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Comment by JTBooth | Hacker News Reader

As the amount of data tends to 0 (idk why the quote is using 1), if course your belief tends to whatever your belief was before you saw any data. What else could it possibly tend to? Of course it's very sad that we don't have any data, but that's no fault of Bayesian.

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> As the amount of data tends to 0 (idk why the quote is using 1)

The smallest amount of samples you can use is 1, isn't it? If you have 0 samples then you do nothing because you have no data. Is there a way to have half a sample?

> if course your belief tends to whatever your belief was before you saw any data

Your beliefs should tend to that, sure, but if you're trying to produce an actual number for sharing then your beliefs shouldn't be a huge factor, and an uninformative prior being a huge factor is also bad.

For numbers that leave my head/notebook, I'd rather keep the new evidence by itself and say it's weak.

Does Bayesian have a concept for absence of belief? I don't feel like believing anything is equally likely is equivalent to absence of belief. But maybe it is?

There is a concept of minimum knowledge (maximum entropy). There is a concept of invariance (like translation invariance where you have no reason to prefer one position to another because the origin could be anywhere - or scale invariance where the value of a magnitude could be high or low if you don't know anything about the unit of measurement).

I'm not sure if by "absence of belief" you mean "ignorance" or something else.

I think about something like known ignorance. I know that I don't know anything about this thus I refuse to have any belief about what it might be as a I know any belief would be unwarranted.

You need at least something to be ignorant about but for a given "this" you can specify what you do know and calculate a probability distribution representing just that knowledge avoiding any unwarranted belief.

If you have a die and you don't know anything else about it you should assume that the probability for each side is 1/6.

If you also know that the expected value is 4 (instead of 3.5 for a fair die) there is a way to calculate the probability distribution that reflects that constraint - and nothing else.

Now, if you don't even want to think about anything Bayesians can do that too.

It's just weird that the end result depends on something assumed. It reminds of LLMs that can't really express absence of knowledge so they make stuff up kind of assuming they know something.

> It's just weird that the end result depends on something assumed.

It would be weirder if the result didn’t depend on the things assumed.

I don’t know what kind of questions are you thinking of but outside of mathematics they are rarely fully specified.

If the answer changes enough depending on the additional assumptions to seem weird that is a sign that the question was not completely clear.

Of course Bayesians can also say that there is not enough information to provide an answer when that’s the case, just like they can make additional assumptions explicit to provide one.

For me it looks a bit as if whether Schrodinger's cat is dead or alive depended on chosen set of coordinates.

I know it's not like that. But it's still weird that at the end of Bayesian analysis the best you can deliver is if-by-whiskey style deliberation.

I know it's still valuable. Just weird.

Note that there is no way to answer the question “what’s the probability of X conditional on the data observed” without taking into account “what was the probability of X before that observation”.

The thing with non-Bayesian analysis is that they don’t answer at all the question “what’s the probability of X conditional on the data observed”.

The end results of any statistical exercise (frequentist or Bayesian) depend on something assumed.

Frequentist approach gives you something solid and independent of assumptions. Probability of observing this particular dataset accidentally if there was no change between two contexts.

On the positive side, the frequentist approach doesn’t need assumptions about the pre-data probability of the thing of interest.

On the negative side, the frequentist approach doesn’t produce a post-data probability for the thing of interest either.

It provides the probability of something else - as you mention - which can also be interesting but it’s not what people really would like to know (as the generalized misinterpretation of the meaning of frequentist results makes clear).

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