Michael Boo-tancourt
@betanalpha.bsky.social
2.7K followers 160 following 1.6K posts
Zealous modeler. Annoying statistician. Reluctant geometer. Support my writing at http://patreon.com/betanalpha. He/him.
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betanalpha.bsky.social
Are you excited about the elegant philosophy of Bayesian inference, but struggling to see how it can be applied beyond the idealized examples in introductory texts and tutorials? Over the past few months I’ve released a series of demonstrative analysis that might help. 👇
betanalpha.bsky.social
While I was walking back from some errand, one of my earbuds slipped out and fell to the ground. I panicked that it had broken but then I couldn't find it. Turns out if fell right into the narrow, soft pocket formed by the mask slipped over my wrist.

I will celebrate this as a small favor of fate.
Reposted by Michael Boo-tancourt
betanalpha.bsky.social
The probability allocated to a subset is always equal to the expectation value of the indicator function of that subset. Indeed this relationship is how general expectation values are derived from probability allocations. For much more see Section 2 of betanalpha.github.io/assets/chapt....
Measured-Informed Integration and Expectation
betanalpha.github.io
betanalpha.bsky.social
In practice quantiles are estimated from samples by iteratively checking differences in interval probabilities, or equivalently differences in corresponding indicator function expectation values. Consequently in practice all we ever do is compute (or more accurately estimate) expectation values.
betanalpha.bsky.social
If by "uncertainty interval" you mean a quantile interval, however, then things become a bit more complicated. Quantiles are defined as _inverse_ interval probabilities, or equivalently inverses of the corresponding indicator function expectation values.
betanalpha.bsky.social
The probability allocated to a subset is always equal to the expectation value of the indicator function of that subset. Indeed this relationship is how general expectation values are derived from probability allocations. For much more see Section 2 of betanalpha.github.io/assets/chapt....
Measured-Informed Integration and Expectation
betanalpha.github.io
Reposted by Michael Boo-tancourt
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.
Reposted by Michael Boo-tancourt
betanalpha.bsky.social
I wrote about my logo and my recent experiment with some topologically-accurate swag over on patreon dot com, www.patreon.com/posts/logo-h....
betanalpha.bsky.social
I wrote about my logo and my recent experiment with some topologically-accurate swag over on patreon dot com, www.patreon.com/posts/logo-h....
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.
Reposted by Michael Boo-tancourt
betanalpha.bsky.social
“Black box modeling assumptions.”
impavid.us
In honor of spooky month, share a 4 word horror story that only someone in your profession would understand

I'll go first: Six page commercial lease.
betanalpha.bsky.social
Zeroeth-order jet, first-order jet, and second-order jet is alphabetical if you just reverse cycle the alphabet by one character…
betanalpha.bsky.social
Agreed! If you're don't find derivatives useful then you're just differentiating the wrong thing. :-p
betanalpha.bsky.social
An explicit target functional, of course, would make this all much less confusing, which nicely builds off of your initial joint modeling comment!
betanalpha.bsky.social
I think the missing gap is that people are implicitly smoothing/mean-fielding the simulation output, but because it's implicit it's not obvious that the same should be applied to derivatives.
betanalpha.bsky.social
The push back I had from my limited conversations with people doing weather/climate forecasting in particular is that the systems tend to be so chaotic that point derivatives aren't that meaningful.
Reposted by Michael Boo-tancourt
konsta.happonen.eu
Relatedly, ages ago @betanalpha.bsky.social wrote "Remember that using Bayes' Theorem doesn't make you a Bayesian. Quantifying uncertainty with probability makes you a Bayesian". I still think about this regularly.
Reposted by Michael Boo-tancourt
banalplay.bsky.social
When your custom character appears in a cut scene
The Portland frog backing down an army of jackboots
Reposted by Michael Boo-tancourt
betanalpha.bsky.social
Friendly reminder that on Dec 10 I will be offering my Bayesian regression modeling course at a steep discount in an effort to raise funds for World Central Kitchen and United Farm Workers. Details about the course and registration process can be found on my website, betanalpha.github.io/courses/.
Courses
betanalpha.github.io
betanalpha.bsky.social
Friendly reminder that on Dec 10 I will be offering my Bayesian regression modeling course at a steep discount in an effort to raise funds for World Central Kitchen and United Farm Workers. Details about the course and registration process can be found on my website, betanalpha.github.io/courses/.
Courses
betanalpha.github.io
betanalpha.bsky.social
Good news! There’s nothing predictive about them. Functions like that implement _retrodictive_ comparisons, making them PR checks which is slightly less embarrassing to say.

<steps off soapbox>