Consulting and Training

If you are interested in consulting or training engagements or even commissioning me to create a presentation on a topic of interest then don’t hesitate to reach out to me at inquiries@symplectomorphic.com.

Recent Writing

Are you interested in any of the following,

 - novelty dice

 - simplex geometry

 - practical Bayesian decision theory

 - table top role playing games

 - hierarchical modeling on multi-dimensional and constrained spaces?

If so then do I have a shiny new case study for you.

In my latest piece I use Bayesian inference to address just how fair my promotional dice are.

HTML: https://betanalpha.github.io/assets/chapters_html/die_fairness.html

PDF: https://betanalpha.github.io/assets/chapters_pdf/die_fairness.pdf

Along the way I struggle with what exactly "fair" means in practice and dive into the rich geometry of simplices in order to measures distances and model heterogeneity. If anything this case study demonstrates why statistics rarely offers simple answers for questions we might expect to be simple…

Upcoming Office Hours Livestream

On Wednesday, September 11 at 1:30 PM EDT I’ll be hosting Back to School Office Hours were I'll take questions on any statistics topic including, but not limited to, visualization; model building, critique, and implementation, and statistical computation.

Drop questions now and watch live at https://www.patreon.com/posts/back-to-school-9-110594928.

Support Me on Patreon

If you would like to support my writing then consider becoming a patron, https://www.patreon.com/betanalpha. Right now all supporters have access to exclusive posts on topics like upcoming figure previews and translating causal inference notation into probabilistic modeling notation, and covector+ supporters have early access to my next case study as well as a three hour review video.

Probabilistic Modeling Discord

I’ve recently started a Discord server dedicated to discussion about (narratively) generatively modeling of all kinds, https://discord.gg/CC9ZfmAk.

Recent Rants

On Conditional Probability Theory

Formally probability distributions are conditioned on (measurable) subsets,

 pi( A ) -> pi( A | B ).

Most of the time these subsets are defined by the level sets of a function,

 pi( A ) -> pi( A | f^{-1}(y) ).

Level sets, however, are often confused with the output value that defines them

 f^{-1}(y) <-> y.

This is where we get common, albeit misleading when the function f is implicit, notations like

 pi( A ) -> pi( A | y ).

If you want to dive into conditional probability theory in more depth then check out my recent chapter on the topic, https://betanalpha.github.io/assets/chapters_html/conditional_probability_theory.html.

On Isomorphisms And The Tension Between Pure And Applied Math

In math isomorphisms allow us to identify different kinds of objects: because each instance of one kind of object is paired with a unique instance of the another kind of object we can always derive one from the other. 

This allows us to, for example, translate operations particular to one kind of object to operations that we can apply to the other kind of object. For example an operation on the second kind of objects induces an operation on the first kind of objects by.

  1. Taking an initial instance of the first kind of object.

  2. Identifying its paired second kind of object.

  3. Applying the operation to give a new second kind of object. 

  4. Identifying the new first kind of object that pairs with the new second kind of object.

To be clear this is all incredibly powerful, not only in pure theory but also in applied practice. On the other hand it is also a bit of a double edged sword when it comes to interpretability and comprehension. In particular problems arise when mathematicians go too far <cough category theory cough> and treat the different kinds of objects as equivalent, completely disregarding the contextual interpretations that are actually really important in applications.

Once an isomorphism has been identified the different kinds of objects are then often used interchangeably, confusing the objects and making it really difficult to translate the results back to the context of explicit applications.   

This is especially true when the isomorphisms are not universal but rather conditional on other, often obscured, assumptions.  

For example this is one reason why applied probability theory is such a mess, with probability distributions, probability density functions, and even certain interpretations of "random variable" all used interchangeably. Yes they can be mathematically equivalent in some circumstances, but those circumstances are not universal in applications. Without understanding how those objects are distinct from each other we cannot identify violations of the circumstances, let alone the consequences.