Michael Boo-tancourt
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betanalpha.bsky.social
Michael Boo-tancourt
@betanalpha.bsky.social
2.7K followers 160 following 1.7K posts
Zealous modeler. Annoying statistician. Reluctant geometer. Support my writing at http://patreon.com/betanalpha. He/him.
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betanalpha.bsky.social
Randomly sampling from SO(3).
A painting of the word “AROUND” with each letter three-dimensional and curved and surrounded by a red arrow indicating various directions of rotation.
November 23, 2025 at 5:02 PM
betanalpha.bsky.social
Did I tweak nearly every slide of my regression deck in preparation for next month’s charity course? Only one way to find out!

Join us by dropping a 50 USD donation to World Central Kitchen or United Farm Workers. A few sponsored spots available. Details at betanalpha.github.io/courses/.
The title slide for my regression modeling decks, titled “Foundations of Regression Modeling” with a, dare I say elegant, faded image of curves interpolating through observed data in the background.
November 18, 2025 at 5:26 AM
betanalpha.bsky.social
Curious how to justify statements like “linear is good enough”? Join us on Wed Dec 10 for a comprehensive introduction to regression to raise funds for World Central Kitchen and United Farm Workers. Course details and registration instructions at betanalpha.github.io/courses/.
A slide with the text “This Taylor approximation perspective informs how we can use linear functional models robustly in practice.” and a figure of a one-dimensional nonlinear function y = f(x), observations (x_n, y_n) that cluster within a small neighborhood of x values, and linear Taylor approximations of f(x) that interpolate through those observations.
November 12, 2025 at 3:10 PM
betanalpha.bsky.social
The Legend of Zelda: Skyward Sword
A cloud formation that looks like a long sword, with a long fluffy cloud forming the blade and handle and short, streaky cloud in the opposite direction forming the hilt.
November 7, 2025 at 7:05 PM
betanalpha.bsky.social
🥂
A tipple of Meilleur Ouvriers de France Sommeliers Chartreuse to celebrate a good day.
November 5, 2025 at 2:49 AM
betanalpha.bsky.social
Wednesday, December 10!

Bayesian regression modeling!

Stan exercises!

Raising money for World Central Kitchen and United Farm Workers!

betanalpha.github.io/courses/!
A slide with the text “This predictive task then motivates a natural variate-covariate decomposition of the full Bayesian model.” followed by equations for the six possible conditional decompositions of the probabilistic model p(y, x, theta). The conditional decomposition p( y, x, theta ) = p( y | x, theta ) p( x | theta ) p( theta ) is highlighted.
November 4, 2025 at 2:33 PM
betanalpha.bsky.social
epsilon > 0
The 2025 NYC Halloween Early Voting sticker featuring a pigeon in a witch’s hat with a pumpkin basket in its beak.
October 31, 2025 at 4:46 PM
betanalpha.bsky.social
Oh, do you not check your retros?
Posterior retrodicive checks between a Bayesian linear regression model and the four data sets from Anscombe’s quartet. Because the data sets all share the same summary statistics the likelihood functions are the same. Consequently so too are the posterior and posterior predictive disruptions. The retrodictive checks, however, demonstration varying tensions between the common posterior predictive distribution and the observed covariation in each data set.
October 28, 2025 at 2:16 PM
betanalpha.bsky.social
Tesselate this
A visualization of a doubly-connected edge list representing the Voronoi diagram for ten randomly positioned points. The edges bordering on one the sites are highlighted.
October 26, 2025 at 2:31 AM
betanalpha.bsky.social
Not all graphical models are the same. Join us in December to dig into the probabilistic modeling structure of Bayesian regression analysis while raising money for World Central Kitchen and United Farm Workers. For details on the course and how to register check out betanalpha.github.io/courses/.
The Geordi LaForge meme demonstrating hesitation for a conventional “causal” direct graphical model, showing only observed variables and unobserved confounders, and enthusiasm for a directed graphical model that represents a full joint probabilistic model including all observed variables and all latent/unobserved variables.
October 21, 2025 at 2:24 PM
betanalpha.bsky.social
Up late balancing trees.
An initial red-black binary search tree and a balanced update after inserting the key “3”.
October 14, 2025 at 4:10 AM
betanalpha.bsky.social
On Wed Dec 10 join me to learn about what a regression model is, and what a regression model is not, while raising funds for World Central Kitchen and United Farm Workers. For details on how to register, sponsored registration possibilities, and more see betanalpha.github.io/courses/.
A slide with the text “Predicting a missing variate for a fully observed covariate, however, is not always the relevant predictive task.”, a probabilistic graphical model for predicting a missing variate given a partially observed covariate, and a corresponding equation for the posterior prediction distribution.
October 13, 2025 at 1:22 PM
betanalpha.bsky.social
👀👀👀
October 12, 2025 at 7:13 PM
betanalpha.bsky.social
I don't think there's anything that will satisfy anyone expecting a one sentence explanation (which, sadly, is most people) but given little bit of time I think the geometric picture where the odds ratio is a slope,
OR = N_success / N_failure
N_success = OR * N_failure
is reasonably intuitive.
September 25, 2025 at 2:57 AM
betanalpha.bsky.social
Probabilistic raster (4K).

www.symplectomorphic.com/assets/chapt...
A figure demonstrating the law of total expectation by comparing the probability allocated to a subset to the expectation value of the function defined by the intersection of that subset and an uncountable partition defined by the level sets of a function.
September 11, 2025 at 2:28 PM
betanalpha.bsky.social
Probabilistic raster.

www.symplectomorphic.com/assets/chapt...
A figure demonstrating the law of total probability by comparing the probability allocated to a subset to the probability allocated to the intersections of that subset with the disjoint elements of a countable partition.
September 10, 2025 at 1:54 PM
betanalpha.bsky.social
A cathedral for worshipping conditional probability theory.

www.symplectomorphic.com/assets/chapt...
A collection of properly normalized, one-dimensional conditional probability density functions formed by conditioning a symmetric, two-dimensional density function on the level sets of a radial function.
September 9, 2025 at 1:33 PM
betanalpha.bsky.social
Recollection of a dream.
Reflections of skyscrapers in gently rippling water.
September 9, 2025 at 12:12 AM
betanalpha.bsky.social
Cinderella and the Three Attempted Partitions

www.symplectomorphic.com/assets/chapt...
A collection of disjoint subsets whose intersection does not cover the entire ambient space does not define a formal partition. A collection of subsets whose intersection does cover the entire ambient space but are not disjoint does not define a formal partition. A collection of disjoint subsets whose intersection does cover the entire ambient space does define a formal partition.
September 8, 2025 at 1:56 PM
betanalpha.bsky.social
Sliced to order.

www.symplectomorphic.com/assets/chapt...
A function f from the input space X to the output space Y can be used to decompose a subset x of the input space into the intersections of x with the level sets of f.
September 5, 2025 at 1:16 PM
betanalpha.bsky.social
Haha, or not.
Silk Song absolutely crushing the Nintendo eShop servers.
September 4, 2025 at 2:20 PM
betanalpha.bsky.social
Testing...
September 4, 2025 at 1:20 PM
betanalpha.bsky.social
Graphical fractions.

www.symplectomorphic.com/assets/chapt...
A figure demonstrating the probability of a subset x conditioned on a subset c defined as ratio of the probability allocated to the intersection of the two subsets divided by the probability allocated to the conditioning subset c.
September 4, 2025 at 1:17 PM
betanalpha.bsky.social
Rise, my pretties! Rise!

www.symplectomorphic.com/assets/chapt...
A two-dimensional probability density function plotted over a discrete partition of the ambient space. The restriction of the probability density function to each element of the partition. The restricted probability density functions renormalized into conditional probability density functions.
September 3, 2025 at 2:20 PM
betanalpha.bsky.social
Icy to dull the transformation and hot to relax it away.

www.symplectomorphic.com/assets/chapt...
A warped grid demonstrating the effect of a nonlinear transformation on a two-dimensional plane, with colors visualizing the magnitude of the Jacobian correction. The Jacobian correction is larger when the transformation locally shrinks areas and small when the transformation locally expands areas.
September 2, 2025 at 1:13 PM