Allen Downey

Thank you for asking. I find this stuff super interesting. I write about it on my blog

https://ravinkumar.com/

and here's a video for the most common question I get about bayes vs frequentist

https://www.youtube.com/watch?v=foSPfzYs4yY

For recommendations here's my suggestions split by persona

* I want a PHD in statistics or to write novel research - Go read BDA3 cover to cover. Gelman etal are amazing, and amazingly brilliant. The book is dense though, even after years of experience I need to now read chapters 2 or 3 times and write out proofs

* I want have a smooth on ramp into Bayesian stats with lots of code and beautiful writing. I also like video lectures and undergraduate college courses - Statistical Rethinking. As noted below Richard does a wonderful job explaining these concepts with metaphors like golems, interspersing it with this experience as an anthropologist, and using his teaching experience to write well structured introduction into Bayesian stats. This book does assume you understand basic statistics and probability theory.

* I want a great comparison of Bayesian vs Frequentist stats- This book covers both topics well, compares them fairly, and has all the proofs to back things up https://www.routledge.com/Understanding-Advanced-Statistical-Methods/Westfall-Henning/p/book/9781466512108

* I'm a programmer type person that likes hands on "build from scratch" using code - Allen Downey's think bayes builds up bayes theorem from Numpy arrays. He's also…

So I've read this article a couple of times and I still don't quite understand it. Can anyone summarize the key argument for a layperson?

Here's my best interpretation thus far:

This particular post is a continuation of his two earlier posts[1], [2] which seems to critique the way statistical significance is simplistically calculated from a gaussian distribution when effect size is small. This leads to an argument that the statistics community is too dependant on generative models for their interpretation, given that these models are typically to simplistic outside of hard sciences:

> "But in biology, medicine, social science, and economics, our models are much less accurate and less grounded in natural laws. Most of the time, models are selected because they are convenient, not because they are plausible, well motivated from phenomenological principles, or even empirically validated. Freedman built a cottage industry around pointing out how poorly motivated many of the common statistical models are."

This part I am a little unclear on, but it seems like this leads him to suggest focusing on the random sampling as a way to get counts that you can then plug into various statistical formulas, without the need to assume a probabalistic model:

> "So what is the remedy here? The thing is, we already know the answer: if we randomized the assignment, we can estimate log odds by counting the number of positive outcomes under treatment and control, and then just plugging these…

There are six (maybe more, but I have six so far) factors in low nuptiality (marriage rates)[1] and consequently sub-replacement fertility, under the headings of religion, medicine, technology, geography, sociology, and ethics.

1. Secularism. Secular populations are less fertile than highly religious populations.

2. Infant survival (low infant mortality).

3. Mechanisation particularly of agriculture.

4. Urbanisation.

5. Credentialism, the social requirement for people to spend an increasing fraction of their fertile years in pre-employment education. Simple literacy is also pretty important in causing early fertility decline in developing countries.

6. Universalism together with a tolerance for inequality. Universalism is applying the same rules to everyone, so women can enter the workforce and make their own life decisions just as men do. Tolerance for inequality I hope I don't have to explain. (I am split whether this is one factor or two.)

There is some interlinkage in these, they are not all totally orthogonal, but they are all fairly distinct dimensions of the problem.

Japan (and South Korea, and China) max out on credentialism and tolerance for inequality but also score highly in all of the others.

Finally this is a great example of one of Iain Banks's "Outside Context Problems".

More than a black swan, it's a problem that governments are simply not equipped to understand or in some cases even see, so they can't do anything to solve it.

1.…

Back in the days of slatestarcodex, the comment policy [1] was you can comment if your post is at least two of these three things: true, necessary, or kind.

This post is all three: what they're describing is true (these dynamics in meetings do exist, very often), it is kind (in the sense they're giving you a skill to help both yourself and others), and I'll give it necessary in the sense it's used in the original definition (if you want to get ahead in an organization with a nontrivial amount of internal politics - which is most places - you need to have at least some of this skill).

And yet, something about this post gives me "weird vibes".

Basically, with a bit of sarcasm you could sum it up as "DON'T BE AUTISTIC", and if you are then at least get therapy until you can act normal.

When the author says "We [humans] are wired to spidey sense this [vibes] stuff", it turns out some humans are above and some below the mean in this skill distribution. [2]

And sometimes, in a meeting to decide about how you're going to set up your database sharding, it helps the business' bottom line if you pay more attention to the database specialist than the soft-eye-contact specialist.

(Don't you want to hire people who are good at both? Yes, but unless you're really, really lucky, you're going to hit Berkson's paradox [3]. And then if you want your databases to run smoothly, you're going to have to compromise.)

[1]…

Downey published a (big-endian, SPARC) method in 2007:

https://allendowney.com/research/rand/

And Lemire in 2017 asked the question

https://lemire.me/blog/2017/02/28/how-many-floating-point-numbers-are-in-the-interval-01/

The basic approach: collect top 60 bits of a 64-bit PRNG. (Assume the LSBs are corrupt or zero or nonrandom). Set exponent zero. If the top mantissa bit is zero, shift left, subtract one from exponent. Repeat. When you run out of bits, collect another PRNG from your generator and resume until you have 56 bits of mantissa. When done, your floating-point PRNG is 2^exponent * mantissa.

My short explanation: Suppose you want a random distance. Multiplying a PR integer is the same as selecting a random tile in the distance, and measuring the distance to the (far) edge of the tile. This is the multiply method.

But if you want a real-valued distance even for very near distances, you need to scale your random number and ensure you have random bits throughout the mantissa. So reduce the exponent for every leading zero in your PR integer and shift. Add more bits if needed.

Test: the histogram of exponents for a large-enough set of samples is linear, give or take. Very small floating numbers (less than say 1/32768) are 1/16 as likely as numbers in [0.5,1).

I saw Allen Downey speak about this concept a year ago in a small forum at the University of Richmond. Several professors in the audience challenged his thinking. I approached one after that and asked what he thought and the answer was basically that Dr. Downey's approach is spot on. This coming from a CS professor.

I have just started reading his Think Stats book http://www.allendowney.com/wp/books/ which is starting to help me better understand statistics. Not far enough into the book yet to make a complete judgement however.

Got to say I like seeing different perspectives on traditional subjects. My youngest is going to Olin next year in Mechanical Engineering and seeing these sorts of articles keeps me excited about her unconventional engineering education at Olin.