no Problem for Bayesians

The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaikes Information Criterion (AIC), a non-Bayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallaces Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1-to-1 re-parametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forsters objections to Bayesianism. Hence an important part of the attack on Bayesianism fails. 1. Introduction2. The Curve Fitting Problem 2.1 Curves and families of curves 2.2 Noise 2.3 The method of Maximum Likelihood 2.4 ML and over-fitting3. Akaikes Information Criterion (AIC)4. The Predictive Accuracy Framework5. The Minimum Message Length (MML) Principle 5.1 The Strict MML estimator 5.2 An example: The binomial distribution 5.3 Properties of the SMML estimator 5.3.1  Bayesianism 5.3.2  Language invariance 5.3.3Generality 5.3.4  Consistency and efficiency 5.4 Similarity to false oracles 5.5 Approximations to SMML6. Criticisms of AIC 6.1 Problems with ML 6.1.1  Small sample bias in a Gaussian distribution 6.1.2  The von Mises circular and von Mises—Fisher spherical distributions 6.1.3  The Neyman–Scott problem 6.1.4  Neyman–Scott, predictive accuracy and minimum expected KL distance 6.2 Other problems with AIC 6.2.1  Univariate polynomial regression 6.2.2  Autoregressive econometric time series 6.2.3  Multivariate second-order polynomial model selection 6.2.4  Gap or no gap: a clustering-like problem for AIC 6.3 Conclusions from the comparison of MML and AIC7. Meeting Forsters objections to Bayesianism 7.1 The sub-family problem 7.2 The problem of approximation, or, which framework for statistics?8. ConclusionA. Details of the derivation of the Strict MML estimatorB. MML, AIC and the Gap vs. No Gap Problem B.1 Expected size of the largest gap B.2 Performance of AIC on the gap vs. no gap problem B.3 Performance of MML in the gap vs. no gap problem Introduction The Curve Fitting Problem 2.1 Curves and families of curves 2.2 Noise 2.3 The method of Maximum Likelihood 2.4 ML and over-fitting Akaikes Information Criterion (AIC) The Predictive Accuracy Framework The Minimum Message Length (MML) Principle 5.1 The Strict MML estimator 5.2 An example: The binomial distribution 5.3 Properties of the SMML estimator 5.3.1  Bayesianism 5.3.2  Language invariance 5.3.3Generality 5.3.4  Consistency and efficiency 5.4 Similarity to false oracles 5.5 Approximations to SMML Criticisms of AIC 6.1 Problems with ML 6.1.1  Small sample bias in a Gaussian distribution 6.1.2  The von Mises circular and von Mises—Fisher spherical distributions 6.1.3  The Neyman–Scott problem 6.1.4  Neyman–Scott, predictive accuracy and minimum expected KL distance 6.2 Other problems with AIC 6.2.1  Univariate polynomial regression 6.2.2  Autoregressive econometric time series 6.2.3  Multivariate second-order polynomial model selection 6.2.4  Gap or no gap: a clustering-like problem for AIC 6.3 Conclusions from the comparison of MML and AIC Meeting Forsters objections to Bayesianism 7.1 The sub-family problem 7.2 The problem of approximation, or, which framework for statistics? Conclusion Details of the derivation of the Strict MML estimator MML, AIC and the Gap vs. No Gap Problem B.1 Expected size of the largest gap B.2 Performance of AIC on the gap vs. no gap problem B.3 Performance of MML in the gap vs. no gap problem

Sceptical Theism and Evidential Arguments from Evil

Sceptical theists--e.g., William Alston and Michael Bergmann--have claimed that considerations concerning human cognitive limitations are alone sufficient to undermine evidential arguments from evil. We argue that, if the considerations deployed by sceptical theists are sufficient to undermine evidential arguments from evil, then those considerations are also sufficient to undermine inferences that play a crucial role in ordinary moral reasoning. If cogent, our argument suffices to discredit sceptical theist responses to evidential arguments from evil.

Reply to Trakakis and Nagasawa

Abstract Nick Trakakis and Yujin Nagasawa (2004) criticise the argument in Almeida and Oppy (2003). According to Trakakis and Nagasawa, we are mistaken in our claim that the sceptical theist response to evidential arguments from evil is unacceptable because it would undermine ordinary moral reasoning. In their view, there is no good reason to think that sceptical theism leads to an objectionable form of moral scepticism. We disagree. In this paper, we explain why we think that the argument of Nagasawa and Trakakis fails to overthrow our objection to sceptical theism.

On ‘a new cosmological argument’

Richard Gale and Alexander Pruss contend that their ‘new cosmological argument’ is an improvement over familiar cosmological arguments because it relies upon a weaker version of the Principle of Sufficient Reason than that used in those more familiar arguments. However, I note that their ‘weaker’ version of the Principle of Sufficient Reason entails the ‘stronger’ version of that principle which is used in more familiar arguments, so that the alleged advantage of their proof turns out to be illusory. Moreover, I contend that, even if their argument did rely on a weaker version of the Principle of Sufficient reason, nontheists would still be perfectly within their rights to refuse to accept the conclusion of the argument.

Salvation in heaven

Abstract The aim of this paper is to examine the difficulties that belief in a paradisiacal afterlife creates for orthodox theists. In particular, we consider the difficulties that arise when one asks whether there is freedom in Heaven, i.e., whether the denizens of Heaven have libertarian freedom of action. Our main contention is that this ‘Problem of Heaven’ makes serious difficulties for proponents of free will theodicies and for proponents of free will defences against arguments from evil.

Effective linearization by noise addition in threshold detection and implications for stochastic optics

We present some computer simulation results pertaining to the restoration of a weak sinusoidal input signal after threshold detection with additive random noise. We show how, if stochastic optics is regarded as a viable theory, these results may cast doubt upon some conclusions drawn from seven experimental realizations of the Einstein-Podolsky-Rosen thought experiment performed between 1982 and 1998.

Mind, Body and Spirit

We begin with a naturalistic account of the identity conditions over time for human beings, and of the way in which mind and body are related. We then consider ways in which this naturalistic account might be challenged by proponents of religious worldviews, and the significance of these challenges for other metaphysical and ethical issues, including cosmic justice and life after death.

Religious Language Games

Version of Record: in A. Moore and M. Scott (eds.) Realism and Religion London: Ashgate, 2007, 103-29

THE REJECTION OF LOCAL REALISM IS PREMATURE

We discuss the assumptions made in deriving some of the Bell-type inequalities. We evaluate a large representative set of performed Einstein–Podolsky–Rosen experiments and conclude that there is no good reason for believing that local realism has been empirically refuted. This suggests that proposed new technologies requiring a quantum degree of inseparability (or entanglement) may not be viable.

Reinventing Philosophy of Religion

Preface -- Acknowledgments -- Introductory remarks -- Part I. Epistemology. Disagreement, opinion and expertise -- Belief, faith and evidence -- Debate, reason and argument -- Part II. Metaphysics. Science, nature and transcendence -- Mind, body and spirit -- Cause, freedom and responsibility -- Part III. Ethics. Flourishing, virtue and happiness -- Trust, violence and power -- Meaning, understanding and narrative -- Postscript.