Reverse engineering the Mersenne Twister random number generator with Linear Algebra https://www.johndcook.com/blog/2026/05/10/reverse-mersenne-twister/

Heavy-tailed probability distributions.

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Four digs into probability theory in its full conceptual glory, from additivity and sigma-algebras to uniformity and non-zealous interpretations, betanalpha.github.io/assets/chapt....

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Three discusses how sets and their structures can be combined together to form product spaces, betanalpha.github.io/assets/chapt....

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Two sets the stage for more complexity, reviewing the sets and structures that make the mathematical spaces we all love but often take for granted, betanalpha.github.io/assets/chapt....

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter One starts as simply as possible, discussing abstract measure and probability on finite sets where the math is explicit and straightforward, betanalpha.github.io/assets/chapt....

Kiss from a rose.

Friendly reminder that if you're not using a contemporary Markov chain Monte Carlo sampler, or running a contemporary sampler for more than a thousand iterations and abusing its adaptation settings, then you can't really argue that Bayesian inference is slow.

Extremely accessible humor.

Is this something?

Victoria Beckham: “This method is optimal in practice”. David Beckham: “Be honest.” Victoria Beckham: “I am being honest.” David Beckham: “Under what assumptions?” Victoria Beckham: “Asymptotics.” David Beckham: “Thank you.

<Navi voice> Hey!  Listen!  Check your modeling assumptions, Link.

(Left) You: Complaining that extrapolation is impossible or making some strong claim based on a single extrapolation. (Right) Me: Unbothered. Moisturized. Happy. In My Lane.  Bayesian.

Not quite but good try.

Check yourself before you wreck yourself.

Dropping my new line this fall. It’s better than the competition.  By construction.

Friendly reminder that if you're not using a contemporary Markov chain Monte Carlo sampler, or running a contemporary sampler for more than a thousand iterations and abusing its adaptation settings, then you can't really argue that Bayesian inference is slow.

Kiss from a rose.

The boss music transitions in MIO: Memories in Orbit are all great, but the drop into the Sol and Vin fight, www.youtube.com/watch?v=I5-F..., is exceptional.

This kind of mixed use urban planning is illegal in America

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Four digs into probability theory in its full conceptual glory, from additivity and sigma-algebras to uniformity and non-zealous interpretations, betanalpha.github.io/assets/chapt....

Black box statistical models.

this is why, following @betanalpha.bsky.social and others, I prefer the term “retrodiction” for what ML often calls prediction. in assessing explanations, the difference matters!

Old ones on #starwarsday

more old ones for #starwarsday

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Three discusses how sets and their structures can be combined together to form product spaces, betanalpha.github.io/assets/chapt....

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter Two sets the stage for more complexity, reviewing the sets and structures that make the mathematical spaces we all love but often take for granted, betanalpha.github.io/assets/chapt....

In preparation for drafting new probability theory chapters, I've been cleaning up my existing chapters. Chapter One starts as simply as possible, discussing abstract measure and probability on finite sets where the math is explicit and straightforward, betanalpha.github.io/assets/chapt....

Hustle culture.

Statistics / Machine Learning / Artificial Intelligence

Statistics / Machine Learning / Artificial Intelligence

You may have heard that the Banach-Tarski paradox is a consequence of the group of spatial rotations SO(3) having a subgroup that is free on two generators. But what does that look like? Answer: Roughly like this! kyleormsby.github.io/F2-in-SO3/ 1/n 🧮

Update from Tumblr: Lizzie was in a podcast! Click directly on the link in our Bluesky description, or copy and paste the below: https://temporalecology.tumblr.com/post/815254430103502848

Measuring time in seconds is a useful way of showing the scale of large numbers. 1e3 seconds is a bit more than a quarter hour. 1e6 seconds is a week and a half. How long is 1e9 seconds? Over three decades. 1e12 is the height of the last Ice Age. 1e15 is 54 million times longer than all of time.

"Hey Stwong Bad! The old wowld is dying, and the new wowld stwuggles to be bown! I'm pwetty sure now is the time of monsters. Yep! Time of monsters. Isn't that gweat?"

"Can you review this paper..."

"Can you review this paper..."

One of my favorite Bayesian modeling traps is that, in the standard parameterization of many families of probability density functions, the reasonable parameter configurations are often not between zero and some upper bound but rather between some lower bound and infinity.

One of my favorite Bayesian modeling traps is that, in the standard parameterization of many families of probability density functions, the reasonable parameter configurations are often not between zero and some upper bound but rather between some lower bound and infinity.

A little bit of Levy in my life A little bit of Uhlenbeck by my side A little bit of Ornstein is all I need A little bit of Weiner is what I see A little bit of Ito in the sun A little bit of Stratonovich all night long A little bit of Langevin I must fess A little bit of noise makes it a process

Hello. Over on www.patreon.com/cw/betanalpha I recently released a chapter draft on Bayesian discrete choice modeling that spans over 200 pages of math and demonstrative exercises. This one is going to be exclusive for a bit!

A little bit of Levy in my life A little bit of Uhlenbeck by my side A little bit of Ornstein is all I need A little bit of Weiner is what I see A little bit of Ito in the sun A little bit of Stratonovich all night long A little bit of Langevin I must fess A little bit of noise makes it a process

Hello. Over on www.patreon.com/cw/betanalpha I recently released a chapter draft on Bayesian discrete choice modeling that spans over 200 pages of math and demonstrative exercises. This one is going to be exclusive for a bit!

With a lower bound this weak you would think that a theoretical statistician made this olive oil.

With a lower bound this weak you would think that a theoretical statistician made this olive oil.

Friendly reminder that one cannot formally take the logarithm, or really apply any non-linear function, to a unitful quantity. What one can do, however, is take the logarithm of the _ratio_, i.e log( x [units] / 1 [units] ).