My paper “The choice of effect measure for binary outcomes: Introducing counterfactual outcome state transition parameters” has just been published in the journal Epidemiologic Methods. In this paper, we propose a new class of effect measures for causal effects. While this new effect measure is not generally identified from the data, we argue that it can be used to formalize biological knowledge relevant to effect modification and to the choice between standard, identifiable measures of effect such as the risk ratio and the risk difference.
The published version is available at https://www.degruyter.com/view/j/em.ahead-of-print/em-2016-0014/em-2016-0014.xml?format=INT (behind paywall). A preprint is available at https://arxiv.org/abs/1610.00069.
An informal discussion of COST parameters has been posted to Less Wrong, at https://www.lesswrong.com/posts/K3d93AfFE5owfpkx4/counterfactual-outcome-state-transition-parameters
I would very much appreciate any comments, especially critical ones. As always, I invoke Crocker’s Rules for all discussion of this paper.
I guess this could extend to proving with a very large example too. The point being that it would be nice, when explaining the importance of rigorous proofs to new mathematicians, to show some examples where “proof by checking up to a quintillion” doesn’t work.
To be clear I’m not looking for extremely large numbers where it was known that the number existed (or that maybe it was infinity) but numbers that were perhaps posited not to exist and were only found after much brute forcing (or some other non-rigorous method).
Given that there is a mathematical finance flair in this sub, I’m guessing at least a few people have an interest in Economics/Finance.
Background for people not familiar with the subject: I’ve always been somewhat skeptical of mainstream Economics theory in the courses I’ve taken, and my objections to the way economic academic research is conducted happens to coincide with Austrian Economics, if anyone cares to read more about that subject. But that’s not necessary for this post, as I will explain my objections as briefly as possible for the unitiated. In a lot of really complex systems, some essential properties are simply not measurable, or the data is too hard to obtain. Economics on a macro scale is an example of such a system. Mainstream Economics ignores this, and tries to come up with mathematical models which ignore the ridiculous complexity of the system being studied, and the non-quantifiability of some essential data. This leads to disastrous, completely wrong predictions in some cases, and multiple economic crashes. I’m used to absolute rigour in Mathematics, and recognize this is not possible in Economic systems, so I make no claims that the two subjects should be equal in rigour. What I do oppose, however, is the misleading being produced by flawed theories that only concern themselves with quantifiable data, and that leads to people being more confident than they should be. Assumptions may work well in the physical sciences, but I don’t think they do in social sciences. I was thinking that it might be nice to get the opinion of fellow mathematicians (used to the same level of rigour and logic) on this topic, and on the way econ research is conducted. Note: If an argument is good enough, I am willing to completely change my view on Economics, so I don’t want anyone to think I’m stuck in my ways of not trusting the subject matter and that I’m attacking the subject without willingness to change.
I’m inspired by this thread of course: https://www.reddit.com/r/math/comments/92buiu/what_are_some_obviously_false_theorems_which_are/
By converse I mean “some ‘obviously false’ theorems which are actually true in constructive mathematics, which are false in classical mathematics”
I’m aware that “constructive mathematics” has different definitions. Pick whichever applies and specify if you like.
I know that in some forms of constructive mathematics the Axiom of Choice isn’t allowed in its full form. So I guess in those systems some of the unintuitive results from AC don’t exist?
I think it’s an interesting question to compare ‘unintuitions’ in different systems. Unfortunately less people are experienced with constructive mathematics so I expect less responses. Any responses are appreciated.
1) Is “forcing” the only method for proving the consistency of a formal system?
a) If not, what other methods are there? b) Where can I learn how forcing works in a not-too-technical way?
2) Do Godel’s incompleteness theorems imply that any formal system cannot prove its own consistency? If so, then what formal system was used to prove the consistency of ZFC? (And ZF not C)
What are some cars, trucks, or SUV’s out there that you absolutely love, but would never buy? Whether it’s because of poor reliability, out-of-reach cost, how rare the vehicle is, or pure irrationality. You may love its aesthetics or performance, but because of your personal needs it just wouldn’t make any sense whatsoever.
Let’s say you’d kill to have a Mustang GT350, but you live in the mountains and have to deal with snow/off-roading/dirt roads most of the time. Or, let’s say you’d love to have an F-150 Raptor, but you live in the congested city of San Francisco or NYC. Or maybe you’re tempted to buy a Giulia Quadrifoglio, but you’re scared of its potential unreliability.
For me, it would have to be the 1993 Land Rover Defender 110 NAS, specifically modified to look like this. It’s extemely expensive (here in America), rare (again, here in America), and unreliable. But good lord is it sexy. I’ve only seen 3 or 4 Defender 110’s on the road that I can remember. It’s basically a dream car of mine. Sure, if I started making lots and lots of money, I would probably try to buy one. But it’s far out of reach as it stands right now.
Honorable mentions for me would be…
991 911 GT3 manual and a slew of older German super saloons…like an E28 M5, E34 M5, E39 M5, facelifted W211 E63 AMG sedan and wagon, and the facelifted C7 S6 with Black Optics Package (because we can’t have the RS6).
So let’s get this conversation going!