[kolbe]

I work with probably as it relates to financial markets, and my gripe with probably is at an even lower level. Even with dice, the fact of the matter is that you will roll dice with almost entirely Newtonian forces acting on it, and it will settle on a number. This is not unknown to physics. It’s just unknown to us. And because we don’t have the data and computational power to know with any certainty where the dice will land, we call it random.

Everything I do is centered around creating probability distributions of where a stock will be in in the future. I don’t do this because it is fundamentally unknowable, but because I cannot access all of the data necessary to know.

So, I’ve come to regard probably measure as an interesting and useful tool, but one that has no connection to the reality of existence.

[EbTech]

Fair enough! I'd like to point out that the Kolmogorov complexity approach can make sense of subjective probability too. Since you lack precise enough information to predict the dice roll, the most compressed way to write down your observations will involve a Shannon-style code with your subjective probabilities. If you have enough information but not enough computational power, the resource-bounded variants of Kolmogorov complexity may be more applicable.

[jtsuken]

Can you please define Shannon-style code? (Obviously, you don't have the shannon code, the compression method, in mind).

Also, isn't Kolmogorov complexity uncomputable and you run into multiple "who shaves the barber" issues, when trying to determine it?

[EbTech]

The compression code can be specified first. If you have a lot of data, the specification will be negligible in length, compared to the code itself. Together, the specification and the Shannon code give an upper bound on the Kolmogorov compmlexity. If this is the shortest known program, we may consider the Shannon code probabilities as our "best explanation" of the data.

You can also get posterior probabilities using a universal prior such as 2^-K(x), but of course, this can only be approximated in the limit of infinite runtime.