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Ongoing set of comments from reading through this.

section "Our Strategy" 4th paragraph:

In this introduction we will not ignore the abstractions of probability theory. As with more formal treatments we will instead being by discussion the abstract theory

"we will instead being" should be: "we will instead begin by"
"by discussion the abstract" should be either: "by discussing the abstract" or "by discussion of"

final sentence in same paragraph:

As we develop representations we’ll discuss more and more specific examples to develop as much intuitive context as can

"as can" should be: "as we can" or "as possible"

We could simultaneously add more structure to the longer sections and emphasize key points by adding some additional headers (maybe sub-sub-sections without numbers, possibly styled differently than other section styles).

For example, the way the Conditional Probability Distributions section is written it could be naturally divided into

• Definition
• Joint distributions implied by expectations
• Marginalization collapses joint distribution onto component spaces
• Generative modeling is building joint distribution from conditionals

or something along those lines.

Some questions and comments not addressed in any of the PRs:

• In Stochastic Representations of Probability Distributions (3.4)
  Is the equation for recovering expectations (lim_{N \to \infty} ...) missing a summation?

• In Concentration of Measure (4.1)
  From the context I don't think it's immediately clear to the reader exactly what "these two contributions" is referring to in the sentence beginning with

  Consequently the integrand, which is the product of these two contributions, concentrates in a singular...

• In Big Worlds and Small Worlds (7.2), I'm not sure how to fix the sentence below. Do you mean to say that it only has some probability of containing the latent DGP?

  Because any small world is likely to be only a shallow approximation of reality, for example, it is probability to contain the latent data generating process (Figure 15b).

I think it would be easier on the eyes if the size (or font or some other distinguishing attribute) of the text in the figure captions were different from the main text.