27
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 ...
- 26.5k
18
votes
Accepted
Can Bayes' theorem be used non-fallaciously to argue for miracles?
If we assume that the probability of a witness testifying to an event is higher if the event actually happened (a reasonable assumption), then it is true that observing that testimony makes the event ...
- 1,650
17
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 ...
- 3,963
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 ...
- 6,076
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.
...
- 379
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 ...
- 673
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 ...
- 17.5k
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 &...
- 14k
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 ...
- 3,963
6
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 ...
- 865
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 ...
- 18.9k
5
votes
Is the goal of science explanatory power rather than increasing our belief for true theories?
It's both. Scientific endeavour is complex and answers to many different requirements and objectives. Science itself has many different branches that have different paradigms of theories and ...
- 31.7k
5
votes
Can Bayes' theorem be used non-fallaciously to argue for miracles?
There's an interesting anecdotal example of this. Since you're looking for an intuitive answer, I think a compelling anecdote is meaningful. This example centers around this famous picture:
This ...
- 18.8k
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 ...
- 3,904
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 ...
- 26.5k
4
votes
Is the principle of indifference invalid?
The short answer is that sometimes it is OK to use the principle of indifference, but it is not generally applicable. Under some circumstances, it can be considered to be a special case of an ...
- 31.7k
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. ...
- 26.5k
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 ...
- 8,168
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 ...
- 31.7k
4
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 ...
- 18.9k
4
votes
Accepted
Does Bayesian epistemology provide mechanisms to prevent arbitrariness in the selection of one's priors and belief update rules?
What you are referring to are called strong priors in that they are highly concentrated around a particular value.
This is not always bad: In the classic example of medical testing, the base rate is ...
- 4,555
4
votes
Does Solomonoff's theory of inductive inference justify Occam's razor?
The Wikipedia article explicitly states that it is a formalization that combines Occam's Razor and a couple other theories, so in a circular sense, yes it does. However, this is because it was ...
- 4,555
4
votes
Is it irrational to assign a probability to a metaphysical proposition?
For something that appears to be false, I'd simply assign a 0 probability.
As someone who doesn't use probabilistic epistemology for things for which we have no reasonable probability estimates, all ...
- 14k
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, ...
- 26.5k
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 ...
- 3,965
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 ...
- 1,204
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 ...
- 24.4k
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 "...
- 5,990
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 ...
- 31.7k
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