Will Lowe

@conjugateprior.org

3.4K followers 750 following 10K posts

Señor Research Scientist, NPC at the Hertie School in Berlin 🇩🇪 via Princeton, Mannheim, Edinburgh and a bunch of other ivory towers that will probably be billiard balls and decorative boxes by the end of the decade.

Rome Statute appreciator. .. more

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Will Lowe @conjugateprior.org · Apr 15

For Monty Hall problem aficionados: a #causal DAG, with explanation in the alt text.

Who knew that the M in M-bias stood for Monty?

A DAG for the Monty Hall problem.

G, the door Monty opens, is a function of your first door choice D_F and of where the car is C.

Conditioning on G, which happens because it determines your door choices when you have the opportunity to switch, induces collider bias between C and D_F, such that they are now less likely to be equal. (Why? because G cannot be C and G cannot be D_F. These are in the same 'direction' so, conditional on G, D_F is less likely to be C.)

You decide to switch conditional on G, which you just observed, and D_F, because that defines what you can switch to.

Conditional on G you now know D_F is less likely to be equal to C. So you switch.

Note: In the original problem, W is a deterministic function of C and D_S so it's slightly cheeky to put it in a DAG, but I'm going to do so anyway. The argument doesn't require it, but if you want to think informally about opening paths to W from D_F via C, it's helpful.

That makes this problem a variation on M-bias (or a clipped wing butterfly bias, if you prefer insects to goats).

Will Lowe @conjugateprior.org · 1d

There's related logic on the other side of things, in that if you had a suitably friendly statistic s and were interested in being able to rule out a particular value, say \theta=2, then, in a similar logic, P(s(Y) | \theta=2) is a distribution you might be interested in tail areas of.

Will Lowe @conjugateprior.org · 1d

Maybe "prior as unconditional distribution [of the observations]"? That is, if you have prior on parameters theta, then (roughly) \int P(Y | theta) P(theta) d theta is what the distribution of what this prior expects you would observe - the 'prior predictive distribution', in the jargon.

Will Lowe @conjugateprior.org · 1d

"Reform introduces new 'bang to rights' policy"

Will Lowe @conjugateprior.org · 1d

Great news: Gläßel & Scharpf's Making a Career in Dictatorship is *finally* out

It's great stuff & one of my favourite sources of collider bias examples. However, these are modest & retiring guys so under no circumstances should you chase them down at conferences & loudly insist they sign your copy

Adam Scharpf @ascharpf.bsky.social · 1d

Here is what the book is about in a nutshell.
👇

Will Lowe @conjugateprior.org · 1d

Huh. I've not seen quotations marks used this way. Also, while math bio is ordinary enough to have an NSF program I can imagine the math of biology could seem odd (I live in a weird info environment, so 🤷🏻)

By sophistry I guess you mean the caption's doctored. Where might I read more about this?

Will Lowe @conjugateprior.org · 1d

imo the weird thing about the HS great books version is that although they do leave a lot out, what's there has so much internal variation that will jump out under even light intellectual prodding that it's hard to miss the basic implausibility of an actual monolith under all the unitary rhetoric.

Will Lowe @conjugateprior.org · 1d

Characteristically, for the inventors of foi gras, they hold his nose closed with the padded pliers, turn this device on its side and open the tap at the top for the required amount every centijour*.

*because Lagrange, obvs.

Will Lowe @conjugateprior.org · 1d

You have to be kidding. Where do I sign?

Richard Pettigrew @wiglet1981.bsky.social · 1d

I sometimes worry our advertising material isn’t as welcoming as it might be

An information poster about studying philosophy at university of Bristol with an image of a skeleton skewering a peasant as illustration

Will Lowe @conjugateprior.org · 1d

'Among these were Edge darlings Martin Nowak, a “mathematical biologist”, and evolutionary biologist Robert Trivers'

I don't really get why evolutionary biologists are real but mathematical biologists get scare quotes.

And, apropos Dennett, this correction/adjustment/fudge is interesting:

Reposted by Will Lowe

Adam Scharpf @ascharpf.bsky.social · 1d

Here is what the book is about in a nutshell.
👇

Reposted by Will Lowe

Richard Pettigrew @wiglet1981.bsky.social · 1d

I sometimes worry our advertising material isn’t as welcoming as it might be

Will Lowe @conjugateprior.org · 1d

in this moral economy?

Reposted by Cyrus Samii