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26 votes

What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?

Bayes' theorem is just that- a theorem. It is no more based on prejudice than Pythagoras' theorem. All calculations are subject to the 'garbage in, garbage out' rule. If I make wild guesses about the ...
Marco Ocram's user avatar
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16 votes

What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?

So does Bayes’ theorem reduce to ordinary prejudice? In some circumstances, you could say that, you could say that priors are arguably just rooted in personal biases, but not all applications of ...
TKoL's user avatar
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16 votes

What principle protects the objective nature of the prior and the conclusion in Bayes’s theorem?

Bayes' theorem does not dictate how one selects the prior probabilities. Certainly one can fill a Bayesian model with bigotry and unjustified biases, but this is not necessary. One can even use what ...
Lowri's user avatar
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11 votes

Can a zero prior probability for some theories be justified?

I argue that, for any falsifiable hypothesis, a prior probability of exactly 0 or 1 is irrational; to assign such a prior is to explicitly abandon one's capacity for reasoning in the face of evidence. ...
Scott McPeak's user avatar
7 votes

At what point should we suspect unfair game?

The question is a bit confused in it's use of statistical terminology and ideas, but I think there is an answer, so I'll address the terminology as I go: From a frequentist standpoint, each spin of a ...
Dikran Marsupial's user avatar
6 votes

Does a 100% degree of belief imply that no amount of evidence can change your mind?

is it wrong to assume that a 100% degree of belief implies that no amount of evidence can change your mind? You can think of this as a definition rather than an assumption. Within the Bayesian ...
Christian Hennig's user avatar
6 votes

Does psychophysical harmony strongly point toward theism?

The paper correctly points out that physicalist naturalism requires a large number of mind-body relationships. However, it falsely claims that these are difficult to explain in principle within ...
Dcleve's user avatar
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6 votes

Does psychophysical harmony strongly point toward theism?

The paper seems to be largely framed as an argument against some sort of dualist naturalist. But I would argue that reductive materialism has no problem explaining what they're trying to explain. The &...
NotThatGuy's user avatar
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6 votes

How is this Linda example addressed by Bayesian thinking?

Suppose that you see Linda go to the bank every single day. Presumably this supports the hypothesis H = Linda is a banker. But this also supports the hypothesis H = Linda is a Banker and Linda is a ...
TKoL's user avatar
  • 3,692
6 votes

At what point should we suspect unfair game?

You start with some estimate of how likely it is, before the spins, that the wheel is rigged to only roll black. Then you look at the chance the wheel would have produced the sequence of spins if it ...
causative's user avatar
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4 votes
Accepted

Is Occam's Razor a Prior?

You might be interested in Epistemic Justification by Richard Swinburne (he was applying Bayes to philosophical issues before Bayesian epistemology became cool), especially the section The Criterion ...
Adam Sharpe's user avatar
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4 votes

Does a 100% degree of belief imply that no amount of evidence can change your mind?

I think we have had a related discussion in which I made the claim that Bayes' theorem is just that- a theorem, so it is mathematically correct; however, as with any faultless method of computation it ...
Marco Ocram's user avatar
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4 votes

Can a zero prior probability for some theories be justified?

Yes, if you have reason to suppose a phenomenon is impossible, you can allocate a zero probability to it. If later you find it is possible after all, then you were wrong in your initial assessment. ...
Marco Ocram's user avatar
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4 votes

Can a zero prior probability for some theories be justified?

It's not impossible to assign priors of 0 or 1 in the Bayesian framework it's just pointless. Like assigning a probability of 0 or 1 expresses your firmly held believe that something does or doesn't ...
haxor789's user avatar
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4 votes

How is this Linda example addressed by Bayesian thinking?

A few preliminary points, for information: The discussion within the interview that you are referring to starts at timestamp 1:06:55 in the linked video. In the example, Deutsch refers to Linda ...
Bumble's user avatar
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4 votes

At what point should we suspect unfair game?

You start with "From a frequentist standpoint, each spin of a fair roulette wheel ..." (emphasis mine). The frequentist approach you describe is in response to this question, where "the ...
JonathanZ's user avatar
  • 540
3 votes
Accepted

Bayes' Theorem and Science

It depends on what you mean by true. Scientific theories such as relativity and quantum mechanics are models of reality. An accepted meaning of 'true' is 'in accord with facts or reality'. Therefore, ...
Marco Ocram's user avatar
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3 votes

Is Occam's Razor a Prior?

Without any background information of a specific situation, generally Occam's Razor is not considered a priori first principle but aesthetic and heuristic according to reference here: The ...
Double Knot's user avatar
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3 votes
Accepted

Consequences and importance of the "No Free Lunch Theorem"?

The No Free Lunch theorem states that when averaged across all possible problems, any two strategies have equivalent performance. At first glace, this might suggest it doesn't matter what strategy you ...
Nuclear Hoagie's user avatar
3 votes

Logical Interpretations of Probability

It's important to notice that the section being referenced is talking about the interpretation of logical probabilities, not the logical interpretation of probabilities. The second suggests a ...
Ted Wrigley's user avatar
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3 votes
Accepted

Logical Interpretations of Probability

A useful paradigm for this is to think about a deck of cards. Shuffle it up, and draw one. What is the probability that the top card is black? A logical interpretation of this would be to say "...
Paul Ross's user avatar
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3 votes

Using Bayes Theorem in a Court Case - dementia and testamentary capacity

I presume you are concerned with cases where a witness is called to give testimony but there is doubt about whether their testimony is acceptable, because they suffer from dementia and this affects ...
Bumble's user avatar
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3 votes

Are there any examples of two theories that accurately describe a phenomenon where the more complex one was found to be correct?

Certainly. Here are a few: General relativity replaced newtonian gravity as the more correct explanation, but it is substantially more complicated. Note that for small mass densities, they yield the ...
niels nielsen's user avatar
3 votes

Does psychophysical harmony strongly point toward theism?

It's basically an argument from incredulity, one of the poorest form of theist apologetics, to the point of being a cliché. The author just lists a bunch of ocurences they hold to be improbable, ...
armand's user avatar
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3 votes
Accepted

Bayesian conditional probability and material implication

So example 6, on page 228 of your linked text, goes like this, translated to modern notation. Given that P(y ∨ ¬x¬y) = p, what is P(y | x) ? To answer this Boole introduces a constant c. He says that ...
causative's user avatar
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2 votes

Probability vs Possiblity vs gambling knowledge gap for a beginner

I think you are confused because of usage of these term in English language. Rather than the mathematical standpoint. To make this clear I am going to define each term (using Google dictionary). ...
White Mars's user avatar
2 votes

Is Occam's Razor a Prior?

(After MacKay, 1992, Neural Comput. 4(3):415-447, doi:10.1162/neco.1992.4.3.415) No. The Bayesian version of Occam's razor doesn't arise from the prior, it arises from the likelihood, i.e. from the ...
Daniel Hatton's user avatar
2 votes

Is Occam's Razor a Prior?

Yes, the theory of algorithmic probability describes a "universal prior" that encodes Occam's razor. There exist infinitely many possible hypotheses, and more hypotheses of higher complexity ...
nanoman's user avatar
  • 141
2 votes

Is Occam's Razor a Prior?

Occam's razor occurs in the context of science. Very often, the focus is on novel phenomena, so with no priors available. The generalisation, we call: physics. In hypothesis generation to account for ...
CriglCragl's user avatar
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