Post ASIkcRbZ5xvLx86SSO by tiago@social.skewed.de
(DIR) More posts by tiago@social.skewed.de
(DIR) Post #ASHYLkc5m9abNLfBh2 by tiago@social.skewed.de
2022-01-04T08:52:59Z
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New blog post!"Is Bayesian inference subjective?"tl;dr: not quite! A nice way of showing this is to explore its formal connection to data compression.https://skewed.de/tiago/blog/objective-inference
(DIR) Post #ASHe08DlvC9jwpMVpg by david_colquhoun@mstdn.social
2023-02-02T22:59:52Z
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@tiago If you invent a prior, ie it isn't based on experimental observations, then Bayes must surely have a subjective basis?
(DIR) Post #ASHfTNxQaoy16bELsu by tiago@social.skewed.de
2023-02-02T23:16:23Z
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@david_colquhoun It depends on what you mean. There's a lot of misunderstanding of what “subjective” means in this context. Bayesian statistics are “subjective” only insofar as probabilities represent rational degrees of belief. This does not mean that probabilities are subject to opinion, or personal choice, as the common meaning of “subjective” would imply. You still need to justify your priors, and you have no freedom at all to compress your data — this will happen only if you manage to detect its actual structure.
(DIR) Post #ASHgapkBmWvXGU9a4W by david_colquhoun@mstdn.social
2023-02-02T23:28:53Z
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@tiago The number of cases in which there is genuine prior info is very small. And so are the number of cases where there is good info about distribution of observations etc. In real life, statistical calculations involve many untested assumptions.
(DIR) Post #ASHgoTgYakhSuCxcrg by david_colquhoun@mstdn.social
2023-02-02T23:31:23Z
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@tiago I take 'subjective' to mean that different people will come to different conclusions from the same data.
(DIR) Post #ASHgrsmtic91cyYAXg by tiago@social.skewed.de
2023-02-02T23:32:00Z
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@david_colquhoun Having “no prior information” translates to having very specific priors, the so-called non-informative ones. Lack of data does not mean you are free to use whatever prior — it's pretty much the opposite.
(DIR) Post #ASHh49e0s6D7NnFJqa by david_colquhoun@mstdn.social
2023-02-02T23:34:13Z
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@tiago But there's an infinitude of non-informative priors. There's a big difference between a uniform prior, and one that has a point null
(DIR) Post #ASHhLDmmj7s99NUGPI by david_colquhoun@mstdn.social
2023-02-02T23:37:18Z
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@tiago but it's bed time here -hope we can return to it tomorrow
(DIR) Post #ASHhOzOQBJQFfZt6v2 by tiago@social.skewed.de
2023-02-02T23:38:00Z
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@david_colquhoun That's nonsense. Pretty much the whole purpose of Bayesian statistics is that it allows for model selection. It's the whole point of the equivalence with compression that I highlight above. If different people come up with different encodings for the same file, only the shortest one represents the most plausible account of the data. It's not subjective at all.
(DIR) Post #ASHhY3FfCiLcFA73IG by david_colquhoun@mstdn.social
2023-02-02T23:39:38Z
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@tiago It's the very definition of subjective, IMO
(DIR) Post #ASHhaW62vkZ4Hdn22q by tiago@social.skewed.de
2023-02-02T23:40:06Z
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@david_colquhoun If there's more than one non-informative prior in a given context, then surely they are conveying different prior beliefs.
(DIR) Post #ASHhsJDHZKjhXUesxU by david_colquhoun@mstdn.social
2023-02-02T23:43:17Z
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@tiago Yes of course. And the fact that you never know which is right is the Achilles heel of Bayesianism. But sadly the relevant questions ARE Bayesian. Perhaps that's why science is harder than most people think.
(DIR) Post #ASHhvKEUEdoNZNezIW by tiago@social.skewed.de
2023-02-02T23:43:50Z
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@david_colquhoun I don't follow. If I say that the earth is flat, and you say it's round, one of us is wrong. We just need to determining which hypothesis best fits the data. There's nothing subjective.
(DIR) Post #ASHi11HtaLHiYAyC7U by tiago@social.skewed.de
2023-02-02T23:44:52Z
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@david_colquhoun Then we must be talking about wildly different concepts.
(DIR) Post #ASHiGZZcOSFlEIfxa4 by tiago@social.skewed.de
2023-02-02T23:47:41Z
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@david_colquhoun Of course you know which one is right. If the true hypothesis happens to be in the candidate set, Bayes will consistently find it! This is also embodied in Shannon's theorem: only the true model will yield optimal compression.
(DIR) Post #ASHiU76x0qR30divWC by david_colquhoun@mstdn.social
2023-02-02T23:50:06Z
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@tiago Well I'm talking about how to interpret the results of an experiment. Sadly statisticians can't agree on how to test whether there is a real difference between the means of two independent samples. That failure has done much harm IMO
(DIR) Post #ASHiWyWxN5PLGYFh7w by david_colquhoun@mstdn.social
2023-02-02T23:50:39Z
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@tiago OK tomorrow Good night
(DIR) Post #ASHicLiqZXmWdrNOOO by tiago@social.skewed.de
2023-02-02T23:51:37Z
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@david_colquhoun You do know which one is right, unless they yield the same posterior probability — in which case they are equivalent. I don't see the alleged Achilles' heel.
(DIR) Post #ASIfQDJNuansNRwqTg by david_colquhoun@mstdn.social
2023-02-03T10:50:29Z
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@tiago How can you know which uninformative prior is right without relevant data? You can't, IMO
(DIR) Post #ASIjAFN0tFcDweHsPY by tiago@social.skewed.de
2023-02-03T11:32:26Z
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@david_colquhoun Of course you can. If you have two prior hypotheses (encoded as different priors) you can determine how plausible they are relative to each other by computing their corresponding posterior probability given some data. That's entirely standard.
(DIR) Post #ASIkcRbZ5xvLx86SSO by tiago@social.skewed.de
2023-02-03T11:48:39Z
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@aleabdo Indeed, but I think this notion of subjectivity is quite misleading. Of course if people operate on different data, they will reach different conclusions. This has very little to do with Bayes itself.However, people like de Finetti argue for a notion of probability itself that not only is inherently subjective, but that is supposedly the *only* admissible form of probability. I find this hard to swallow, and I think that purely *objective* notions of probability, as proposed by Cox and advocated by Jaynes, are not only admissible but more meaningful.The exact correspondence to compression makes this very clear. If two people have access to the *same* data (wich must include whatever personal experiences) there is only *one* way to maximally compress it. This does not vary from person to person.Also, I don't understand why these discussions tend to have such a personified perspective of probability and science. There are so many scientific questions like the origin of the universe, what are the fundamental laws of physics, what killed the dinosaurs, what is the composition of the core of Venus, etc, which surely cannot depend at all on anyone's personal experience.
(DIR) Post #ASIlXmiZGoqPwJikQi by david_colquhoun@mstdn.social
2023-02-03T11:59:07Z
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@tiago But it can't tell you which of the priors is preferable when you in fact have no prior information. The fact that you rarely have solid evidence about the prior -about how to formulate it. as well as the numbers - is surely the Achilles heel.I've argued for a lump of prior prob on a point null and another lump on observed value, a skeptical formulation in that it implies a bigger false pos risk than other uninformative priors
(DIR) Post #ASImhXawS5GJt1Myie by tiago@social.skewed.de
2023-02-03T12:12:04Z
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@david_colquhoun The formulation of the prior is inherently tied to your model likelihood, and sometimes being non-informative about an aspect of the model means you are actually being very informative of another aspect, so you either commit to one choice (given proper justification) or you create a mixture model that includes both of them and then you determine a posteriori.My point is precisely this: if the choice of prior has an effect on the posterior probability, and you are unsure, then this becomes part of your set of hypotheses, and then you have to use the data to decide.
(DIR) Post #ASInKqrAlrGgv4hqrI by david_colquhoun@mstdn.social
2023-02-03T12:19:10Z
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@tiago I certainly agree with your final sentence. I maintain that its truth shows that Bayesian arguments are subjective. They are also unavoidable, IMO.
(DIR) Post #ASIo1SMhhmj5PelpAW by tiago@social.skewed.de
2023-02-03T12:26:52Z
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@david_colquhoun I fail to grasp why this is subjective. Two different people, with the same set of hypotheses, and the same data, must arrive the same conclusion — if they're rational.
(DIR) Post #ASIp0mc52Q6jsLCmzA by david_colquhoun@mstdn.social
2023-02-03T12:37:57Z
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@tiago It's subjective because no two people will choose the same set of hypotheses 🙂
(DIR) Post #ASJFOCN42DpDEM0WsC by tiago@social.skewed.de
2023-02-03T17:33:32Z
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@david_colquhoun But this not about Bayesian inference in particular. It's true also for frequentist inference, and human activity in general.Indeed there's no formalism in science that allows hypotheses to be generated automatically from data. The uncomputability of Kolmogorov complexity pretty much proves this.Bayesian inference really only kicks in *after* hypotheses have been postulated. From this point onward, it is not subjective.
(DIR) Post #ASJG65lbwxENURQ3P6 by david_colquhoun@mstdn.social
2023-02-03T17:41:27Z
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@tiago I'm not convinced that mathematical theorems (eg "uncomputability of Kolmogorov complexity") can "prove" anything about the real physical world -they are, at best, just analogies to reality.
(DIR) Post #ASJHNLEBosJGJnZkXo by tiago@social.skewed.de
2023-02-03T17:55:45Z
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@david_colquhoun Hypotheses don't belong to the “real world” they are part of a formal system of induction. It's a modeling apparatus.As soon as hypotheses are formulated mathematically, and belong to system of induction, proofs of uncomputability limit what can be discovered.