The process of throwing away the actual experimental result, and substituting a class of possible results which contains the actual one—that is, deliberately losing some of your information—introduces a dose of real subjectivity.
Edit: didn’t mean to retract this, hit the button by accident.
Another example of him having poor knowledge and going on confused and irrelevant for pages. LW is very effective at throwing away anyone who has a clue by referencing to highly loved incorrectness.
LW is very effective at throwing away anyone who has a clue by referencing to highly loved incorrectness.
In the name of Cryonics, Bayesianism, MWI, FAI, FOOMing, physical realism and whatever other ideas that lesswrong folks endorse but you have a problem with I banish you!
It’s not even at the point of what ideas are endorsed, but how. E.g. I like MWI, okay? The arguments in favour of MWI here are utter crap, confused and irrelevant and go on for pages. Then the Bayes , irrelevant and confusing and for pages again every time, and with a poor style explanation to top it off, which is not even Bayesian but frequentist (and poor style in terms of useful stuff vs wankery ratio). The general pattern of ‘endorsing’ an idea on LW consists of very poor understanding of what idea is, how it differs from the rest, and some wankery slash signalling like “look at me i can choose correct idea in some way that you ought to understand if you are smart enough”. If you read LW you would think that e.g. frequentists are people whom reject Bayes rule and can’t solve the problem like in OP or something, the non-multiworlders are people who believe collapse literally happens when you look at stuff (which may well be the case among those ‘non many worlders’ whom don’t know jack shit about quantum mechanics). Then the cryonics, for many times it’s been told by experts that current methods lose a lot of important information irreversibly, you just go on with some crap about super-intelligence that will deduce missing info from life story, never mind algorithmic complexity or anything. Supposedly because you’re a ‘rationalist’ you don’t need to know anything or even think it over taking into account the subtleties, you’ll be more correct without the subtleties than anyone would be with. (If it worked like that it’d be awesome).
If you read LW you would think that e.g. frequentists are people whom reject Bayes rule and can’t solve the problem like in OP or something...
You’d only arrive at this conclusion if you didn’t read very carefully. No one claims that frequentists reject Bayes’ rule. But Bayes’ rule only applies when we have coherent conditional probabilities. Frequentists deny that one always has conditional probabilities of the form P(data | parameter), because in many cases they deny that the parameter can be treated as the value of a random variable. So the difference in methods comes not from a disagreement about Bayes’ rule itself, but a disagreement about when this rule is applicable.
Frequentists deny that one always has conditional probabilities of the form P(data | parameter), because in many cases they deny that the parameter can be treated as the value of a random variable.
If this is really what you mean, can you clarify it? Are you talking about going from P(data ; parameter) to P(data | parameter) by abuse of notation and then taking the conditioning seriously?
I’m not sure what you mean by “abuse of notation”. I don’t think P(data ; parameter) and P(data | parameter) are the same thing. The former is a member of a family of distributions indexed by parameter value, the latter is a conditional distribution. I do think that, from a Bayesian point of view, the former determines the latter.
As a Bayesian, you treat the parameter value m as the value of an unobserved random variable M. The observed data y is the value of a random variable Y. Your model,
),
can be used to straightforwardly derive the conditional distribution
).
In conjunction with your prior distribution for M, this gives you the posterior probability of the parameter value being m.
I’m not a statistician, so I might be using notation in an unorthodox manner here, but I don’t think there’s anything wrong with the content of what I said. Is there?
Frequentists deny that one always has conditional probabilities of the form P(data | parameter), because in many cases they deny that the parameter can be treated as the value of a random variable.
What cases? Where does this what you said come from the view that probability is the limit in infinitely many trials?
This post doesn’t clarify that. I’m still not sure what you mean exactly (or based on what you determined what ‘frequentists’ do, survey of literature? some sort of actual issue with interpreting probability as limit in many trials?).
Suppose I’m performing an experiment whose purpose is to estimate the value of some physical constant, say the fine structure constant. Can you make sense of assigning a probability distribution to this parameter from a frequentist perspective? The probability of the constant being in some range would presumably be the limit of the relative frequency of that range as the number of trials goes to infinity, but what could a “trial” possibly be in this case?
Let’s see how Bayesianists here propose to assign probability distribution to something like that: Solomonoff induction, ‘universal prior’. Trials of random tape on Turing machines (which you can do by considering all possible tape). The logic that follows afterwards should be identical; as you ‘update your beliefs’ you select states compatible with evidence, as per top post in that thread; mathematically, Bayes rule.
Not convinced that this issue is something specific to frequentism.
Eliezer got this straight from Jaynes.
And he wrote a sizable post about the conflict: Frequentist Statistics are Frequently Subjective
Edit: didn’t mean to retract this, hit the button by accident.
Another example of him having poor knowledge and going on confused and irrelevant for pages. LW is very effective at throwing away anyone who has a clue by referencing to highly loved incorrectness.
In the name of Cryonics, Bayesianism, MWI, FAI, FOOMing, physical realism and whatever other ideas that lesswrong folks endorse but you have a problem with I banish you!
Did it work?
Didn’t work on me yet, coz i’m bored.
It’s not even at the point of what ideas are endorsed, but how. E.g. I like MWI, okay? The arguments in favour of MWI here are utter crap, confused and irrelevant and go on for pages. Then the Bayes , irrelevant and confusing and for pages again every time, and with a poor style explanation to top it off, which is not even Bayesian but frequentist (and poor style in terms of useful stuff vs wankery ratio). The general pattern of ‘endorsing’ an idea on LW consists of very poor understanding of what idea is, how it differs from the rest, and some wankery slash signalling like “look at me i can choose correct idea in some way that you ought to understand if you are smart enough”. If you read LW you would think that e.g. frequentists are people whom reject Bayes rule and can’t solve the problem like in OP or something, the non-multiworlders are people who believe collapse literally happens when you look at stuff (which may well be the case among those ‘non many worlders’ whom don’t know jack shit about quantum mechanics). Then the cryonics, for many times it’s been told by experts that current methods lose a lot of important information irreversibly, you just go on with some crap about super-intelligence that will deduce missing info from life story, never mind algorithmic complexity or anything. Supposedly because you’re a ‘rationalist’ you don’t need to know anything or even think it over taking into account the subtleties, you’ll be more correct without the subtleties than anyone would be with. (If it worked like that it’d be awesome).
You’d only arrive at this conclusion if you didn’t read very carefully. No one claims that frequentists reject Bayes’ rule. But Bayes’ rule only applies when we have coherent conditional probabilities. Frequentists deny that one always has conditional probabilities of the form P(data | parameter), because in many cases they deny that the parameter can be treated as the value of a random variable. So the difference in methods comes not from a disagreement about Bayes’ rule itself, but a disagreement about when this rule is applicable.
If this is really what you mean, can you clarify it? Are you talking about going from P(data ; parameter) to P(data | parameter) by abuse of notation and then taking the conditioning seriously?
I’m not sure what you mean by “abuse of notation”. I don’t think P(data ; parameter) and P(data | parameter) are the same thing. The former is a member of a family of distributions indexed by parameter value, the latter is a conditional distribution. I do think that, from a Bayesian point of view, the former determines the latter.
As a Bayesian, you treat the parameter value m as the value of an unobserved random variable M. The observed data y is the value of a random variable Y. Your model,
can be used to straightforwardly derive the conditional distribution
In conjunction with your prior distribution for M, this gives you the posterior probability of the parameter value being m.
I’m not a statistician, so I might be using notation in an unorthodox manner here, but I don’t think there’s anything wrong with the content of what I said. Is there?
What cases? Where does this what you said come from the view that probability is the limit in infinitely many trials?
This post doesn’t clarify that. I’m still not sure what you mean exactly (or based on what you determined what ‘frequentists’ do, survey of literature? some sort of actual issue with interpreting probability as limit in many trials?).
Suppose I’m performing an experiment whose purpose is to estimate the value of some physical constant, say the fine structure constant. Can you make sense of assigning a probability distribution to this parameter from a frequentist perspective? The probability of the constant being in some range would presumably be the limit of the relative frequency of that range as the number of trials goes to infinity, but what could a “trial” possibly be in this case?
Let’s see how Bayesianists here propose to assign probability distribution to something like that: Solomonoff induction, ‘universal prior’. Trials of random tape on Turing machines (which you can do by considering all possible tape). The logic that follows afterwards should be identical; as you ‘update your beliefs’ you select states compatible with evidence, as per top post in that thread; mathematically, Bayes rule.
Not convinced that this issue is something specific to frequentism.