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Many people say that the priors in Bayesianism for certain kinds of theories are subjective. But there is a difference between an unfalsifiable but wrong theory and a theory that just hasn't been confirmed yet: the former is pseudo-science.

For example, we haven't observed anything supernatural or mystical or magical act on anything ever. Why should a person who thinks the prior for this is high be given any sort of credence?

If one can have a subjective prior for anything, then what's the point of differentiating between claims?

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  • i'm having a hard time trying to work out what you are asking or saying. are you saying that subjective bayesian reasoning is unfalsifiable and asking if that means we should reject the former
    – user64361
    Commented Jan 24, 2023 at 5:07
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    The point of differentiating claims is that they have not only priors but also posteriors, after priors are refurbished and painted over many times as a result of study. The reason for subjectivity of priors, and even of some Bayesian updates, is that there is no "we" on some kinds of observations. You never interpret what you see as supernatural, whereas they interpret what they see as miracles, purpose-driven events or divine interventions. We'd have to dismiss too many people as irrational if they are judged so for this alone. There is much more agreement on basic perceptions.
    – Conifold
    Commented Jan 24, 2023 at 6:38
  • You'd better contemplate why someone's prior probability may be different from yours? Does such prior have its own prior? Is subjective really contradictory with objective here at least in Bayesianism?
    – Double Knot
    Commented Jan 24, 2023 at 22:14
  • Not falsifiable is not falsifiable, with bayesian methods or otherwise.
    – kutschkem
    Commented Jan 25, 2023 at 15:16
  • If something is unfalsifiable, what exactly does it mean for it to be wrong? Also, theories are usually defined to be falsifiable.
    – Sandejo
    Commented Jan 26, 2023 at 21:51

2 Answers 2

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You can't have a measured probability without a sample set in which to count a frequency. And: Although you can stretch the inferrence chain a long way (with ever expanding error bars), you can't have an inferred probability either without a measured frequency at the bottom of the chain of logical inferences.

Intuitive guesses about prior probability can be useful for extrapolating intuitions on one subject into good guesses about another, but a formal probabilistic argument that ends with a number, not an unknown variable, must point to one or more measured samples and the (potentially very long) chain of logical inference from there to here.

Arguments that can do so can be evaluated on the basis of the reliability of the underlying frequency measurements and the quality of the logical inferences. Arguments that cannot are guesses with extra steps.

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    A very sensible answer. Bayesianism is as susceptible to 'garbage in, garbage out' as any other computational procedure.
    – Professor Sushing
    Commented Jan 26, 2023 at 22:18
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    @MarcoOcram ... but at least it forces you to explicitly state (and quantify) exactly what garbage you are putting in. ;o)
    – user6527
    Commented Aug 30, 2023 at 14:15
  • The problem with frequentist definitions of probability is that you can't assign a non-trivial probability to the truth of a proposition (as it has no long run frequency - it is either true or it isn't), including the proposition "the true value lies in this interval". Both frameworks are useful, both have advantages and disadvantages.
    – user6527
    Commented Aug 30, 2023 at 14:17
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    @DikranMarsupial sure you can. You count, you construct a model that models what you can count, and you infer. E.g. the probability of finding solid exoplanets was near 1 long before we found any, because the frequency of silicate and water molecules being sticky and having gravitation was near 1.
    – g s
    Commented Aug 30, 2023 at 16:22
  • @gs "the probability of finding solid exoplanets" is not a proposition. "solid exoplanets exist" is a proposition and it is either true or it is false and has no long run frequency other than 0 or 1.
    – user6527
    Commented Aug 30, 2023 at 16:28
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To take your last question first... "If one can have a subjective prior for anything, then what's the point of differentiating between claims?" There are convergence theorems in Bayesian theory that show that if two people start from different priors and update those priors by Bayesian conditioning on a sufficiently large quantity of independent evidence, then their posteriors will converge. The result is rather idealised, because if the two priors are a long way apart then convergence may not be feasible in practice. But the 'point' of the Bayesian approach is that updating one's beliefs based on evidence is better than not doing so, and people who initially disagree may come to agree when presented with sufficient evidence.

"Why should a high prior for God for example be seen as rational as a low prior?" The rationality of the prior is not the issue in subjective Bayesianism. Your priors are just whatever they are. The rationality lies in the use of Bayesian conditioning as an updating mechanism. At the end of the day, your priors are just a matter of what seems plausible to you, and what seems plausible to you may not seem plausible to others.

"What's the difference between an unfalsifiable but wrong theory and a theory that just hasn't been confirmed yet?" An unfalsifiable theory has no practical use. A theory that is in principle falsifiable but has never been tested yet might be useful if it can be corroborated by surviving lots of testing.

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  • Are you referring to Aumann's agreement theorem?
    – Durden
    Commented Jul 2, 2023 at 23:34
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    No, Aumann is concerned with what happens when two reasoners start from the same prior, update on separate evidence and then 'compare notes' by updating on each other's posteriors. What I have in mind here is the case where two reasoners start with different priors and both update on a large quantity of shared evidence, so that their posteriors converge because the effect of the evidence overwhelms the priors.
    – Bumble
    Commented Jul 3, 2023 at 11:18
  • Ah, I see. Thanks for the clarification. Just out of curiosity: is there a name for the convergence theorem(s) you've described in your answer?
    – Durden
    Commented Jul 6, 2023 at 16:35
  • One of these is called the Likelihood Ratio Convergence Theorem. It is described in the SEP article on Inductive Logic plato.stanford.edu/entries/logic-inductive/#LikeRatiConvTheo. There is also some material in this paper: researchgate.net/publication/…
    – Bumble
    Commented Jul 6, 2023 at 17:08
  • I'd say the "point" of the Bayesian approach is to minimize the error of small samples by applying prior knowledge. That you update your priors is clear and goes without saying; that you start with that bias (and correct, perhaps "correct" the naked sample data) is the interesting part.
    – Peter - Reinstate Monica
    Commented Jun 24 at 14:48

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