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Bayesian ‘old evidence’ problems

Summary:
Bayesian ‘old evidence’ problems Why is the subjective Bayesian supposed to have an old evidence problem? The allegation … goes like this: If probability is a measure of degree of belief, then if an agent already knows that e has occurred, the agent must assign P(e) the value 1. Hence P(e|H) is assigned a value of 1. But this means no Bayesian support accrues from e. For if P(e) = P(e|H) = 1, then P(H|e) = P(H). The Bayesian condition for support is not met … How do subjective Bayesians respond to the charge that they have an old evidence problem? The standard subjective Bayesian response is  … “The Bayesian interprets P(e|H) as how likely you think e would be were h to be false” … But many people — Bayesians included — are not too clear about how this

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Bayesian ‘old evidence’ problems

Bayesian ‘old evidence’ problemsWhy is the subjective Bayesian supposed to have an old evidence problem?

The allegation … goes like this: If probability is a measure of degree of belief, then if an agent already knows that e has occurred, the agent must assign P(e) the value 1. Hence P(e|H) is assigned a value of 1. But this means no Bayesian support accrues from e. For if P(e) = P(e|H) = 1, then P(H|e) = P(H). The Bayesian condition for support is not met …

How do subjective Bayesians respond to the charge that they have an old evidence problem? The standard subjective Bayesian response is  …

“The Bayesian interprets P(e|H) as how likely you think e would be were h to be false” …

But many people — Bayesians included — are not too clear about how this “would be” probability is supposed to work.

Yes indeed — how is such a “would be” probability to be interpreted? The only feasible solution is arguably to restrict the Bayesian calculus to problems where well-specified nomological machines are operating. Throwing a die or pulling balls from an urn is fine, but then the Bayesian calculus would of course not have much to say about science …

Lars Pålsson Syll
Professor at Malmö University. Primary research interest - the philosophy, history and methodology of economics.

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