101–110 of 227 posts
Earlier quoted context omitted.
This is basically the Bayesian interpretation of probability.
Saying that "the probability of a coin toss of 50% talks about you" is not an interpretation of probability. Saying that we are "50% sure" is also not an interpretation of probability. It's a nonsensical statement. It's like saying we are "50% angry". It doesn't really mean anything.
I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin.
The first person guesses a 66% chance of heads. The second guesses a 50% chance of heads. I, having seen the coin, say it's a 0% chance of heads.
None of these probabilities are wrong. They're all correct given the set of knowledge that person had. Probability is subjective.
Isn't declaring "the raison d’être of probability theory is to explain the decision-making of individuals facing uncertainty" basically a claim that the sole purpose of probability theory is an economist's approach? It's entirely possible that much more work in probability is done without a bet or payoff in sight than is done for the sake of decision-making models. It seems like basing epistemological arguments about…
One way to deal with probability is: defer interpretation until after one has axiomatized calculation by measure theory. I have a quick video on the topic here: https://youtu.be/DnTTAd1TDyQ .
Akin to physics, studying the wave equation doesn't tell you what the wave equation is in the real world.
Earlier quoted context omitted.
For me, it comes down to what kinds of these risky models are most interesting. Some can be interesting because of potential profit or minimizing loss (financial or actuarial) and others are inherently (theoretical physics). To add to your tail risk point - I wonder how many people foresaw the Venezuelan oil crisis way back when, or even less likely, the Saudi Arabian oil complex attack in 2019. And of course, the cu…
>as an aside, do insurance companies significantly alter their policies when such a cat-5 hurricane is imminent? What preparations would they make in the face of that sort of event? You cannot retroactively alter a policy, for obviously good reasons. The main preparation policy-wise is that insurance companies do not knowingly write new policies in the affected area when disaster is ongoing or imminent. Reinsurers wi…
Sure you can. Insurers refuse claims all the time. You just claim that the assumptions of the policy were not met. Since assumptions are always idealizations of the messy real world, such a claim is *always" true
Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…
I don't think "first forty digits of pi" should be admissible. As it depends on an external definition that's not computed by the representation. I could come up with a mathematical definition for any prefix of digits, give it a name and say the 'first x digits of C'.
E.g. a program may be very complex in Kolmogorov terms, like describing 1000 random numbers - easy to understand: you have a database of numbers, and a simple procedure that would scan through it. You can also imagine some real-world microservices-based program with a good architecture and a lot of code that handles all the exception cases of incoming data, all easily understandable.
And now imagine an optimizing compiler for prolog programs. It may have much less code but the algorithm will be so complex that it might be impossible to fully understand its behaviour. E.g. fast-downward is a great example of such a program.
So I'm wondering what does Kolmogorov complexity actually tell? Or does it tell anything useful in "real"-world?
I don't think "first forty digits of pi" should be admissible. As it depends on an external definition that's not computed by the representation. I could come up with a mathematical definition for any prefix of digits, give it a name and say the 'first x digits of C'.
Transmitting a program to compute pi would be shorter than the data needed by any compression algorithm that isn't somehow based on knowing the trick.
The same trick could be used for any mathematically interesting number. The point is that incompressible random sequences exist that are not like that. You can't do better than transmitting the sequence itself.
Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…
There's that phrase again - "true probability" (implying the word "True" == "Real"). You could imagine a system that yields non-linear results, such that no matter how many observations were made, your ability to accuratelt predict outcomes in the system never increases. In this case, you might conclude that you're dealing with one of two special cases: 1.) a non-probablistic event (i.e. a purely random (0% predicatable) event or 2.) on the other end of hyperbole, a purely deterministic event (100% predictable)).