Timeline for Isn’t everything absurdly improbable?
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32 events
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| Aug 2, 2023 at 15:26 | comment | added | g s | @galen I don't think it would be useful to reply, so I won't, but I suggest that if you want to do phrase-by-phrase arguing on future posts, it should be done in a linked chat-room, which you can create by clicking the top right button on the SE window and selecting 'chat', then scrolling to the bottom and selecting 'create a new room', if SE doesn't prompt you to create one automatically after a few comments. SE archives chats, so it won't be lost. | |
| Aug 2, 2023 at 15:09 | comment | added | Galen | "the priors are hard to measure but easy to make good guesses about" Fundamentally a rule has to be chosen for how priors are obtained. You cannot 'measure' priors. But you can assign them to be an estimated distribution as in empirical Bayes. | |
| Aug 2, 2023 at 15:00 | comment | added | Galen | "the frequency measurement provides indirect evidence about the priors" This doesn't make sense in terms of Bayesian interpretations of probability. You're putting the cart before the horse. | |
| Aug 2, 2023 at 14:59 | comment | added | Galen | "the frequency of the thing calculated is easier to measure than the frequencies that give rise to the priors" I don't understand what you're saying here. | |
| Aug 2, 2023 at 14:57 | comment | added | Galen | "The point of doing statistical calculations with guesses about priors is to obtain a guess about measurable frequency at the end." Notwithstanding the misunderstanding about priors, the priors can be guesses about measurable frequencies. But also note that they do not have to be. | |
| Aug 2, 2023 at 14:55 | comment | added | Galen | "Like all guesses about facts, they can turn out to be right, a little bit wrong, or a lot wrong." Yes, the accuracy in guesses about facts can be variable. George Box: "All models are wrong, but some are useful". | |
| Aug 2, 2023 at 14:53 | comment | added | Galen | "The reason why expert opinions are valued is not because experts are somehow better at having feelings, it's because experts are likely to have better guesses about what measurements would be." This is a nice explanation, sans the implied assumption of uniqueness. | |
| Aug 2, 2023 at 14:51 | comment | added | Galen | For example, Bayesian agents with priors matching subjective opinions in a game theory simulation can be useful in showing how adaptive those real-world opinions would be in a hypothetical setting. | |
| Aug 2, 2023 at 14:48 | comment | added | Galen | "Wikipedia's framing is extremely misleading." Like any encyclopedia, the accuracy and completeness is imperfect in Wikipedia. If you're alluding to it saying "A prior can also be elicited from the purely subjective assessment of an experienced expert.", it is not inaccurate. You really can select priors this way, but there are often better ways IMO. But it also depends on what you're trying to do. | |
| Aug 2, 2023 at 14:42 | comment | added | Galen | "as regards reality, so-called subjective priors about reality are guesses about real priors." Priors are assigned, and are not guesses at a "real prior". You're getting at something reasonable on this point, but real prior as an estimand doesn't fit with how Bayes' works. Rather, priors can be chosen to represent background/external knowledge or belief. In this sense you can assign your priors as guesses at what you think the target population distribution looks like. But the target population is not "the real prior". The only real prior is your prior. | |
| Aug 2, 2023 at 14:39 | comment | added | Galen | "[...] the set of all possible physical configurations in which this die ends up showing a 1 [...]" This description has the appearance of defining a random variable, which is a measurable function of the outcome space of a probability space. It also has the appearance of assigning a state space to be such an outcome space, which is fine. A derived distribution will exist on the image of the random variable. This is definitely a thing you can do, but it isn't necessary for having a probability measure. | |
| Aug 2, 2023 at 14:39 | comment | added | Galen | "To build a probability measure, you essentially have to define an equivalence class [..]" A sigma algebra is required in order to have a probability measure. An equivalence class doesn't have enough structure. | |
| Aug 2, 2023 at 14:39 | comment | added | Galen | "It's impossible to define a probability measure that includes literally all possible context to every possible physical event [...]" I get the gist of that, and I agree. | |
| Aug 2, 2023 at 14:39 | comment | added | Galen | "Specific abstracted events." I'm not sure what this distinction adds. All notions are abstractions. Which abstractions are you considering? | |
| Jul 31, 2023 at 16:45 | comment | added | Paul Ross | @gs, I appreciate your point on probabilities under descriptions, but my contest is to the idea that you're specifically talking about expectations of future measurements, not that there is no such thing as the abstract or concrete event simpliciter. One can talk about the abstract probability of an event with no specific temporal sense as long as one is talking about a probability space. The topology of the probability space does not necessarily need to collapse down to the temporal idiom of events and points in time - for example, in the use of continuous probability density functions. | |
| Jul 31, 2023 at 15:59 | comment | added | g s | I agree with Justin Hilyard re: events. | |
| Jul 31, 2023 at 15:56 | comment | added | g s | [...]The point of doing statistical calculations with guesses about priors is to obtain a guess about measurable frequency at the end. This provides two possible advantages. 1: the frequency of the thing calculated is easier to measure than the frequencies that give rise to the priors, in which case the frequency measurement provides indirect evidence about the priors. 2: the priors are hard to measure but easy to make good guesses about, in which case the stats translates being able to make a good guess about priors to being able to make a good guess about frequencies. | |
| Jul 31, 2023 at 15:46 | comment | added | g s | @Galen as regards reality, so-called subjective priors about reality are guesses about real priors. Wikipedia's framing is extremely misleading. The reason why expert opinions are valued is not because experts are somehow better at having feelings, it's because experts are likely to have better guesses about what measurements would be. Like all guesses about facts, they can turn out to be right, a little bit wrong, or a lot wrong. [...] | |
| Jul 31, 2023 at 13:50 | comment | added | Idran | @Galen "A probability measure assigns a probability to specific events." Specific abstracted events. It's impossible to define a probability measure that includes literally all possible context to every possible physical event, which is what the OP is talking about. To build a probability measure, you essentially have to define an equivalence class over the specific possible groups of events and abstract them down to the categories of events you care about, like "the set of all possible physical configurations in which this die ends up showing a 1", "...ends up showing a 2", etc. | |
| Jul 31, 2023 at 10:00 | comment | added | Galen | "This relationship is based off of past measurements of one or more countable frequencies in one or more corresponding finite samples." It can be, but one can also choose priors in other ways. | |
| Jul 31, 2023 at 9:59 | comment | added | Galen | "Probabilities express a relationship between measurements of initial conditions and expectations of future measurements." I guess it can be... But by definition probabilities are elements of the image of a probability measure, which doesn't make explicit mention of initial conditions or expectation operators. | |
| Jul 31, 2023 at 9:57 | comment | added | Galen | "Specific events don't have probabilities." That statement confused me. A probability measure assigns a probability to specific events. | |
| Jul 30, 2023 at 22:35 | comment | added | Scott Rowe | This is why time travel is so fraught: no one can figure out how to say anything! "The past sure is tense." | |
| Jul 30, 2023 at 18:09 | comment | added | g s | [...] We can discuss what probabilities of future-of-the-past measurements would have been for a certain set of past-of-the-past measurements, and we can and often do use misleading linguistic shorthand to do it (framing it in the simple past tense and not making explicit which set of past-of-the-past measurements we mean because they are clear from context). But there is no well-defined the probability of the past event: 0 != 1/6 != 1. | |
| Jul 30, 2023 at 18:08 | comment | added | g s | [...] The probability that Bob would have written down a 5 given what Bob or we knew at t=-1 year is approximately 0, since none of us knew anything about the experiment a year ago. For all anyone knew, Bob could have been watching TV or dead or any number of other things instead of writing down any numbers at all, let alone having rolled the die in just such a way as he ended up doing. [...] | |
| Jul 30, 2023 at 18:03 | comment | added | g s | @PaulRoss suppose that Honest Bob has rolled a die already and looked at it. Bob tells us that he will write down the number of his dice roll. Bob reveals the note and we measure that it says "5". The probability that another future measurement of Bob's note will indicate that Bob wrote down a 5 is near unity. The probability that Bob would have written down a 5 given what Bob knew at t=0 is near unity. The probability that Bob would have written down a 5 given what we knew at t=0 is 1/6. [...] | |
| Jul 30, 2023 at 17:49 | comment | added | Paul Ross | Not downvoting, but this does appear loose to me. Probability is a measure of a state in a space, and it’s absolutely reasonable to talk about the probability of a discrete event that has already happened - c.f. the result of a roll of a dice on a particular game turn. In a sense, yes, we know with certainty that it happened, but that doesn’t mean the probability measure of the event as a function of the sides of the dice cannot be given, or is not a probability, because the behaviour of the measure still satisfies the Kolmogorov axions. | |
| Jul 30, 2023 at 16:41 | comment | added | g s | @doot_s I would suggest Experimentation by D. C. Baird, pp 40-46 in the 3rd ed, for an excellent discussion of how to move from measurement to statistical statements and vice versa. | |
| Jul 30, 2023 at 6:24 | comment | added | user66760 | i intuitively agree with this answer, but you might want to cite something for your leading claim | |
| Jul 30, 2023 at 6:05 | history | edited | g s | CC BY-SA 4.0 |
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| Jul 30, 2023 at 5:50 | history | edited | g s | CC BY-SA 4.0 |
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| Jul 30, 2023 at 5:41 | history | answered | g s | CC BY-SA 4.0 |