Is there a way to address it without relying on accurate priors and general knowledge of the world? Typically with science it seems like we don’t have accurate priors or very good contextual awareness. (I posted a concrete example here)
To be fair, my analysis was actually more of a frequentist analysis because all I did was count the number of occurrences of each thing without using a prior!
I think I understand why frequentist-ism is clearly separated from bayesianism broadly speaking, but it also seems to me that in the absence of anything better, taking a frequency is not a bad way to get a starting point.
Is that common/accepted as part of bayesianism? Because if it’s not, I don’t know where priors would come from besides random allocation or evenly split between all hypotheses (which is problematic because there are many).
Sorry for the delayed replay. My comments are being held for review.
If you have weak/uncertain priors, the thing to do is run low-cost experiments that differentiate between your different hypotheses of what’s going on.
A real cheap experiment in relation to the question “is this a scam?” is to Google to see if others have received similar letters and what their outcomes were. If it’s a scam, you’re likely to surface evidence of this, if it’s not a scam, you’re likely to surface both people saying it went well for them, and debunking sites that explain what’s going on, where the letters came from, etc. If you get no information at all based on a google search, just no results come back, someone went to a lot of effort to make that be the case, and you should be suspicious, it’s evidence something’s amiss.
In a case where you’re at the forefront of scientific discovery, there may be no cheap tests available, but you still devise tests which you predict, based on what you currently know, will go one way if a theory is correct, another way if it’s incorrect, and see what happens.
If you have weak/uncertain priors, the thing to do is run low-cost experiments that differentiate between your different hypotheses of what’s going on.
CF kind of agrees here. CF says that any contradiction between theories can be used to create meaningful hypotheses that will refute one or both theories; and CF doesn’t have a concept of weak or strong arguments, instead it uses decisive criticisms and claims are either refuted or unrefuted.
What does Bayesianism say if you have strong priors? Is there an objective breakpoint that separates weak from strong priors? (e.g., P < 0.5?)
There isn’t a set breakpoint that separates weak from strong priors, it’s a continuum from “it seems extremely unlikely that everything I know about the world is false, but it’s not technically impossible” to “it seems extremely likely that I’m typing on a keyboard right now, but there’s a tiny possibility that something else is going on, like a hallucination or me being a brain in a vat or some other possibility I haven’t thought of”.
Bayesianism says that if you have strong priors about a particular matter, you should be surprised with corresponding strength if something your priors said shouldn’t happen, happens. Some occurrences mean “I adjust what I think slightly, but this was within what I guessed might happen”, while others mean “halt and catch fire—either I should fundamentally rethink my notions of how reality works, or I’ve deeply misunderstood what just happened”.
I haven’t read about CF (I skimmed your link extremely rapidly, which doesn’t count) but it sounds pretty binary. Bayesian thinking is not that.
I haven’t read about CF (I skimmed your link extremely rapidly, which doesn’t count) but it sounds pretty binary. Bayesian thinking is not that.
re: binary. Yes… well you could argue that technically it’s ternary in that ‘unsure’ is an option, but CF says there’s always a way to get from ‘unsure’ to yes/no.
It’s similar to critical rationalism (CR) but removes all degrees for beliefs. CR was already pretty light on degrees/credence/weights (pun not intended), CF removes them entirely. CF also integrates some ideas from other schools (so it’s not a pure descendant of CR).
Bayesianism says that if you have strong priors about a particular matter, you should be surprised with corresponding strength if something your priors said shouldn’t happen, happens.
What kind of event would cause you to update your prior about bayesianism?
Does bayesianism say anything about things that cannot be observed directly?
e.g., many moral arguments are about what is right/wrong to do, and we often don’t see consequences, and even if we do see consequences, those aren’t outputs of an experiment in the same way science experiments work. So it’s not clear to me that (from bayesian pov) we even should use our observations about the world to update our ideas about morality.
(note: we don’t need to focus on morality particularly, it was just an example I thought we’d both agree involves things we can’t observe directly)
Sorry for the delayed replay. My comments are being held for review.
initial reaction to your several replies today: I feel like writing several replies that would be quite long, but a) I don’t have time to do that within the next few days and b) I don’t want to spam you with walls of text you’re not interested in. I’ll try and refine my thoughts down to something more short and focused, but, how interested are you in reading the longer less-focused version? This is a “I wrote you a long letter because I didn’t have time to write you a short one” situation—longer is easier, but potentially less useful.
“Does Bayesianism say X” is a complex question to answer—there are a cluster of ideas that are implemented among the group here, that I personally have noticed, but I don’t have a canonical source for what “Bayesianism” says or does not say, so I’d be sharing my current impressions and understandings, and as I’ve said before, I’m not an expert Bayesian, and what I think might not be representative of the group.
As for “What kind of event would cause you to update your prior about Bayesism?”… well at the core of this set of ideas is a mathematical formula. And I understand why that formula is what it is (I walked through the reasoning once, years ago, and it made sense). So if the question was “what kind of event would make my believe Bayes’ formula is incorrect” then it would have to be the same sort of thing that would cause me to question the validity of math more generally—something that would make me think “maybe the Pythagorean theorem doesn’t reliably describe characteristics of triangles”. There are things that could do that, but it’d be a pretty fundamental questioning of the nature of reality. Or, I guess if some mathematician found some fundamental flaw in Bayes’ formula and I could walk through their reasoning? But “Bayesianism” and “Bayes’ formula” are not the same thing, and I could give up on various ideas that cluster around Bayes’ formula much more easily. If I saw this group systematically making errors in thinking that I could trace back to a Bayes-adjacent idea, I’d update my thinking based on that evidence fairly easily. What I’ve seen instead is that members of this group using this form of reasoning have reached conclusions that turned out correct, well ahead of society in general coming to the same conclusions. if that changed, I’d learn from that.
When I said “Bayesianism says”, a few messages above, I was just running with your conceptual frame for the sake of discussion—and there are certain things that are implied by Bayes’ formula which I think everyone would agree on, like “if you have a high prior on something happening that doesn’t happen as expected, that causes a big update, and similarly for low priors on something that happens”. Inputting certain numbers into Bayes’ formula means other numbers come out, and in that sense “Bayesianism says/Bayes’ formula says” consistent things. But there are other ideas that kind of come along for the ride and might be grouped under the label “Bayesianism” while being less directly connected to the formula, and it’s there where I go “I may not be the best person to comment on that/it’s a bit fuzzy/complex”.
I’d suggest picking something you think we disagree about to focus on if we want to make some progress (helps keep discussion tree width small). But you’re also welcome to write down your thoughts with less structure—I’m still interested in that and I get that it can be easier sometimes. If you do, it might be good to, at the end, point out what you think the strongest or most important point / disagreement is, and I’ll focus on that and/or suggest something of my own.
FWIW, I’m already familiar-in-passing with more modern retreats from like hardcore bayesianism. IMO it’s a bit unprincipled but necessary because bayesianism isn’t complete (eg hypothesis generation, evidence modelling, etc). One thing I don’t like about the state of bayesianism is everyone seems to have their pet theory about how to handle the problems. IMO this is a sign that bayesianism is failing (but doesn’t mean it’s irredeemable). If b-ism weren’t failing, we’d know of a more consistent integrated position that people point to and say ‘see X’s book/essays for the gold standard’.
If there is one thing in particularly that I take issue with, it’s the idea that Bayesianism is the logic of science. I disagree with that wholeheartedly. The problem is the leap from applying a statistics method epistemologically. Bayes has no epistemic insights that aren’t covered elsewhere, and the domains where it works aren’t useful for getting to the truth and understanding the world proper. It doesn’t help us to explain how and why scientific progress happens and is possible.
Edit/Addendum: to (loosely and reductively) analogize to pythagoras: bayesianism is to bayes what pyramid power is to pythagoras.
This isn’t exactly a fair analogy, but the point I want to make is that the belief that bayes’ theorem applies to epistemological matters is a massive leap. I can see how it’s tempting and it’s much easier to see how intelligent people would fall into the trap. I don’t mean to be insulting or offensive btw, and I’m sorry if I am, but I don’t want to lie about what I think and am a little short on time.
Is there a way to address it without relying on accurate priors and general knowledge of the world? Typically with science it seems like we don’t have accurate priors or very good contextual awareness. (I posted a concrete example here)
To be fair, my analysis was actually more of a frequentist analysis because all I did was count the number of occurrences of each thing without using a prior!
I think I understand why frequentist-ism is clearly separated from bayesianism broadly speaking, but it also seems to me that in the absence of anything better, taking a frequency is not a bad way to get a starting point.
Is that common/accepted as part of bayesianism? Because if it’s not, I don’t know where priors would come from besides random allocation or evenly split between all hypotheses (which is problematic because there are
Sorry for the delayed replay. My comments are being held for review.
If you have weak/uncertain priors, the thing to do is run low-cost experiments that differentiate between your different hypotheses of what’s going on.
A real cheap experiment in relation to the question “is this a scam?” is to Google to see if others have received similar letters and what their outcomes were. If it’s a scam, you’re likely to surface evidence of this, if it’s not a scam, you’re likely to surface both people saying it went well for them, and debunking sites that explain what’s going on, where the letters came from, etc. If you get no information at all based on a google search, just no results come back, someone went to a lot of effort to make that be the case, and you should be suspicious, it’s evidence something’s amiss.
In a case where you’re at the forefront of scientific discovery, there may be no cheap tests available, but you still devise tests which you predict, based on what you currently know, will go one way if a theory is correct, another way if it’s incorrect, and see what happens.
CF kind of agrees here. CF says that any contradiction between theories can be used to create meaningful hypotheses that will refute one or both theories; and CF doesn’t have a concept of weak or strong arguments, instead it uses decisive criticisms and claims are either refuted or unrefuted.
What does Bayesianism say if you have strong priors? Is there an objective breakpoint that separates weak from strong priors? (e.g., P < 0.5?)
There isn’t a set breakpoint that separates weak from strong priors, it’s a continuum from “it seems extremely unlikely that everything I know about the world is false, but it’s not technically impossible” to “it seems extremely likely that I’m typing on a keyboard right now, but there’s a tiny possibility that something else is going on, like a hallucination or me being a brain in a vat or some other possibility I haven’t thought of”.
Bayesianism says that if you have strong priors about a particular matter, you should be surprised with corresponding strength if something your priors said shouldn’t happen, happens. Some occurrences mean “I adjust what I think slightly, but this was within what I guessed might happen”, while others mean “halt and catch fire—either I should fundamentally rethink my notions of how reality works, or I’ve deeply misunderstood what just happened”.
I haven’t read about CF (I skimmed your link extremely rapidly, which doesn’t count) but it sounds pretty binary. Bayesian thinking is not that.
re: binary. Yes… well you could argue that technically it’s ternary in that ‘unsure’ is an option, but CF says there’s always a way to get from ‘unsure’ to yes/no.
It’s similar to critical rationalism (CR) but removes all degrees for beliefs. CR was already pretty light on degrees/credence/weights (pun not intended), CF removes them entirely. CF also integrates some ideas from other schools (so it’s not a pure descendant of CR).
What kind of event would cause you to update your prior about bayesianism?
Does bayesianism say anything about things that cannot be observed directly?
e.g., many moral arguments are about what is right/wrong to do, and we often don’t see consequences, and even if we do see consequences, those aren’t outputs of an experiment in the same way science experiments work. So it’s not clear to me that (from bayesian pov) we even should use our observations about the world to update our ideas about morality.
(note: we don’t need to focus on morality particularly, it was just an example I thought we’d both agree involves things we can’t observe directly)
Sorry for the delayed replay. My comments are being held for review.
initial reaction to your several replies today: I feel like writing several replies that would be quite long, but a) I don’t have time to do that within the next few days and b) I don’t want to spam you with walls of text you’re not interested in. I’ll try and refine my thoughts down to something more short and focused, but, how interested are you in reading the longer less-focused version? This is a “I wrote you a long letter because I didn’t have time to write you a short one” situation—longer is easier, but potentially less useful.
“Does Bayesianism say X” is a complex question to answer—there are a cluster of ideas that are implemented among the group here, that I personally have noticed, but I don’t have a canonical source for what “Bayesianism” says or does not say, so I’d be sharing my current impressions and understandings, and as I’ve said before, I’m not an expert Bayesian, and what I think might not be representative of the group.
As for “What kind of event would cause you to update your prior about Bayesism?”… well at the core of this set of ideas is a mathematical formula. And I understand why that formula is what it is (I walked through the reasoning once, years ago, and it made sense). So if the question was “what kind of event would make my believe Bayes’ formula is incorrect” then it would have to be the same sort of thing that would cause me to question the validity of math more generally—something that would make me think “maybe the Pythagorean theorem doesn’t reliably describe characteristics of triangles”. There are things that could do that, but it’d be a pretty fundamental questioning of the nature of reality. Or, I guess if some mathematician found some fundamental flaw in Bayes’ formula and I could walk through their reasoning? But “Bayesianism” and “Bayes’ formula” are not the same thing, and I could give up on various ideas that cluster around Bayes’ formula much more easily. If I saw this group systematically making errors in thinking that I could trace back to a Bayes-adjacent idea, I’d update my thinking based on that evidence fairly easily. What I’ve seen instead is that members of this group using this form of reasoning have reached conclusions that turned out correct, well ahead of society in general coming to the same conclusions. if that changed, I’d learn from that.
When I said “Bayesianism says”, a few messages above, I was just running with your conceptual frame for the sake of discussion—and there are certain things that are implied by Bayes’ formula which I think everyone would agree on, like “if you have a high prior on something happening that doesn’t happen as expected, that causes a big update, and similarly for low priors on something that happens”. Inputting certain numbers into Bayes’ formula means other numbers come out, and in that sense “Bayesianism says/Bayes’ formula says” consistent things. But there are other ideas that kind of come along for the ride and might be grouped under the label “Bayesianism” while being less directly connected to the formula, and it’s there where I go “I may not be the best person to comment on that/it’s a bit fuzzy/complex”.
Heh, I know what you mean.
I’d suggest picking something you think we disagree about to focus on if we want to make some progress (helps keep discussion tree width small). But you’re also welcome to write down your thoughts with less structure—I’m still interested in that and I get that it can be easier sometimes. If you do, it might be good to, at the end, point out what you think the strongest or most important point / disagreement is, and I’ll focus on that and/or suggest something of my own.
FWIW, I’m already familiar-in-passing with more modern retreats from like hardcore bayesianism. IMO it’s a bit unprincipled but necessary because bayesianism isn’t complete (eg hypothesis generation, evidence modelling, etc). One thing I don’t like about the state of bayesianism is everyone seems to have their pet theory about how to handle the problems. IMO this is a sign that bayesianism is failing (but doesn’t mean it’s irredeemable). If b-ism weren’t failing, we’d know of a more consistent integrated position that people point to and say ‘see X’s book/essays for the gold standard’.
If there is one thing in particularly that I take issue with, it’s the idea that Bayesianism is the logic of science. I disagree with that wholeheartedly. The problem is the leap from applying a statistics method epistemologically. Bayes has no epistemic insights that aren’t covered elsewhere, and the domains where it works aren’t useful for getting to the truth and understanding the world proper. It doesn’t help us to explain how and why scientific progress happens and is possible.
Edit/Addendum: to (loosely and reductively) analogize to pythagoras: bayesianism is to bayes what pyramid power is to pythagoras.
This isn’t exactly a fair analogy, but the point I want to make is that the belief that bayes’ theorem applies to epistemological matters is a massive leap. I can see how it’s tempting and it’s much easier to see how intelligent people would fall into the trap. I don’t mean to be insulting or offensive btw, and I’m sorry if I am, but I don’t want to lie about what I think and am a little short on time.