Michael "Shapes Dude" Betancourt

Determining the mediant of two rational numbers graphically. The slopes of the blue and red segments from the origin to two points in the first quadrant are two rational numbers, using these as two edges of a parallelogrom, the slope of the diagaonal, drawn as a green segment, is their mediant.

The 'mediant' of two fractions a/b and c/d is (a+c)/(b+d).

Beginners sometimes add fractions this way by mistake.

But it's important in number theory...

... and I just learned it has a simple geometrical meaning, too!

don't even care

Today, in honour of WEB DuBois's birthday in 1868, the @publicdomainrev.bsky.social features the hand-drawn infographics DuBois made with his students to depict the conditions of African-American life in 1900.

Arts-based pedagogy all those years ago!
buff.ly/3kdWqRD

Happy 40th anniversary to "The Legend of Zelda" (released on February 21, 1986).

Give up all hope ye who model here…

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INCOMING CASE STUDY
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HTML: betanalpha.github.io/assets/chapt...
PDF: betanalpha.github.io/assets/chapt...

The _real_ cool kids aren’t -maxxing everything, they’re -uncertaintyquantifyying.

Get more from Michael Betancourt on Patreon writing about modeling building and statistical inference.

As always, a huge thanks to my supporters over on patreon dot com, www.patreon.com/c/betanalpha. Covector+ supporters have enjoyed not only early access to this case study for the past month but also a long video review where I work through the entire piece.

Perhaps just for my own entertainment I also spend way too much time doing some software archeology to investigate some awkward behaviors and then demonstrate various ways to accommodate discretized observations.

The models considered demonstrate pairwise comparison modeling and mixture modeling techniques, as well as how those techniques can be integrated together into consistent models. Each is also complemented with extensive prior modeling, prior checking, and retrodictive checking.

In this case study I analyze reading time data, comparing and contrasting — and ultimately combining! — two popular hypotheses for how we comprehend words as we parse them. Who needs model comparison when we have joint models?

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INCOMING CASE STUDY
< begin Star Fox boss music >

HTML: betanalpha.github.io/assets/chapt...
PDF: betanalpha.github.io/assets/chapt...

Image from This close-up image of a tree core was captured using “TIM”, the lab’s homemade high-resolution…

Image from This close-up image of a tree core was captured using “TIM”, the lab’s homemade high-resolution…

Update from Tumblr: This close-up image of a tree core was captured using “TIM”, the lab’s homemade high-resolution…
Click directly on the link in our Bluesky description, or copy and paste the below:
https://temporalecology.tumblr.com/post/808864438750969856

The _real_ cool kids aren’t -maxxing everything, they’re -uncertaintyquantifyying.

Fun times: a paper of ours is finally "properly published" in AAP:

'Weak Poincaré inequalities for Markov chains: Theory and applications'
- Christophe Andrieu, Anthony Lee, Sam Power, Andi Q. Wang

This was the final part of a trilogy of joint works during Andi's and my postdoc.

We’ll be starting in just under an hour!

This book is positioned in my partner's section of bookshop right at my eye line. It taunts me every day.

We're pleased to have @betanalpha.bsky.social join us in Princeton tomorrow (Feb 17th) to talk about generative modeling!

Talk: 11am
Workshop (with Stan): 12:15pm

The zoom is open to public (see flyer).
@princeton.edu

Shout out to throngs. Don't just run around with a group and whatnot. Make sure that shit is a throng.

Do it for the (histo)gram:

Looks like I'll have some availability Tuesday afternoon. If anyone at Princeton wants to talk stats then don't hesitate to reach out.

Looks like I'll have some availability Tuesday afternoon. If anyone at Princeton wants to talk stats then don't hesitate to reach out.

Michael Betancourt - Chief Research Scientist, Symplectomorphic, LLC Generative ModelingOver the last few years the term "generative modeling" has become increasingly popular.  The precise definition of the term, however, tends to be vague and often inconsistent across...

Friendly reminder that on Tuesday February 17th I'll be in Jersey talking about (narratively) generative modeling, psychology.princeton.edu/news-events/..., and the talk (if not also the paired workshop) will be live-streamed for those interested in attending remotely.

www.arts-et-metiers.net/les-collecti...

Michael Betancourt - Chief Research Scientist, Symplectomorphic, LLC Generative ModelingOver the last few years the term "generative modeling" has become increasingly popular.  The precise definition of the term, however, tends to be vague and often inconsistent across...

Friendly reminder that on Tuesday February 17th I'll be in Jersey talking about (narratively) generative modeling, psychology.princeton.edu/news-events/..., and the talk (if not also the paired workshop) will be live-streamed for those interested in attending remotely.

Lines? I thought we were talking about local representations of linear operators?

We all have more math to learn and have to learn it from somewhere!

Can I tell you something?

Linear algebra question:

Let X be positive-definite, (J x J) matrix and Y a rectangular (I x J) matrix with I > J. Moreover, let rank(Y) < J and construct the matrix product Z = Y * X * Y^{T}. Because Y is rank-deficient Z will not be positive-definite, but we can isolate the non-singular part.

Am I just getting lucky with my experiments or does the QR decomposition isolate non-singular behavior like this even though R is not generally rank-revealing?

Thanks!