Comment by wolajacy on Where can I find good explanations of the central limit theorems for people with a Bayesian background? · 2020-11-14T00:48:52.243Z · LW · GW

If you don't have a given joint pobability space, you implicitly construct it (for example, by saying RV are independent, you implicitly construct a product space). Generally, the fact that sometimes you talk about X living on one space (on its own) and other time on the other (joint with some Y) doesn't really matter, because in most situations, probability theory is specifically about the properties of random variables that are independent of the of the underlying spaces (although sometimes it does matter).

Your example, by definition, P = Prob(X = 6ft AND Y = raining) = mu{t: X(t) = 6ft and Y(t) = raining}. You have to assume their joint probability space. For example, maybe they are independent, and then it P = Prob(X = 6ft) \* Prob(Y = raining), or maybe it's Y = if X = 6ft than raining else not raining, and then P = Prob(X = 6ft).

Comment by wolajacy on Where can I find good explanations of the central limit theorems for people with a Bayesian background? · 2020-11-13T20:32:39.371Z · LW · GW

Answering the last question: If you deal with any random variable, formally you are specifying a probability space, and the variable is a measurable function on it. So, to say anything useful about a family of random variables, they all have to live on the same space (otherwise you can't - for example - add them. It does not make sense to add functions defined on different spaces). This shared probability space can be very complicated by itself, even though the marginal distributions are the same - it encodes the (non-)independence among them (in case of independent variables, it's just a product space with a product measure).

Comment by wolajacy on Where can I find good explanations of the central limit theorems for people with a Bayesian background? · 2020-11-13T18:00:10.545Z · LW · GW

Don't have any good source except univeristy textbooks, but:

  1. The simplest proof I know of (in 3 lines or so) is to just compute characteristic functions.
  2. In general, the theorem talks about weak convergence, i.e. convergence in distributions.
  3. The sample mean converges to expected value of the distribution it was taken from almost surely (i.e. strong convergence). This is a different phenomenon than CLT, it's called the law of large numbers.
  4. CLT applies to a family of random variables, not to distributions. The random variables in question do not have to be identically distributed, but do have to be independent (in particular, independence of a family of random variables is NOT the same as their pairwise independence).
  5. The best intuition behind the CLT I know of: Gaussian is the only distribution with a finite variance where a linear combination of two independent variables has the same distribution (modulo parameter shift) as they have (i.e. it is a stable distribution). So, if try to "solve" the recursive equation for the limit in CLT, you'll see that, if it exists, it has to be Gaussian. The theorem is actually about showing that the limit exists. 

    In general, as someone nicely put this: The importance of stable probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed (iid) random variables.
Comment by wolajacy on Against Victimhood · 2020-09-18T09:50:44.173Z · LW · GW

On the exactly the same phenomenon, but from a different perspective - C. S. Lewis in The Great Divorce goes to explain the Christian Hell as the place that people are stuck in because they choose to wallow in despair/grief/anger/victimhood, instead of just forgiving and letting go.

For example, he talks about a mother that lost her child, and is now stuck on anger of this child being unfairly treated by the word/God. The crucial fact is that she is indulging in that anger as a way of signalling her own self-rightioussness, not for any productive purpose.

Quite interesting, how all these different worldviews converge on that one :)

Comment by wolajacy on Escalation Outside the System · 2020-09-08T20:04:25.431Z · LW · GW

This reminds me of the "The Toxoplasma of Rage" post by SSC:

The question of "why do the left play into violent confrontation, even though it's suboptimal from their perspective" is another version of the central question discussed in the article.

Comment by wolajacy on What posts on finance would your find helpful or interesting? · 2020-08-23T00:39:31.520Z · LW · GW

1) Meta-level post listing interesting sources to learn different aspects: assets pricing, relevant parts of macro (for example, it seems that in academia, there's a number of different, conflicting, business cycle theories - but as financial institutions actually have skin in the game, it'd seem reasonable that they came up with a "correct" version of it), HFT, general info.

2) Examples of (obviously, already-dead) strategies that made significant profit before - if such descriptions are available anywhere.

2) Books reviews - having recently read Flash Boys and When Genius Failed, I'd be really interested in an expert evaluation of those. Also, other books recommendations (as in 1), but with a more documentary(or even fiction?)-focus.

Comment by wolajacy on On Need-Sets · 2020-08-18T19:03:02.881Z · LW · GW

The categories are good, but I feel that the list is incomplete. Where would you put, for example, stability?

Comment by wolajacy on On Need-Sets · 2020-08-16T13:03:35.384Z · LW · GW
While the visualizations may be pleasant, saying one is grateful for something seems like it may (at least subconsciously) involve comparing it to a world in which that thing does not exist.

Are you trying to say that it should work similarly to a desensitization therapy? But then, there might exist the reversed mode, where you get attached to things even more, as you meditate on why are they good to have. Which of these modes dominates is not clear to me.

Additionally, by cultivating good feelings about the things one already has, it may aid with the grieving process; the process is likely to be set up to struggle less when letting go of a supposed need, the more positive feelings one experiences.

I don't think I get this. Doesn't this apply to any positive thing in life? (e.g. why single out the gratitude practise?)

Comment by wolajacy on (Ir)rationality of Pascal's wager · 2020-08-04T19:57:46.839Z · LW · GW
Here is why I think so:
I think that in this case, option B is the right choice.
But, what if someone decides to make just one decision, which is worse in expectation but very improbable to have any negative consequences? Of course, if this person would start to make such decisions repeatedly, then she will predictably end worse off, but if she is able to reliably restrict herself to making just this single decision solely on the basis of its small probability, and following the expected utility otherwise, then for me it seems to be rational.
It seems to me that the Sam’s strategy achieve the best result at the end.

So, I'm not really seeing any argument in your post. You claim to answer the question "why", but then just present the cases/stories and go on to say "for me, this is the right choice". Therefore, it's difficult to provide any comment on the reasoning.

So, my question would be: in what sense it's the right choice/rational/achieving best result? The only passage that seems to start addressing that is the one with "it's worse in expectation, but very improbable".

(One way to judge a decision rigorously, as you seem to be doing in the "ordinary" case, would be to create a model and a utility function - in your text: a long sequence of decisions, a payoff at each one, aggregated utility measured by a sum or mean).

Comment by wolajacy on Billionaire Economics · 2020-07-28T21:39:24.742Z · LW · GW

(I've never understood this line of reasoning. But again, a lot of people here take that argument seriously, which probably means I'm making some mistake here. I had never been able to get what it could be, so if someone can explain where is the issue with my reasoning, I'll be glad.)

tl;dr We should taboo "money redistribution" and instead only talk about "consumption redistribution" and "power redistribution", which are two almost-separate things. I argue that in light of none of them, it's a good idea to take billionares' wealth.

Ok, so, what matters is consumption. A billionare does not buy a million cars, or sausages for BBQ, and generally there's not much difference in consumption between Warren Buffett and "just" very rich Beyoncé. [citation needed]. Redistribution of wealth, even if it was very liquid, does not cause additional economic output to appear. It might happen in a short term, when everyone is getting this $10,000 and spending it, boosting the economy, but it's the same effect as increasing money supply by a central bank. In the long term, any effect that can be caused by such intervention (of wealth transfer) can also be caused by Fed policy. The only way we could really make a change would be to set an extremely high tax on consumption. And most of the consumption that we would redistribute is done by the middle class.

If the billionares money does not go to consuption, where does it go? It's invested. So maybe the reason to redistribute is not to generate output, but to limit the power of the rich. But the free market is specifically set up in this way to transfer the power to manage money from the incompetent to competent - and that would be exactly reversing this trend! If Joe The Plumber gets a voting share in some company, he will most probably make worse decisions than Warren Buffett. Personal freedom is of course dependent on economic freedom, but it's a far-reaching link - if Joe controlled a voting share in the company he personally works, he could make a decision to switch from plumbing to gardening, or laying and watching TV, which would free him from the power Warren Buffett currently has over him, forcing him to do plumbing instead, but this is not because Warren is - it is because it's an optimal market decision, and he, coincidentally, is just an executor of this will (again, because the market granted him this power through Darwinian process of wealth redistribution to people most competent in generating/holding into it).

Comment by wolajacy on Cost/Benefit analysis of School Closures in the US · 2020-07-18T18:27:41.448Z · LW · GW

You're right about the small sample, I read the paper some time ago and forgot/didn't notice that.

I think you're also right about the K-12 school purpose as being more a daycare facility than anything else. I wouldn't necessary expect custom-tailoring the education on a large scale - parents still have to work (from home or not) or need to take care of many other issues araising from the current situation.

My prediction would be that the inequality araising from that factor would stay ~the same, because first, I feel that education on that level doesn't matter that much in the long run, second, because many extracurricular activities for middle/upper class are not available, and third, when it does matter, there is a greater focus on producing quality learning materials online, which further bridges the gap.

Comment by wolajacy on Cost/Benefit analysis of School Closures in the US · 2020-07-11T20:37:42.035Z · LW · GW
Now, these studies are not perfect, but there have been several of them and they tend to get similar results. Thus, I think it's fair to conclude that years of schooling, particularly at the high school level, have a positive impact on income.

This study takes into account only university attendance, on a yes/no scale, measuring impact relatively to non-attending twins.

(side note: the second link is broken, but judging from the address, it points to the first study, probably a typo).

From the second study (about K-12 funding)

Event-study and instrumental variable models reveal that a 10 percent increase in per-pupil spending each year for all twelve years of public school leads to 0.27 more completed years of education, 7.25 percent higher wages, and a 3.67 percentage-point reduction in the annual incidence of adult poverty.

This paper again talks about the boost relative to underfunded students.

I would also say those two say very little about high-school level.

As far as I understand, the whole argument against schooling (which for example Caplan makes) is that it serves mostly as signalling, i.e. benefits from schooling are relative to the position of other members of the society. By limiting it across the society, you are thus not losing much - even if you find the correlation between school-ness and success in life later in the normal conditions, you should not expect it to be present if everyone is handicapped in the same way.

Also, no school is probably qualitatively different than heavily-underfunded school, as more funding can just remove the horrible-ness of the environment. The paper talks about the relative advantage of students left to do their own thing ("unschooled"), compared to normal ones - and finds that going to school actually gives you just 1 year boost in education, which is, to say, not much.

Comment by wolajacy on The Illusion of Ethical Progress · 2020-06-30T15:51:03.855Z · LW · GW

Philosophy of empiricism and empiricism itself (such as in physics) are two different things, as the first is a metatheory of the second. I interpret the text as talking about the lack of empirical method in philosophy.

Comment by wolajacy on Building brain-inspired AGI is infinitely easier than understanding the brain · 2020-06-02T14:46:06.036Z · LW · GW

Good post, I actually hold a similar-ish views myself.

However, I'd be interested if you elaborated more on the last paragraph - what specific examples of that kind of research do know about/recommend to check out?

Comment by wolajacy on Signaling: Why People Have Conversations · 2020-05-19T21:12:15.773Z · LW · GW

I'd also be good to cite the source here, as pretty much the whole argument is copied from it: The elephant in the brain, by Hanson & Simler.

Comment by wolajacy on If a tree falls on Sleeping Beauty... · 2020-05-06T02:14:17.411Z · LW · GW

Does this have some connection to the unbiased/maximal likelihood estimator dichotomy?

I don't really have a clear picture, so this should be treated only as a vague intution that someone could hopefully formalize, but I feel that somehow the maximal likelihood estimator would be in the 1/3 camp, since it optimizes just for the payoff - and, on the other hand, unbiased estimator would be in the 1/2 camp, since it optimizes for accuracy. Then, the whole problem comes down to the well-known issue that in some cases, MLE are not unbiased (e.g. classic problem with variance estimator).