Timeline for How do Bayesian Statistics handle the absence of priors?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2018 at 17:10 | comment | added | Alecos Papadopoulos | I am in a "scenario" where I do not even know that it is a normal. I just have the data, and what I know (or assume), is that they come from the same distribution, say. | |
| Feb 15, 2018 at 15:08 | comment | added | probabilityislogic | So, you are saying we are more in "scenario 2" (eg know it's normal but don't know the parameters). In this case the data are not "independent" because $p (x_i|x_jA) \neq p (x_i|A) $ (I've used $A$ to denote the assumptions of normal). If we assume the parameters are known (scenario 1), then we have $p (x_i|x_j\mu\sigma^2A) = p (x_i|\mu\sigma^2A) $ - then they are "independent". You can't tell from the phrase "statistically independent" which condition you are assuming to be true. | |
| Feb 15, 2018 at 9:56 | comment | added | Alecos Papadopoulos | I am not sure I follow here. How did the $N(0,1)$ came up? Do I understand correctly that what you are saying is "if I already know that data come from $N(0,1)$, what good are independent observations for learning about the next one?" Or am I misreading you? If I am not, then my previous comment and the whole discussion here is whether we can use independent observations to learn something when what we have is data, not when we have data and knowledge about the distribution they come from. | |
| Feb 15, 2018 at 9:18 | comment | added | probabilityislogic | Really? and these are giving you better info over and above what you can infer from the N(0,1) pdf/cdf? For example, you're saying you can get a better estimate of the 95th percentile for obs 100 than 1.645? Please show me what this is? | |
| Feb 14, 2018 at 17:33 | comment | added | Alecos Papadopoulos | @probabilisticlogic "Independent in probability" is an expression that can be found usually in older works, and means what statistical independence means as expressed through distribution functions. The 99 rv's will allow me to learn all sorts of properties, characteristics etc of the 100th, moments, quantiles, you name it. | |
| Feb 14, 2018 at 7:31 | comment | added | probabilityislogic | Your phrasing "independent in probability" is not clear to me, and I suspect this is why I disagree with what you are saying. If this is replaced by "conditionally independent" or "exchangeable" then what you say makes sense. I'm also still waiting for something that could be learned from 99 iid standard normal rvs that helps with the 100th (need not be about prediction). | |
| Feb 4, 2018 at 21:46 | comment | added | Alecos Papadopoulos | Commenting on the last sentence of your post, the fact that we can learn something about the common structure as you point out, does not make the random variables involved "statistically dependent". They remain "independent in probability", which is another way to say "statistically independent", a concept that has a very precise meaning mathematically. That they share common characteristics (here, their range is characterized by the same probability distribution), does not make them statistically dependent. | |
| Feb 4, 2018 at 21:28 | comment | added | probabilityislogic | @Alecos Papadopoulos - the point is you cannot learn without making things statistically dependent. Taking my example, what is learnable in scenario 1?Additionally the common structure needs to be unknown, not just present. | |
| Feb 4, 2018 at 12:40 | comment | added | Alecos Papadopoulos | (+1) Thank you for your thoughtful answer. A clarification regarding the "blatantly wrong" assertion: it was made because "learning" (and I am talking about the general meaning of the word) is a much more wider concept than "predicting". If two events are structurally similar, we can learn things related to the one by studying the other, even though they may be statistically independent. You also talk about the "common structure" in your answer, that's all there is to it. | |
| Feb 4, 2018 at 10:01 | history | answered | probabilityislogic | CC BY-SA 3.0 |