How to Tell When Simpler, More Unified, or Less<i>Ad Hoc</i>Theories will Provide More Accurate Predictions

Forster, Malcolm R.; Sober, Elliott

doi:10.1093/bjps/45.1.1

Cited by 573 publications

(279 citation statements)

References 19 publications

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“…If we have to live with false hypotheses, then it may be wise to lower our sights and aim at hypotheses that have the highest possible predictive accuracy.' (Forster and Sober [1994], p.26, emphasis in the original)…”

Section: The Sub-family Problemmentioning

confidence: 99%

“…'Predictive accuracy' is the term coined by Forster and Sober ([1994]) to describe the goal of maximising the expected log-likelihood of resampled data (that is, future data sampled from the same source as the data D r a f t we have already). This is equivalent to minimising the expected Kullback-Leibler distance, a concept we explain in section 6.1.4.…”

Section: The Predictive Accuracy Frameworkmentioning

confidence: 99%

“…The key model selection problem discussed in (Forster and Sober [1994]) is that of univariate polynomial regression, which they call the 'curve-fitting problem'. In this problem, the task is to choose the degree of a polynomial approximation to an unknown function.…”

Section: Univariate Polynomial Regressionmentioning

confidence: 99%

“…Then for any consistent assignment of priors and for any possible data, p(B| data) ≥ p(A| data). How, ask Forster and Sober (Forster and Sober [1994]; Forster [2000], p.214), can Bayesians explain the fact we sometimes prefer model family A to model family B?…”

Section: The Sub-family Problemmentioning

confidence: 99%

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Bayes not Bust! Why Simplicity is no Problem for Bayesians

Dowe

Gardner

Oppy

2007

The British Journal for the Philosophy of Science

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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 Akaike's 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 Wallace's 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 reparametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster's objections to Bayesianism.Hence an important part of the attack on Bayesianism fails.

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Section: The Sub-family Problemmentioning

confidence: 99%

Section: The Predictive Accuracy Frameworkmentioning

confidence: 99%

Section: Univariate Polynomial Regressionmentioning

confidence: 99%

Section: The Sub-family Problemmentioning

confidence: 99%

See 2 more Smart Citations

Bayes not Bust! Why Simplicity is no Problem for Bayesians

Dowe

Gardner

Oppy

2007

The British Journal for the Philosophy of Science

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“…Perhaps the most interesting of the standard arguments in favor of simplicity is based upon the concept of "overfitting" (Forster and Sober 1994). The idea is that predicting the future by means of an equation with too many free parameters compared to the size of the sample is more likely to produce a prediction far from the true value.…”

Section: The Simplicity Puzzlementioning

confidence: 99%