9
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.
...
- 367
5
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 ...
- 573
5
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. ...
- 13.3k
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 ...
- 3,784
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 ...
- 13.3k
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 ...
- 4,487
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 ...
- 7,772
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, ...
- 13.3k
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 ...
- 1,177
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 ...
- 3,843
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 ...
- 18.5k
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 "...
- 5,277
2
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 ...
- 22.9k
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).
...
- 131
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 ...
- 20.5k
2
votes
Is modal logic too coarse-grained?
Modal logic, if you think of it as just the augmentataion of an underlying logic with the box and diamond operators, is indeed limited in many ways, but it is still highly useful. The possible worlds ...
- 22.9k
2
votes
Questions on "Bayes or Bust?" by Earman
For the first question, he's just conditioning everything on the "background knowledge" -- this is a way of making explicit the idea that in formulating this model there are one or more ...
- 5,257
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 ...
- 121
2
votes
Does this Sleeping Beauty problem show conflicting priors?
I think that Bayes' theorem can resolve this issue.
P(Heads|Awake) = P(Awake|Heads) * P(Heads)
-------------------------
P(Awake)
= (1/3) * (...
- 245
1
vote
Does this Sleeping Beauty problem show conflicting priors?
When the halfer argument says "Sleeping Beauty receives no new non-self-locating information," it means that SB (their only subject) new she would be wakened, so that provides nothing that ...
- 166
1
vote
Bayes' Theorem and Science
I would put pressure on your second assumption.
As there many reasons of way and how to choose one scientific hypotheses out of the many that are possible, and parsimony is a leading reason, but for ...
- 11
1
vote
Has Occam's Razor famously helped correctly solved some complex problem?
Short Answer
NO. "Simplicity" is far too much of a judgment call and can be readily rationalized. I have had people argue seriously to me that a multiverse is "simpler" than a ...
- 10.5k
1
vote
Backwards Bayesian argument for alien visitation?
You have some dubious math here. The first issue is, you equivocate over what "E" is; is E a single piece of evidence, or is it all the evidence together?
A second issue is where you do:
...
- 11.1k
1
vote
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 ...
- 131
1
vote
Probability vs Possiblity vs gambling knowledge gap for a beginner
I'm going to use some extracts from an article by Matthew H. Haber to explain the difference between possibility and probability. These extracts set out (some of the) different kinds of possibility; ...
- 35.4k
1
vote
Is modal logic too coarse-grained?
It's basically true that modal operators (alone) have trouble capturing the subtleties of probabilities, in a way that doesn't lose a lot of inference power in the resulting logic.
To give you a basic ...
- 1,942
1
vote
Accepted
Term for this bias kind of probability bias related to choosing the wrong reference class to calculate prior from?
Faulty generalization, or more specifically a fallacy of unrepresentative samples. https://en.wikipedia.org/wiki/Faulty_generalization#Inductive_fallacies
- 11.1k
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