How can I protect my bank account from large, surprise withdrawals? 2021-02-22T18:57:46.784Z
Use conditional probabilities to clear up error rate confusion 2021-01-17T08:27:38.137Z
Netflix's "Start-Up" and sincere work dramatization 2020-12-25T05:32:46.547Z
Probability theory implies Occam's razor 2020-12-18T07:48:17.030Z
How long does it take to become Gaussian? 2020-12-08T07:23:41.725Z
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


Comment by maxwell-peterson on How can I protect my bank account from large, surprise withdrawals? · 2021-02-24T04:05:43.935Z · LW · GW

I’d never heard of that site! Thanks

Comment by maxwell-peterson on How can I protect my bank account from large, surprise withdrawals? · 2021-02-23T14:41:39.933Z · LW · GW

Your answer uses a fair amount of analysis and knowledge in order to avoid this kind of large charge. Maybe perversely, I was asking for methods that do not require analysis or knowledge about contract types. I also doubt that most customers of the Texas company had a good sense of the risk they were exposing themselves too - many might have followed the "scan list for lowest rate, then pick that one" method that I use sometimes.

Comment by maxwell-peterson on How can I protect my bank account from large, surprise withdrawals? · 2021-02-22T19:47:16.268Z · LW · GW

Thanks - that's even better separation than using separate accounts at the same bank. More work, but something I hadn't thought of.

Comment by maxwell-peterson on How can I protect my bank account from large, surprise withdrawals? · 2021-02-22T19:44:52.658Z · LW · GW

Ahh - of course! Thanks!

Comment by maxwell-peterson on Participating in a Covid-19 Vaccine Trial · 2021-02-12T18:18:27.002Z · LW · GW

Nice story! All the little details made it fun to read.

Comment by maxwell-peterson on Does anyone else sometimes "run out of gas" when trying to think? · 2021-02-03T13:37:02.043Z · LW · GW

I’ve never! Not even close.

Comment by maxwell-peterson on [Link] Still Alive - Astral Codex Ten · 2021-01-22T01:23:41.260Z · LW · GW


Comment by maxwell-peterson on Netflix's "Start-Up" and sincere work dramatization · 2020-12-30T21:19:05.896Z · LW · GW

Python, actually! (Who would have guessed?). The camera zooms in on Do-San writing correct Python every now and then. I mean, he keeps writing a function called sigma_prime, which, like, maybe he should import? But it is tech literate even there!

Comment by maxwell-peterson on The Best Visualizations on Every Subject · 2020-12-22T03:50:01.974Z · LW · GW

This isn’t a textbook, but Dataclysm by Christian Rudder was a major inspiration to me when I was new to data analysis. The book is like a long data analysis project around dating on OKCupid (Rudder founded the site), and has a lot of good graphs made just for the book. Unlike some of the popular examples made famous by e.g. Tufte, the graphs in Dataclysm are of the type an analyst in 2020 might typically make in their day-to-day work. Lots of scatter plots and bar plots, but created thoughtfully enough to really be something. Rarely in this book did I think “ah, beautiful” - much more often, I thought “ah, yup, I see the relationship he’s saying exists.”

Comment by maxwell-peterson on Gauging the conscious experience of LessWrong · 2020-12-20T18:33:40.320Z · LW · GW

Great descriptions!

Comment by maxwell-peterson on Gauging the conscious experience of LessWrong · 2020-12-20T18:31:29.942Z · LW · GW

Interesting - I can’t count the points on a star either (my imagination insists on zooming way in on one point when I try to count it, so zoomed-in that the other points are no longer in “sight”). But I consider myself a pretty visual thinker, and rarely do things I imagine seem fake. One of my big accomplishments this year has been learning a lot more math, and that learning started being really successful when I began trying to visually picture as many concepts as I could (like probability regions in 2d and 3d, for example).

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-18T17:28:10.978Z · LW · GW

Thanks for investigating, this is helpful - I added a link to this comment to the post.

Comment by maxwell-peterson on Probability theory implies Occam's razor · 2020-12-18T16:00:08.266Z · LW · GW

Yes, the thing about the age is totally dependent on the actual state of the universe (or, put more mundanely, dependent on the actual things I know or think I know about cows).

In regard to the short laws of the universe... I am saying that, if you’re already in the framework of probability theory, then you know you can’t gain from random guessing. Like how the optimal strategy for guessing whether the next card will be blue or red, in a deck 70% red, is “always guess red”. A hypothetical non-Occam prior, if it doesn’t tell you anything about cards, won’t change the fact that that this strategy is best. To convince someone who disagrees that this is true, using real examples, or actually drawing actual cards, would help. So again there I’d use empirical information to help justify my claim. I guess what I’m trying to say is: I didn’t mean to argue that everything I said was devoid of empiricism.

Comment by maxwell-peterson on The Power of Annealing · 2020-12-15T18:51:44.480Z · LW · GW

I've seen the words "simulated annealing" I don't know how many times, but always figured it was some complicated idea I'd have to actually sit down and study. So this post is actually the first time I got the idea and see how it is useful. I also didn't know that 2-year-old brains had more synapses than adult brains. Good post!

Comment by maxwell-peterson on The Fermi Paradox has not been dissolved - James Fodor · 2020-12-15T02:36:12.503Z · LW · GW

Great post! I moved a lot toward a rare-earth view when I learned of the Sandberg paper, and this post has me back to unsure. Glad I read this.

Comment by maxwell-peterson on Why quantitative methods are heartwarming · 2020-12-14T18:46:46.888Z · LW · GW

Love this! Very much agree. I do work on improving pricing methods in my day job, but I hadn’t been equipped with the emotional lens that this post describes - so this is useful to me (and just nice!). I’m gonna share it with people at work.

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-14T16:21:35.437Z · LW · GW

This is an interesting view. I like the idea of thinking of center and tails separately. At the same time: If the center and tails were best thought of as separate, isn't it interesting that both go to Gaussian? Are there cases you know of (probably with operations that are not convolution?) where the tails go to Gaussian but the center does not, or vice-versa?

Skew doesn't capture everything, but it really seems like it captures something, doesn't it? I'd be interested to see a collection of distributions for which the relationship between skew and Gaussianness-after-n-convolutions relationship does not hold, if you know of one! 

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-14T16:11:52.845Z · LW · GW


Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-12T01:07:37.433Z · LW · GW

Good to hear! Thanks

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-10T17:25:17.458Z · LW · GW

I had a strong feeling from the theorem that skew mattered a lot, but I’d somehow missed the dependence on the variance- this was helpful, thanks.

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-10T04:49:05.489Z · LW · GW


Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-09T16:52:28.916Z · LW · GW

Wow! Cool - thanks!

Comment by maxwell-peterson on An elegant proof of Laplace’s rule of succession · 2020-12-09T07:11:25.019Z · LW · GW

Nice post! I just finished reading a lot about the rule of succession (In Jaynes’ book) and this is a helpful similar-yet-different perspective. Cool circle idea.

Comment by maxwell-peterson on An elegant proof of Laplace’s rule of succession · 2020-12-09T06:54:05.495Z · LW · GW

I don’t know about linkposts, but there’s an editor here with LaTeX, yup. There are two editor modes: The LessWrong Editor, and the Markdown Editor. Looks like you’re in the markdown editor here. The LessWrong editor doesn’t support footnotes, and there are plenty of other differences, so I recommend against converting this post to LessWrong-editor-format - things might get totally messed up. (Though I’ve only written 6 posts here, none in the Markdown editor, so I’m not actually sure).

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-09T00:38:48.759Z · LW · GW

Those possible approximate rules are interesting. I’m not sure about the answers to any of those questions.

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-08T23:51:00.568Z · LW · GW

I think I didn't like the supremum part of the KS distance (which it looks like Total Variation has too) - felt like using just the supremum was using too little information. But it might have worked out anyway.

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-08T23:43:08.173Z · LW · GW

Yes, exactly right: initial kurtosis is a fine indicator of how many convolutions it will take to reach kurtosis = 3. Actually, it’s probably a better indicator than skew, if you already have the kurtosis on hand. Two reasons I chose to look at in in terms of skew:

  1. the main reason: it’s easier to eye skew. I can look at a graph and think “damn that’s skewed!”, but I’m less able to look and say “boy is that kurtose!”. I’m not as familiar with kurtosis, geometrically, though, so maybe others more familiar would not have this problem. It’s also easier for me to reason about skew; I know that income and spend distributions are often skewed, but there aren’t any common real world problems I find myself thinking are more or less kurtose.
  2. I suspect - I’m not sure - but I suspect that distance-from-kurtosis-3 is a monotonically decreasing function of #-of-convolutions. In that case, to say “things that start closer to three stay closer to three after applying a monotonic decreasing function” felt, I guess, a little bit obvious?

Re: the beta(20, 10) making it look like there's a sweet spot around skew=0.25: correct that that isn't real. beta(20, 10) is super Gaussian (has very low kurtosis) even before any convolutions. 

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-08T16:27:40.777Z · LW · GW

I thought about that but didn't try it - maybe the sum of the absolute difference would work well. I'd tried KS distance, and also taking sum(sum(P(x > y) over y) over x), and wasn't happy with either. 

Comment by maxwell-peterson on How long does it take to become Gaussian? · 2020-12-08T16:19:58.285Z · LW · GW

Fixed - thanks! (Although your example doesn't sum to 1, so is not an example of a distribution, I think?)

Comment by maxwell-peterson on On exact mathematical formulae · 2020-12-07T20:34:46.906Z · LW · GW

This is great - I’ve been working on a lot of math lately, and the difference in this post describes is definitely muddied in my mind, but until reading I didn’t realize I was confused about the difference.

Comment by maxwell-peterson on The Incomprehensibility Bluff · 2020-12-07T19:27:54.579Z · LW · GW

When I talk to non-technical people at work or about my work, I am frantically translating all the technical words I usually use into words that fit into something that I hope they can understand. This is very difficult! And I have to do it on the fly. I mess up sometimes. This must happen to a lot of people, and it's all very innocent - because communicating across large inferential distances is hard. I've gotten better at it but it is definitely a skill. I appreciate the edit to call out that there are various options about what's going on besides the Smarter and Bluffing options described in the post, but I still want to stress that bluffing is a small minority of such cases. Certainly no one should be defaulting to thinking that a person is bluffing, just because they're using difficult language or failing to explain well.

Anecdotally, from working with data analysts and data scientists, watching them present to people outside their level of technical expertise, and looking back at certain presentations I've made: I feel embarrassed for a technical person who is failing to bridge the inferential gap. Like another commenter said, failing to model the audience looks bad. If other technical people are listening and notice, they'll think you're just messing up. So even if we imagine that this Bluffing is common, those doing it would probably only want to do it when there are very few people around to notice how bad their explanation is. 

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


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