Post B1lNc13SSxptPRBgzQ by javier@col.social
(DIR) More posts by javier@col.social
(DIR) Post #B1lFL8Crp7x92A1hLc by futurebird@sauropods.win
2025-12-30T03:08:23Z
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And they say "the internet is dead" Here is some entertainment. Highest quality. https://www.youtube.com/watch?v=O9jzr5MqiRY
(DIR) Post #B1lFLut2pcDC0s83km by futurebird@sauropods.win
2025-12-30T03:08:30Z
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gaussian distribution?? more like MOUSEian distribution
(DIR) Post #B1lGNVo59K6UlJ8Gwa by futurebird@sauropods.win
2025-12-30T03:20:02Z
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Here's the thing about that formula for the gaussian distribution. It looks scary, right? Look at all those symbols! The first thing is to realize you are just looking at:y=e^x but changed in a few ways. Don't worry about the fraction at the front. (1/sqrt(2pi sigma^2)) That is just a constant. Now y=e^x is the exponential. It increases faster the larger it is. It shoots up to the right and goes to zero to the left. Now consider y=e^{-x} Same curve flipped along the y-axis. 1/
(DIR) Post #B1lGc9qH5zNKz38qQK by futurebird@sauropods.win
2025-12-30T03:22:41Z
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Consider also y=e^{x*x} that one looks like an over enthusiastic parabola. So, when you take y=e^-{x*x} you get a nice hump, it looks almost like the normal curve already. In fact, everything else is just about moving it around and making the mean and SD do what you'd expect. Not bad at all. 2/2
(DIR) Post #B1lH4FqAO6M3hAUM6a by futurebird@sauropods.win
2025-12-30T03:27:46Z
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I love the gaussian distribution so much but my students get so upset when they see the formula it makes me sad. It's REALLY not that bad I promise. The stats people just want it to have an area under the curve equal to one. So they decorate it with all of this... stuff... It's useful. But the essence of what it is? It's just e raised to the negative x squared. Noting to be upset about.
(DIR) Post #B1lHI4pm6cFvc7tdya by swart@cosocial.ca
2025-12-30T03:30:14Z
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@futurebird I bet they would like it animated
(DIR) Post #B1lIGPz0bTTka5zLFY by javier@col.social
2025-12-30T03:41:08Z
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@futurebird the fact that integrating that bad boy is a pain in the ass does not help either.
(DIR) Post #B1lIIvdRtMvRKP6KIq by eleanor@chaosfem.tw
2025-12-30T03:41:35Z
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@futurebird the first time i saw the standard trick of evaluating the integral of the gaussian by squaring it, rewriting it as an iterated integral, and then converting to polar coordinates was like watching actual magic. And then *and then* pi just drops out of the whole thing, simple as that? I'm pretty sure I literally got goosebumps in math class that day. It was like the universe was speaking.
(DIR) Post #B1lIPqVTMIRvRtfVvk by futurebird@sauropods.win
2025-12-30T03:42:52Z
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@javier The "fancy coffee table" (1/sqrt(2pi sigma^2)) helps things a little...
(DIR) Post #B1lJ1zN4qfyXwivhgm by yaycath@sauropods.win
2025-12-30T03:49:35Z
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@futurebird hey I have been texting you trying to figure out whether we're meeting tomorrow or not
(DIR) Post #B1lJ8A6Jrv8uxf2EF6 by masp@wandering.shop
2025-12-30T03:50:50Z
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@futurebird @javier The context that finally clicked for me was: 1. maximize entropy for pdf with no constraints -> uniform distribution; 2. maximize entropy for pdf with fixed mean -> exponential; 3. maximize entropy for pdf with fixed mean + finite variance -> gaussian.
(DIR) Post #B1lKBucrRl3q4vblr6 by futurebird@sauropods.win
2025-12-30T04:02:45Z
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@masp @javier Never thought of it like that before. I tend to think of the gaussian distribution as coming out of pascal's triangle and it's almost like an analytic version of binomial distribution or the limit of that. OK how do you think of the Cauchy Distribution with this format?
(DIR) Post #B1lKW20jhO6Wm5MwhE by masp@wandering.shop
2025-12-30T04:06:21Z
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@futurebird @javier This was my cheat sheet: https://joshuagoings.com/assets/Maximum_Entropy_Distributions.pdf
(DIR) Post #B1lKxvxLnrKe6Z5fbU by futurebird@sauropods.win
2025-12-30T04:11:26Z
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@javier To learn how to do it "naturally" you'd need to learn an awful lot of integration tips and tricks. I think of it as something that exists in the way that it is *because* it has to integrate to 1. So if you derive it so it's a distribution, you have kind of already integrated it. (don't know if I explained that well. I'm just saying don't feel bad if it stumps you. It's artificial. )
(DIR) Post #B1lNc13SSxptPRBgzQ by javier@col.social
2025-12-30T04:41:05Z
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@futurebird oh, it does not. Thanks for saying it, tho. I was mostly thinking about the place where people struggle when they first see it. Barely ever it comes naturally. It is forced. And it is a hard integral.
(DIR) Post #B1laykh2lMBwjHsJf6 by pdcawley@mendeddrum.org
2025-12-30T07:10:46Z
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@futurebird @javier In an early probability lecture my our prof integrated the Gaussian formula on the board. I don't remember much from forty years ago, but I do remember he took advantage of the fact that the area under the curve had to be one as a short cut.
(DIR) Post #B1ltBS7YvKhY4HU716 by futurebird@sauropods.win
2025-12-30T10:34:47Z
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@flipper That's mean.
(DIR) Post #B1lyXO8WuxkdquDTkG by level98@mastodon.social
2025-12-30T11:34:45Z
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@futurebird I think it does get complicated when you're looking at, say, four layers of abstraction (which can all be gaussian) E.g. A "population" distribution, a sample distribution from that distribution, the distribution of sample means and, for a "Type Ii Error", a posited new distribution!
(DIR) Post #B1m6xNu1D4GYHyKsNM by babelcarp@social.tchncs.de
2025-12-30T13:09:07Z
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@futurebird Gaussian Linux distribution