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United States889 Posts
I've been bothered by what's been happening with people tossing about "Bayes' theorem" in the wider world for a good long while now. I'm not a statistician/mathematician/philosopher, by training, but I have a background in psychological/cognitive modelling. In my line of work, it is common to at least try to model real data with hierarchical Bayesian models, or some simple derivatives/variants.
These models necessarily make use of a subjective interpretation, and their interpretation is simple and uncontroversial. The posterior is a subjective degree of belief, end of story, because we're looking at correlates of human behavior (we're trying in some way to measure a degree of belief). No problem there.
But as I've branched out and been working on modelling in other cases, I've noticed that people use subjective Bayes all the time to model things that really don't seem like they should be subjective Bayes at all.
For example, people use subjective Bayes for propositions like "It will rain tomorrow". But if what we're interested in is the actual probability that it will rain tomorrow, we should consult models of the weather, not what people think, because whether it will rain tomorrow doesn't depend on what people think. I might be mistaken here, but I can't yet see how.
Another particularly troubling example is work by a one Richard Carrier who attempts to calculate the probability that historical events took place with Bayes' theorem. His priors cannot be estimated from data (the data are non-numeric), and so the prior begins life as (his) subjective degree of belief. Consequently, the output is a degree of belief. But he attempts to pass this off as the probability that certain historical events occurred, when definitely, whether or not those events occurred is not dependent on what he or anybody else thinks. This is not even to mention the fact that it doesn't make sense to say "there's a 70% chance that the Ottomans attacked Malta", since they either did (1) or they didn't (0).
What I'm noticing is that certain people really really really stick with subjective Bayes no matter what. It's been my impression that there's something of a cult growing up these days around Bayes' theorem - a useful tool, to be sure, but nothing more significant than the application of a general rule for reversing the order of conditional probabilities. The cult (Bayesian epistemologists) believes that all information should be interpreted in Bayesian terms, and they have a fetish for putting numbers on things that aren't numerical, I guess because it makes them feel superior.
All of this has made me look pretty poorly on passionate subjective Bayesians. Being someone who regularly uses a subjective Bayes interpretation in a place where it should be applied, this is an uncomfortable position to be in. Isn't it obvious that not all reasoning is necessarily Bayesian in form? Surely, it can be applied that way frequently, but that's just grafting an interpretation on something that's probably produced by a different process.
All subjective Bayesians are entitled to attempt to update my subjective degree of belief on the reliability of subjective Bayes with new evidence in this blog thread. Or, y'know, try to convince me.
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Interesting read! The Richard Carrier example does seem pretty awful. For the weather model, would it be wrong to use base rates from how often it actually does rain in your location? For example, a weatherman in Las Vegas might use a lower prior than a weatherman in Florida, and come to a different conclusion when faced with the same data. I'm sure meteorologists have much more sophisticated models, but it seems ok to me in principle.
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It does make sense to say that there is a chance that something happened. Unless we have hard evidence, we really can't be sure it actually happened or if it was just some tale that stuck. Just like in physics, where we are only 99.9995% or so sure that the result of a series of experiments - like the existence of some particle - isn't just a statistical anomaly.
But if you do that for historical events, you better take into account a large amount of historical records and stories from many people from many cultures.
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United States15275 Posts
Expect a strongly worded letter from Eliezer Yudkowsky soon.
The cult (Bayesian epistemologists) believes that all information should be interpreted in Bayesian terms, and they have a fetish for putting numbers on things that aren't numerical, I guess because it makes them feel superior.
Sadly, this is one of the reasons why I've lost interest and a certain measure of respect for the LessWrong community. Their fetishizing of Bayesian epistemology, along with a general inability to think about moral issues beyond the most base utilitarianism, turned a community with potential into something resembling a cult.
I think they want certainty above all things. What provides more comfort in its completeness and indifference to particulars in the world than mathematics/logic? The problem is they get stuck in a law of the instrument situation and everything has to be processed through that particular tool.
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On October 06 2016 02:48 CosmicSpiral wrote:Expect a strongly worded letter from Eliezer Yudkowsky soon. Show nested quote +The cult (Bayesian epistemologists) believes that all information should be interpreted in Bayesian terms, and they have a fetish for putting numbers on things that aren't numerical, I guess because it makes them feel superior. Sadly, this is one of the reasons why I've lose interest and a certain measure of respect for the LessWrong community. Their fetishizing of Bayesian epistemology, along with a general inability to think about moral issues beyond the most base utilitarianism, turned a community with potential into something resembling a cult. I think they want certainty above all things. What provides more comfort in its completeness and indifference to particulars in the world than mathematics/logic? The problem is they get stuck in a law of the instrument situation and everything has to be processed through that particular tool.
It is funny that a person plotting to be world's greatest revolutionary scientist is perhaps best known for his Harry Potter fanfiction.
I really dislike lesswrong, there are some interesting articles there, but the community consists of the type of nitwits that think that e.g. the main fascination with art is how one can view it as a set of inputs that create a positive psychological response and how we can write algorithms or develop methodologies to maximize our output of art. They view everything through some sort of inane rationalist lens that fails to understand that while the human mind might be amazing at many things, it is not rational and that one's allegiance should be to humans, not to some fetishized idea of rationality. So often I saw them analyzing situations by first framing everything into these rationalists terms, after which they called it a day because they diverged so far from common human experience there was nothing insightful or meaningful to add anymore, it was infuriating and I even had to abandon that fanfiction for being so insufferably anti-human.
Anyhow, I bet they are just itching to replace us with hyper rational space robots as they're awaiting the next breakthrough in 'friendly AI'.
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"For example, people use subjective Bayes for propositions like "It will rain tomorrow". But if what we're interested in is the actual probability that it will rain tomorrow, we should consult models of the weather, not what people think, because whether it will rain tomorrow doesn't depend on what people think. I might be mistaken here, but I can't yet see how."
I don't really see what you mean here. Suppose I have a simple logistic regression, with some exogenous variables. The dependent variable is of course if it will rain tomorrow. Why can't I view this in a Bayesian way? I can take a diffuse prior, but even if I don't, with enough data the prior becomes irrelevant if you choose it wisely. After some simulations, you can get some estimate of the expectation that it will rain tomorrow. (actual weather models may be so this doesn't work, but I have no clue how such a model looks like)
I think I agree with the overall sentiment that the prior is a big part of Bayesian statistics, though. If I see Bayesian research without any mention of a prior, I disregard it.
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TL used to have a resident Bayesian poster, DoubleReed. I'm not sure where he went.
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Statistics is the only branch where you have the answer before you know what the question is.
Yes, that's my only contribution.
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Well take these events that happened yesterday as an interesting remark on Bayesian. I think that there's a 100% chance that if I scream at my computer guy there is a 0% chance that screaming at my computer guy can change anything.
Yesterday I screamed at my computer guy and (much to my chagrin) my computer fried almost at the very moment.
So from a psychological standpoint I think there's a 100% chance that if I scream at my computer guy there's a 100% chance that his aura will destroy my computer. On the other hand from a reasoning, thinking standpoint I think there's a 100% chance that screaming at my computer guy can't possibly change anything related to my computer (unless he shows up and bashes it with a hammer).
What we've learned is that screaming at the computer guy can apparently change the longevity of the computer that he built. Does this tell us anything from an empirical perspective? Probably not unless you're arguing that the computer guy is somehow defying the usual laws of physics.
I am not sure what to take away from this line of events. Bayesianism is very odd but certainly does seem to align some ideas of statistics with some ideas of psychology. Since a lot of seemingly impossible events happen there is some grounds for saying that "well we began with a relative impossibility, probably represented by a 0% chance".... "but now the thing has happened so it needs a new probability". I guess we assign a 100% probability to the thing happening, since it happened, but all we appear to learn is that we need an explanation completely other than what we already had.
What probability do we assign to the new explanation? Perhaps 100% because it's the same as our prior 100% explanation (the one we believe). But functionally the explanation is hopefully different and its propositional character is theoretically different. If it isn't different then the cognitive synonymy is different so it means something else. Or nothing has changed and the 0% chance has been updated to a 100% chance without modifying anything else. This seems to be the most interesting case, that stuff could change in the world and in spite of its changing nothing at all changes in our system of belief or what have you.
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"Getting the data" is an intractably difficult problem to solve, I think.
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Imma go further and play a little bit the devil's advocate. When you say that, Arrian :
This is not even to mention the fact that it doesn't make sense to say "there's a 70% chance that the Ottomans attacked Malta", since they either did (1) or they didn't (0).
That is not what Bayes' theorem allows you to calculate.
Bayes' theorem gives you a conditional probability, which means that This sentence is incorrect. If it has been said like that in the text, then it is plain wrong. Bayes allows you to calculate the probability that Ottomans attacked Malta GIVEN smthg. (maybe here, given the reliability of the historical sources one used to do that calculation).
While the result, as I said above, is mathematically bound to the data you inputed in the formula (which are dependant on the credibility you give to one historical source, so in fact which are dependant mostly on your opinion of the credibility of the source (which is why it can lead to different answers for the same problem)), and therefore is mathematically correct, since there is no hypothesis of having two correlated events to use that formula in the defintion of Bayes' theorem.
So, again, this is mathematically correct to calculate the probability that when i fart someone in the world dies.
Even tho it does not even make sense, since the fact that I farted here in my office in France had no effect on the fact that someone died wherever in the world.
So, as a conclusion, i'd say that you cannot prevent stupid people to somewhat use the formula to get perfectly correct mathematical answers, yet totally brain dead. You have to show some common sense and discard yourself all the results that are produced by people giving no valuable information.
As a last example, I could very well calculate the probability that wherever you live there's going to be rain on the 28th october. Just lemme make a forecast on the weather for all the days from now to the 28th. Which will allow me to actually calulate on the long run the probability that it will rain on the 28th of october wherever you live GIVEN a forecast for rain by me.
The result will obviously depends on the luck I get on my predictions, and the fact that you live or not in a rainy area.
This result will be perfectly correct and logical. Yet will it gives you the slightest bit of USEFUL information about the weather you will have on the 28th ?
Nop.
Doesn't change the fact that my forecast might be correct, depending on my luck. And that my math will be correct, too.
So, if I were you, I'd definitely rely on solid forecasting models produced by scientists to chose to take or not your umbrella on the 28th.
Hope this was somewhat useful
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France12908 Posts
Are there really people that try to assess probabilities of events that way? :o (with models out of their ass)
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On October 07 2016 18:24 Poopi wrote:
Are there really people that try to assess probabilities of events that way? :o (with models out of their ass)
Dunno. Apparently there is. Make em feels smart I guess.
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United Kingdom10443 Posts
I'm not really sure how bayes works but it seems to depend very much on the data source.
Sticking with the weather example. If i ask a meteorologist , using very accurate tools if it is going to rain tomorrow and he says no, then I ask some crazy lady who thinks her boobs can tell the weather and she says yes. the bayes approach tells me there is a 50% chance it will rain? If so that seems pretty stupid.
However if you asked a large number of people who have some degree of knowledge then perhaps it will be more relevant. Although all it would seem to do is average out the confidence level of the experts.
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France12908 Posts
It will rain tomorrow for sure tho. The question is at which places :o.
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On October 07 2016 20:57 KelsierSC wrote:
I'm not really sure how bayes works but it seems to depend very much on the data source.
Sticking with the weather example. If i ask a meteorologist , using very accurate tools if it is going to rain tomorrow and he says no, then I ask some crazy lady who thinks her boobs can tell the weather and she says yes. the bayes approach tells me there is a 50% chance it will rain? If so that seems pretty stupid.
However if you asked a large number of people who have some degree of knowledge then perhaps it will be more relevant. Although all it would seem to do is average out the confidence level of the experts.
Nop. Bayes' theorem calculates the probabilty of an event A to produce given an event B happenned.
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On October 05 2016 22:47 Arrian wrote:
I'm not a statistician/mathematician/philosopher, by training, but [long post on stats]
deep sigh....
Yes, for Bayes stats, like any tool, there are places where it can be applied and other places where it can be misleading. And I assume that it is being frequently misused in the social sciences, together with most other maths and stats tools. They have this entire discipline of research, they try to be quantitative, but skip math/stats in undergrad education. Then they feign surprised when they have a reproducibility crisis... Sigh, sigh...
In you post are kindof really vague with what you say though. You kindof seem to push the philosophy of the stats a lot, which maybe shouldn't be surprising... If you give an actual example, it'll be easier to discuss whether it is applied appropriately or not. For example maybe you can link that history modelling paper and point out exactly what your problem with it is, exactly which statement in the paper you don't agree with, so that we can easily see what you are talking about.
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EPT
