Posts

Convolution as smoothing 2020-11-25T06:00:07.611Z
The central limit theorem in terms of convolutions 2020-11-21T04:09:44.145Z
Examples of Measures 2020-11-15T01:44:39.593Z
Where can I find good explanations of the central limit theorems for people with a Bayesian background? 2020-11-13T16:36:01.611Z
Frequentist practice incorporates prior information all the time 2020-11-07T20:43:30.781Z
"model scores" is a questionable concept 2020-11-06T03:19:45.196Z

Comments

Comment by maxwell-peterson on Postmortem on my Comment Challenge · 2020-12-05T00:01:14.422Z · LW · GW

I liked your comments on my posts.

Comment by maxwell-peterson on Open & Welcome Thread – November 2020 · 2020-11-28T21:43:45.497Z · LW · GW

Great work by you and your girlfriend! It takes courage to intervene in a situation like that, and skill to actually defuse it. Well done.

I don't agree about what you're calling the first error. Her job is to take in statements like yours, and output decisions. She could output "send police to ask questions", or "send a SWAT team now", or "do nothing". She chose a decision you don't agree with, but she had to choose some decision. It's not like she could update the database with "update your prior to be a little more suspicious of Alexes in hatchbacks".

I also don't think it's correct to call it arbitrary in the same way that the p < 0.05 threshold is arbitrary. I don't really know how to say this clearly, but it's like... the p < 0.05 rule is a rule for suspending human thought. Things you want to consider when publishing include: "what's the false negative cost here? false positive cost? How bad would it be to spread this knowledge even if I'm not yet certain the studied effect is real?". The rule "p < 0.05 yes or no" is bad because it throws all those questions away. It is arbitrary, like you say. But it doesn't follow that any questionable decision was made by an arbitrary decision rule. If she thought about the things you said, and decided they didn't merit sending anyone out to follow up, that isn't arbitrary! All it takes to not be arbitrary is some thinking and some weighing of the probabilities and costs (and this process can be quick). You did that and came to one decision. She did that and came to another. That difference... seems to me... is a difference of opinion.

I don't know the actual conversation you had with her, and it sounds like she didn't do a very good job of justifying her decision to you, and possibly said obviously incorrect things, like "you have literally 0 evidence of any sort". But I don't think the step from "I think she was wrong" to "I think her decision rule is arbitrary" is justified. Reading this didn't cause me to make any negative update on police department bureaucracy. (the security company is a different story, if indeed someone was there just watching!)
 

Comment by maxwell-peterson on Convolution as smoothing · 2020-11-26T19:26:07.868Z · LW · GW

Hm. What you're saying sounds reasonable, and is an interesting way to look at it, but then I'm having trouble reconciling it with how widely the central limit theorem applies in practice. Is the difference just that the space of functions is much larger than the space of probability distributions people typically work with? For now I've added an asterisk telling readers to look down here for some caution on the kernel quote.

Comment by maxwell-peterson on Convolution as smoothing · 2020-11-26T07:16:56.170Z · LW · GW

Yes, that sounds right - such an  exists. And expressing it in fourier series makes it clear. So the “not much” in “doesn’t much matter” is doing a lot of work.

I took his meaning as something like "reasonably small changes to the distributions  in don’t change the qualitative properties of ". I liked that he pointed it out, because a common version of the CLT stipulates that the random variables must be identically distributed, and I really want readers here to know: No! That isn’t necessary! The distributions can be different (as long as they’re not too different)!

But it sounds like you’re taking it more literally. Hm. Maybe I should edit that part a bit.

Comment by maxwell-peterson on Why are young, healthy people eager to take the Covid-19 vaccine? · 2020-11-25T23:55:19.317Z · LW · GW

Your 20% link is the cardiology link repeated. I think I know the link you meant: this Lancet study

(I'd caution that a number of journalists mis-read the abstract and reported that nearly 20% of people had a first-time mental health diagnosis after COVID - that isn't so! Only 5.8% had a first time diagnosis. The near-20% (18.1%) includes people already diagnosed with a mental health condition. You might have known this already but I wasn't sure from your phrasing, and this specific error on this study is common so I thought I'd mention it.)

Comment by maxwell-peterson on The central limit theorem in terms of convolutions · 2020-11-24T01:54:13.325Z · LW · GW

Ahh - convolution did remind me of a signal processing course I took a long time ago. I didn't know it was that widespread though.  Nice.

Comment by maxwell-peterson on The central limit theorem in terms of convolutions · 2020-11-24T01:49:15.506Z · LW · GW

I definitely was thinking they were literally the same in every case! I corrected that part and learned something. Thanks!

Comment by maxwell-peterson on The central limit theorem in terms of convolutions · 2020-11-22T21:03:22.922Z · LW · GW

Ha - after I put the animated graphs in I was thinking, “maybe everyone’s already seen these a bunch of times...”.

As for the three functions all being plotted on the same graph: this is a compact way of showing three functions: f, g, and f * g. You can imagine taking more vertical space, and plotting the blue line f in one plot by itself - then the red line g on its own plot underneath - and finally the black convolution f * g on a third plot. They’ve just been all laid on top of each other here to fit everything into one plot. In my next post I’ll actually have the more explicit split-out-into-three-plots design instead of the overlaid design used here. (Is this what you meant?)

Comment by maxwell-peterson on The central limit theorem in terms of convolutions · 2020-11-22T18:18:46.111Z · LW · GW

Yup, totally! I recently learned about this theorem and it’s what kicked off the train of thought that led to this post.

Comment by maxwell-peterson on The central limit theorem in terms of convolutions · 2020-11-22T18:15:12.526Z · LW · GW

Gotcha. The non-linearity part “breaking” things makes sense. The main uncertainty in my head right now is whether repeatedly convolving in 2d would require more convolutions to get near gaussian than are required in 1d - like, in dimension m, do you need m times as many distributions; more than m times as many,;or can you use the same amount of convolutions as you would have in 1d? Does convergence get a lot harder as dimension increases, or does nothing special happen?

Comment by maxwell-peterson on Have epistemic conditions always been this bad? · 2020-11-21T18:18:57.237Z · LW · GW

I was at the University of Washington from the beginning of 2013 to the end of 2014 and noticed almost none of this. I was in math and computer science courses, and outside of class mostly hung out with international students, so maybe it was always going on right around the corner, or something? But I really don’t remember feeling anything like the described. I took a Drama class and remember people arguing about... Iraq...? for some reason, with there being open disagreement among students about some sort of hot-button topic. More important, one of the TAs once lectured to the whole entire class of a couple hundred students about racism in theater, and at times spoke in sort of harsh “if you disagree, you’re part of the problem” terms... and some students walked out! Walking out is a pretty strong signal, and not the kind of thing you do if you’re afraid of retribution.

This is all an undergraduate perspective. Any effect like this could be a lot stronger among people trying to actually make a career at the school.

Comment by maxwell-peterson on Comparing Covid and Tobacco · 2020-11-18T00:30:25.116Z · LW · GW

Those are good points.

Comment by maxwell-peterson on Comparing Covid and Tobacco · 2020-11-17T17:17:47.733Z · LW · GW

We already tried really really hard to reduce smoking in the US. I think all these curves, where effort is on the x axis and benefit on the y, see decreasing returns once you have already put in a lot of effort.

Another way of putting it: People I know who I advise to distance more and wear a mask more might disagree and argue with me, but they’ll at least consider my arguments and say why they’re right and engage. A person I know who smokes, who I advise to stop, will just laugh and blow me off: “whatever dude”. They’ve heard it before. So among people I know, “hey beware covid” is a way more effective message than “hey beware smoking”, so I barely ever bother with the latter.

Comment by maxwell-peterson on Examples of Measures · 2020-11-17T01:26:12.059Z · LW · GW

Thanks!

That helps - I wasn't sure whether there might maybe be some small special intuitive difference in Borel or Jordan that could correspond to a different real world example, but now I think that's definitely a No.

Comment by maxwell-peterson on Examples of Measures · 2020-11-16T19:11:17.684Z · LW · GW

Intuitively, a metric outputs how different two things are, while a measure outputs how big something is.

In terms of inputs and outputs: a metric takes two points as input, and outputs a positive real number. A measure takes one set as input, and outputs a positive real number.

Comment by maxwell-peterson on The new Editor · 2020-11-16T06:59:54.376Z · LW · GW

Love it. Never tried the old editor, but had tried writing posts a couple times in the past, on other sites. I'd always get stuck screwing with the editor settings and trying to figure it out, or losing my work, or whatever. This current LW editor makes it so easy that I finally finished a post (and then two more)! The editor isn't the whole reason for that, but it's definitely a factor.  

Comment by maxwell-peterson on Examples of Measures · 2020-11-16T06:01:32.130Z · LW · GW

Yeah, this makes sense. Hmm. I’ll think about this more then edit the post. Thanks

Comment by maxwell-peterson on Examples of Measures · 2020-11-16T04:08:47.960Z · LW · GW

Ahh. I could very well be wrong. Trying to understand this; visualization-wise, are you saying that instead of visualizing the point moving around, with the green circles fixed, we should be visualizing the green circles moving around, with the point fixed?

Comment by maxwell-peterson on Examples of Measures · 2020-11-16T00:32:46.310Z · LW · GW

Nice recommendation - learned multiple things from it

Comment by maxwell-peterson on Examples of Measures · 2020-11-15T16:38:20.787Z · LW · GW

Fixed!

Comment by maxwell-peterson on Examples of Measures · 2020-11-15T16:37:48.441Z · LW · GW

Thanks - fixed

Comment by maxwell-peterson on Where can I find good explanations of the central limit theorems for people with a Bayesian background? · 2020-11-13T21:57:10.972Z · LW · GW

Your comment made me realize that I didn't actually know what it meant to add random variables! I looked it up and found that, according to Wikipedia, this corresponds (if the RVs are independent) to what my main source (Jaynes) has been talking about in terms of convolutions of probability distributions. So I'm gonna go back and re-read the parts on convolution.

But I still want to go out on a limb here and say that 

So, to say anything useful about a family of random variables, they all have to live on the same space

sounds to me like too strong a statement. Since I can take the AND of just about any two propositions and get a probability, can't I talk about the chance of a person being 6 feet tall, and about the probability that it is raining in Los Angeles today, even though those event spaces are really different, and therefore their probability spaces are different? And if I can do that, what is special about the addition of random variables that makes it not applicable, in the way AND is applicable?

Comment by maxwell-peterson on Where can I find good explanations of the central limit theorems for people with a Bayesian background? · 2020-11-13T18:49:59.517Z · LW · GW

Thanks. I think I had the law of large numbers and CLT in the same bucket in my head, so pointing out they're different is helpful. Your point #5, and the attractor bit, are especially interesting - and I've seen similar arguments in Jaynes's book, around gaussians, so this is starting to get into places I can relate to. And knowing that convergence in distribution is called weak convergence should help when I'm searching for stuff. Helpful!
 

CLT applies to a family of random variables, not to distributions.

I guess I consider a family of random variables to be the same thing as a family of distributions? Is there a difference?

Comment by maxwell-peterson on The (Unofficial) Less Wrong Comment Challenge · 2020-11-11T20:51:50.428Z · LW · GW

Here I am a third time, this time with extra convenience :). This is my main, since it has the actual posts. Gonna get rid of the other one... or something.

Comment by maxwell-peterson on The (Unofficial) Less Wrong Comment Challenge · 2020-11-11T20:11:53.923Z · LW · GW

If anyone is confused seeing that my account has no posts... I just discovered that I accidentally have two accounts. This is me too: https://www.lesswrong.com/users/allswellthatsmaxwell

Comment by maxwell-peterson on Sleeping Beauty, Cloning Beauty, and Frequentist Arguments In Anthropic Paradoxes · 2020-11-11T20:07:24.207Z · LW · GW

I agree that the specification of which state of knowledge we're under is critical to the solution. Another way to put it is what I'm seeing over and over again as I go through Jaynes' Probability Theory book: different prior information leading to different probability estimates is not paradoxical. That's why specifying prior information with clarity is so important. Under one set of prior information, the probability is 1/3; under another, it's 1/2.

 

Comment by maxwell-peterson on The (Unofficial) Less Wrong Comment Challenge · 2020-11-11T19:50:32.767Z · LW · GW

I like this idea, selfishly, having two posts in the frontpage-[0-50]-uncommented category last week myself.

Comment by maxwell-peterson on Sunday, Nov 8: Tuning Your Cognitive Algorithms · 2020-11-09T00:37:43.346Z · LW · GW

Although I had trouble logging in at first, I still liked having the whole thing inside the walled garden, rather than starting in zoom and switching. I think it was worth the trouble (and probably that trouble won’t happen every time)

Comment by maxwell-peterson on Sunday, Nov 8: Tuning Your Cognitive Algorithms · 2020-11-08T20:13:04.609Z · LW · GW

The edit with the guest-pass worked!

Comment by maxwell-peterson on Sunday, Nov 8: Tuning Your Cognitive Algorithms · 2020-11-08T20:07:52.014Z · LW · GW

I tried that a couple times, including just now after seeing your recommendation to, but get:

"The Walled Garden is a private virtual space managed by the LessWrong team.

It is closed right now. Please return on Sunday between noon and 4pm PT, when it is open to everyone. If you have a non-Sunday invite, you may need to log in."

Comment by maxwell-peterson on Sunday, Nov 8: Tuning Your Cognitive Algorithms · 2020-11-08T20:06:54.149Z · LW · GW

(Ah, I'm in central time, so that's why mine says 1:45a but MikkW's says 11:45p. Anyway, still locked out)

Comment by maxwell-peterson on Sunday, Nov 8: Tuning Your Cognitive Algorithms · 2020-11-08T20:00:18.507Z · LW · GW

Trying the link at 11:59 california time, I am getting "Your invite code is for an event that has yet started! Please come back at Monday, November 9th, 1:45am"