Open thread, September 25 - October 1, 2017

Yep. This could be because Nick Bostrom's original simulation argument focuses on ancestor simulations, which pretty much implies that the simulating and simulated worlds are similar. However here, in question 11, Bostrom explains why he focused on ancestor simulations and states that the argument could be generalized to include simulations of worlds that are very different from the simulating world.

On the face of it, the goal of campaigning is to win elections by changing people's minds.

That doesn't look obvious to me unless we're talking not about the face but the facade. Campaigning is mostly about telling people what they want to hear, certainly not about informing them they will need to rearrange their prejudices [1].

From the elections point of view there are three groups of people you're concerned with:

• Your own Rabid Base. You want to energise them, provide incentives for them to be loud, active, confident, with contagious enthusiasm.

• Other parties' Rabid Bases. Flip the sign: you want to demoralise them, make them doubtful, weak, passive. You want them to sit inside and mope.

• The Undecideds, aka the Great Middle through which you have to muddle. This is where most of the action is. Do you want to convince them with carefully arranged chains of logical policy arguments? Hell, no. They don't vote on this basis. They vote on the basis of (1) Who promises more; (2) Who seems to be less likely to screw the pooch; and (3) Who exhudes more charisma/leadership -- not necessarily in this order, of course. Most of this is System 1 stuff, aka the gut feeling.

Notice how pretty much none of the above involves changing people's minds.

[1] "A great many people think they are thinking when they are merely rearranging their prejudices" -- William James

i do statistical consulting as part of my day job responsibilities, i'm afraid to say this is not how it works.

if you came to me with this question i would roll back to ask what exactly you are trying to achieve with the analyses, before getting into the additional constraints you want to include. unfortunately it's far more challenging if the data owner comes to the statistician after the data are collected rather than before (when principles of experimental design as ilya mentioned can be considered to achieve ability to successfully answer those questions using statistical methods).

that said, temporarily ignoring the additional constraints you mentioned (e.g. whether and how to transform data; exponential decay and what that actually means with respect to student evaluation scores; magic word "bayes") perhaps a useful search term would be "item response theory".

good luck

Don't know. Ask a statistician who knows about design.

Well, to calculate P(T|S) = p you need a model of how a student 'works', in such a way that the test's result T happens for the kind of students S with probability p. Or you can calculate P(S|T), thereby having a model of how a test 'works' by producing the kind of student S with probability p.
If you have only one of those, these are the only things you can calculate.

If on the other hand you have one or more complementary models (complemenetary here means that they exclude each other and form a complete set), then you can calculate the probabilities P(T1|S1), P(T1|S2), P(T2|S1) and P(T2|S2). With these numbers, via Bayes, you have both P(T|S) and P(S|T), so it's up to you to decide if you're analyzing stundents or tests.
Usually one is more natural than the other, but it's up to you, since they're models anyway.