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Is Probability Real?

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Re: Is Probability Real?

#81

Post by derbOac »

loup-vaillant wrote: post #49

Tow things. First, probability is real: it's a construct in one's mind, and minds are just as real as dice or coins. https://www.lesswrong.com/posts/f6ZLxEWaankRZ2Crv/probabilit... Second, (and the author may be leading up to this), there's Solomonoff's theory of inductive inference, which he has proven complete : when we apply Occam's razor (where the prior probability of each possible theory drops exponentially wit…

Vitanyi -- one of the authors cited in the linked piece -- has a paper where he and his colleagues show that even though ideal compression isn't knowable/computable, you can show that two encodings approach the ideal differentially with some computable probability (I'm being vague and handwavy because it's been awhile since I've read this literature carefully). That is, if you have two encodings A and B, you can compute some probability that A is closer to ideal than B.

It's kind of a Kolmogorov/algorithmic complexity analogue of a p-value.

I think this literature/inferential paradigm in general is far less known than it should be.

Re: Is Probability Real?

#82

Post by sxzxs »

jbeam wrote: post #79

Very interesting article that cuts to the core of many of the issues with pricing insurance products. While the phrase is hardly limited to the actuarial world, "all models are wrong, but some are useful" is definitely an extension of this. The fluid nature of probability is the center of the insurance universe. Probability is always a moving target in the insurance world. Indeed, if it weren't, there wouldn't be muc…

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 current situation we're in with CoVID that an entire university of forward thoughtful looking people didn't call until it was a week away. 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?

Are you talking about chaos theory in the last paragraph? I'll read that article you linked in a bit and see what more I have to say, from skimming through it looks as though my question from the previous paragraph may be answered.

Re: Is Probability Real?

#83

Post by glial »

nieve wrote: post #80

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…

What is a probability? Nearly always, a probability isn’t a statement about the world, it’s a statement about your knowledge and the information you have. Even for frequentist statisticians, equating probabilities with proportions of outcomes is an admission that you only have partial knowledge about the outcomes.

Of course it also has mathematical structure and properties that may be interesting to people for their own sake. And there may be interesting things to say about quantum physics using probability, but I think a historian of mathematics would not claim that quantum physics was the driving force for the development of probability theory.

Anyway, the “raison d’être” != every conceivable use.

Re: Is Probability Real?

#84

Post by willis936 »

jhardy54 wrote: post #58
willis936 wrote: post #48

Earlier quoted context omitted.

Not everything that is true is simple or catchy. Biasing towards it is a trap. PBS SpaceTime has a good discussion on this topic. https://youtu.be/xFKgIOX8IRE

Neat video, but it specifically disagrees with your point. He advocates for applying scientific rigor between leaps oc intuition. There's nothing wrong with GP appreciating beauty.

My point isn’t contradicted by the video. My point is not "beauty should not be appreciated". My point is that we should not dismiss models of nature based on aesthetics. Nature has no preference on what we see as beautiful. The video makes the point that beauty should be treated as a guiding principle, not as a hard and fast rule to sniff out truth.

Re: Is Probability Real?

#85

Post by jbeam »

sxzxs wrote: post #82
jbeam wrote: post #79

Very interesting article that cuts to the core of many of the issues with pricing insurance products. While the phrase is hardly limited to the actuarial world, "all models are wrong, but some are useful" is definitely an extension of this. The fluid nature of probability is the center of the insurance universe. Probability is always a moving target in the insurance world. Indeed, if it weren't, there wouldn't be muc…

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 will also avoid writing new treaties (which is what a standard reinsurance policy is called) -- for these reasons the Florida cat reinsurance market is typically dominated by policies that incept on June 1st and run to May 31st of the next year.

Internally, the companies will start modeling what they think their potential losses will be almost immediately, as investors expect a fairly quick turnaround on getting initial loss estimates out the door.

There's a fairly new paper here, albeit not yet peer reviewed, on the promise of maximum entropy models in an actuarial setting. The appendix has references to the earlier papers: https://www.casact.org/pubs/forum/20wforum/07_Evans.pdf

Re: Is Probability Real?

#86

Post by 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.

Re: Is Probability Real?

#87

Post by fractionalhare »

loup-vaillant wrote: post #75
smallnamespace wrote: post #55

Earlier quoted context omitted.

> the amount of error a perfect Bayesian makes as they observe event and bet on the next one, ad infinitum, is finite. There's a little assumption that you're leaving out, namely that the Kolmogorov complexity of the data generating process is finite . From Wikipedia: > expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic)…

> Whether the universe (or our observations of the universe) have finite complexity is very much an unresolved philosophical question. Every time there was a significant advance in physics, it tended to go towards simplification and unification. Geocentrism required epicycles. Then Keppler came up with his ellipses. Then Newton unified celestial and terrestrial laws. Maxwell & Einstein allowed us to view time as less…

> Every time there was a significant advance in physics, it tended to go towards simplification and unification. Geocentrism required epicycles. Then Keppler came up with his ellipses. Then Newton unified celestial and terrestrial laws. Maxwell & Einstein allowed us to view time as less special dimension than we thought it was…

Unification, maybe. Simplification, no. That's evident if you just scroll down the list of Nobels in physics. You even mentioned Einstein, but I don't know how you could claim general or special relativity are simpler than Newtonian physics.

Re: Is Probability Real?

#88

Post by [deleted] »

enriquto wrote: post #5
EbTech wrote: post #2

Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!

A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…

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