VincentYu

Karma: 2,203

VincentYu Jan 20, 2014, 3:01 PM
36 points
in reply to: jefftk’s comment on: 2013 Survey Results
What if the people who have taken IQ tests are on average smarter than the people who haven’t? My impression is that people mostly take IQ tests when they’re somewhat extreme: either low and trying to qualify for assistive services or high and trying to get “gifted” treatment. If we figure lesswrong draws mostly from the high end, then we should expect the IQ among test-takers to be higher than what we would get if we tested random people who had not previously been tested.

This sounds plausible, but from looking at the data, I don’t think this is happening in our sample. In particular, if this were the case, then we would expect the SAT scores of those who did not submit IQ data to be different from those who did submit IQ data. I ran an Anderson–Darling test on each of the following pairs of distributions:
- SAT out of 2400 for those who submitted IQ data (n = 89) vs SAT out of 2400 for those who did not submit IQ data (n = 230)
- SAT out of 1600 for those who submitted IQ data (n = 155) vs SAT out of 1600 for those who did not submit IQ data (n = 217)
The p-values came out as 0.477 and 0.436 respectively, which means that the Anderson–Darling test was unable to distinguish between the two distributions in each pair at any significance.

As I did for my last plot, I’ve once again computed for each distribution a kernel density estimate with bootstrapped confidence bands from 999 resamples. From visual inspection, I tend to agree that there is no clear difference between the distributions. The plots should be self-explanatory:

(More details about these plots are available in my previous comment.)

Edit: Updated plots. The kernel density estimates are now fixed-bandwidth using the Sheather–Jones method for bandwidth selection. The density near the right edge is bias-corrected using an ad hoc fix described by whuber on stats.SE.

VincentYu Jan 19, 2014, 9:47 PM
23 points
in reply to: jefftk’s comment on: 2013 Survey Results
Here is a kernel density estimate of the “true” distribution, with bootstrapped) pointwise 95% confidence bands from 999 resamples:

It looks plausibly bimodal, though one might want to construct a suitable hypothesis test for unimodality versus multimodality. Unfortunately, as you noted, we cannot distinguish between the hypothesis that the bimodality is due to rounding (at 500 M) versus the hypothesis that the bimodality is due to ambiguity between Europe and the EU. This holds even if a hypothesis test rejects a unimodal model, but if anyone is still interested in testing for unimodality, I suggest considering Efron and Tibshirani’s approach using the bootstrap.

Edit: Updated the plot. I switched from adaptive bandwidth to fixed bandwidth (because it seems to achieve higher efficiency), so parts of what I wrote below are no longer relevant—I’ve put these parts in square brackets.

Plot notes: [The adaptive bandwidth was achieved with Mathematica’s built-in “Adaptive” option for SmoothKernelDistribution, which is horribly documented; I think it uses the same algorithm as ‘akj’ in R’s quantreg package.] A Gaussian kernel was used with the bandwidth set according to Silverman’s rule-of-thumb [and the sensitivity (‘alpha’ in akj’s documentation) set to 0.5]. The bootstrap confidence intervals are “biased and unaccelerated” because I don’t (yet) understand how bias-corrected and accelerated bootstrap confidence intervals work. Tick marks on the x-axis represent the actual data with a slight jitter added to each point.
What links here?
- VincentYu's comment on 2013 Survey Results by Scott Alexander (Jan 20, 2014, 3:01 PM; 36 points)

VincentYu Jan 18, 2014, 3:58 AM
6 points
in reply to: gwern’s comment on: LessWrong Help Desk—free paper downloads and more (2014)
Here.

VincentYu Jan 17, 2014, 7:16 AM
2 points
in reply to: gwern’s comment on: LessWrong help desk—free paper downloads and more
Requested.

VincentYu Jan 4, 2014, 2:53 AM
2 points
in reply to: Gurkenglas’s comment on: Open thread for January 1-7, 2014
Full paper: Jones et al. (2013)

See the label for Figure 1. I’m not sure why army1987 retracted his comment, but he is correct: the y-axis is logarithmic for the survivorship curve. So the graph actually confirms your expectation and shows an exponential decrease in population.

(Unfortunately, the graph label in the National Geographic article is just wrong—there is no reasonable interpretation under which the logarithmic survivorship curve can be interpreted as a raw proportion.)

VincentYu Dec 22, 2013, 12:26 AM
8 points
on: [LINK] Meditation Can Debias The Mind
Paper that the link is reporting on: Hafenbrack, Kinias, and Barsade (2013)

Abstract:

In the research reported here, we investigated the debiasing effect of mindfulness meditation on the sunk-cost bias. We conducted four studies (one correlational and three experimental); the results suggest that increased mindfulness reduces the tendency to allow unrecoverable prior costs to influence current decisions. Study 1 served as an initial correlational demonstration of the positive relationship between trait mindfulness and resistance to the sunk-cost bias. Studies 2a and 2b were laboratory experiments examining the effect of a mindfulness-meditation induction on increased resistance to the sunk-cost bias. In Study 3, we examined the mediating mechanisms of temporal focus and negative affect, and we found that the sunk-cost bias was attenuated by drawing one’s temporal focus away from the future and past and by reducing state negative affect, both of which were accomplished through mindfulness meditation.

Unfortunately, I think they botched the decision tasks from Arkes and Blumer (1985) in studies 2a and 2b. In each study, prior to the decision task, participants in the experimental group listened to a mindfulness-meditation recording whereas those in the control group listened to a neutral recording.

In study 2a:

Participants were asked to play the role of the owner of a printing company who had recently spent $200,000 to buy a new printing press. One week later, a competitor went bankrupt and offered to sell, for $10,000, his computerized printing press, which worked 50% faster than the new $200,000 printing press at about half the production cost. Because the new $200,000 printing press was custom-made for the firm’s needs, it could not be sold to raise money to purchase the competitor’s press. However, participants were informed that they had $10,000 in savings that could be used to buy it. They were then asked to decide whether to buy the competitor’s press. A decision to buy it was taken to indicate that the participant had resisted the sunk-cost bias.

In study 2b:

[P]articipants were asked to play the role of the president of an aviation company that had committed $10 million to developing a radar-blank plane, “a plane that could not be detected by conventional radar.” After $9 million had been spent, a rival company announced the debut of their own radar-blank plane, which had better performance and lower cost. Participants were then asked to decide whether to invest the remaining $1 million in continued development of the company’s inferior plane. A decision to continue to fund the inferior plane was taken as an indication of having succumbed to the sunk-cost bias.

I was initially confused over why the authors think that these studies isolate the sunk-cost bias, as we can easily come up with alternative explanations for preferring one decision over the other (e.g., in 2a: high diminishing returns from additional printing presses and nonlinearity of the utility of savings; in 2b: whether it is worthwhile to invest the $1 million depends on future demand and supply, and withdrawing from R&D at this point may incur large losses in reputation and morale). Since there are alternative explanations, it is plausible that mindfulness-meditation may be moderating some other cognitive or emotional mechanism (independent of the sunk-cost bias) that changes the participants’ propensity to choose one decision over the other. My confusion was resolved after I consulted the reference to Arkes and Blumer. It turns out that Hafenbrack et al. had (unknowingly?) neglected to include the design in Arkes and Blumer’s studies that isolates the sunk-cost bias. In particular, Arkes and Blumer performed two versions of each experiment with the sunk cost being manipulated.

In fact, Arkes and Blumer explicitly noted this, so Hafenbrack et al. should have known (emphasis mine):

Experiments 1 and 2 [not used by Hafenbrack et al.] are relatively pure examples [of the sunk cost effect] in that other explanations of the results are not readily available. Many of the following studies [Hafenbrack et al. used two of these designs] are less pure. They involve much more complex economic decisions than are required in the first two experiments. As a result of using more complex stories, we are creating a stimulus situation in which some explanations of the data other than the sunk cost effect may exist. It is virtually impossible to rule out every alternate explanation in every such story. However, the consistent pattern of results found in all of the stories plus the demonstration of the sunk cost effect in the purer stories lead us to feel confident in our explanation of the data.

The next three experiments differ from the prior two in that pairs of scenarios are presented in each experiment. One member of each pair is as similar to the other member in as many financial aspects as possible. They differ, however, in that only one member of each pair has a sunk cost. In this way we can assess the impact of the sunk cost component of the scenario.

Hafenbrack et al. should have used a full 2x2 design manipulating the sunk cost in the decision and the presence of mindfulness-meditation induction. In addition, I think it would be more appropriate to use experiments from Arkes and Blumer that have more ecological validity for Hafenbrack et al.’s participants, who were recruited from Mechanical Turk—it is unlikely that these participants had made high-level corporate decisions in the past.

For reference, how Arkes and Blumer isolated the sunk-cost effect is also how you construct the Allais paradox—you cannot determine how the participants messed up because you don’t know their utility functions, but you can determine that they messed up if they have consistent utility functions.

(Despite my criticisms of studies 2a and 2b, I think the paper is well written and the models and bootstrap tests in study 3 are nice touches.)

VincentYu Dec 1, 2013, 11:29 PM
6 points
in reply to: RomeoStevens’s comment on: LessWrong help desk—free paper downloads and more
Here.

VincentYu Dec 1, 2013, 11:28 PM
4 points
in reply to: gwern’s comment on: LessWrong help desk—free paper downloads and more
Here.

VincentYu Nov 30, 2013, 11:03 PM
4 points
in reply to: gwern’s comment on: LessWrong help desk—free paper downloads and more
Here.

VincentYu Nov 29, 2013, 4:41 AM
2 points
in reply to: Vaniver’s comment on: The Relevance of Advanced Vocabulary to Rationality

obstropolous

So, obstreperous is an actual word, that means something very similar.

The OED has an entry on “obstropolous” adj.:

Etymology: Humorous alteration of “obstreperous” adj.

Chiefly humorous and regional. Now rare.

There’s also an entry on “obstropolos” n., which was a nonce word coined by James Joyce for Ulysses:

Etymology: Alteration of “obstropolous” adj., perhaps after ancient Greek -ος, ending of masculine singular nouns, probably also with punning reference to classical Latin ōs mouth (see “oral” adj.).

An obstreperous mouth.

VincentYu Nov 3, 2013, 5:28 PM
3 points
in reply to: hyporational’s comment on: Open Thread, November 1 − 7, 2013

Telling others what you’re doing

I read somewhere, might have been on lw, that telling what you’re doing might decrease your chance of success, because it provides a way to get compliments without actually having achieved anything yet. I suppose this depends on how you do it, though.

Gollwitzer et al. (2009). When intentions go public: Does social reality widen the intention-behavior gap?

Abstract (emphasis mine):

Based on Lewinian goal theory in general and self-completion theory in particular, four experiments examined the implications of other people taking notice of one’s identity-related behavioral intentions (e.g., the intention to read law periodicals regularly to reach the identity goal of becoming a lawyer). Identity-related behavioral intentions that had been noticed by other people were translated into action less intensively than those that had been ignored (Studies 1–3). This effect was evident in the field (persistent striving over 1 week’s time; Study 1) and in the laboratory (jumping on opportunities to act; Studies 2 and 3), and it held among participants with strong but not weak commitment to the identity goal (Study 3). Study 4 showed, in addition, that when other people take notice of an individual’s identity-related behavioral intention, this gives the individual a premature sense of possessing the aspired-to identity.

Paper link posted to LW dicussion in 2012 by Barry_Cotter.

VincentYu Oct 29, 2013, 7:24 PM
0 points
in reply to: Paul Crowley’s comment on: Open Thread, October 27 − 31, 2013
I see a Kindle edition on Amazon.

VincentYu Oct 29, 2013, 3:58 AM
6 points
on: Open Thread, October 27 − 31, 2013
Please add the open_thread tag (with the underscore) to the post.

VincentYu Oct 29, 2013, 2:23 AM
6 points
in reply to: JoshuaZ’s comment on: Open Thread, October 27 − 31, 2013
Smith et al. (2013). Dendritic spikes enhance stimulus selectivity in cortical neurons in vivo.

Abstract (emphasis mine):

Neuronal dendrites are electrically excitable: they can generate regenerative events such as dendritic spikes in response to sufficiently strong synaptic input. Although such events have been observed in many neuronal types, it is not well understood how active dendrites contribute to the tuning of neuronal output in vivo. Here we show that dendritic spikes increase the selectivity of neuronal responses to the orientation of a visual stimulus (orientation tuning). We performed direct patch-clamp recordings from the dendrites of pyramidal neurons in the primary visual cortex of lightly anaesthetized and awake mice, during sensory processing. Visual stimulation triggered regenerative local dendritic spikes that were distinct from back-propagating action potentials. These events were orientation tuned and were suppressed by either hyperpolarization of membrane potential or intracellular blockade of NMDA (N-methyl-D-aspartate) receptors. Both of these manipulations also decreased the selectivity of subthreshold orientation tuning measured at the soma, thus linking dendritic regenerative events to somatic orientation tuning. Together, our results suggest that dendritic spikes that are triggered by visual input contribute to a fundamental cortical computation: enhancing orientation selectivity in the visual cortex. Thus, dendritic excitability is an essential component of behaviourally relevant computations in neurons.

VincentYu Oct 16, 2013, 2:50 AM
0 points
in reply to: aspera’s comment on: On the importance of taking limits: Infinite Spheres of Utility

One of the simplest and most intuitive is aggregative utilitarianism, in which we define a utility for each person, add them all together, and make the choice with the larger total utility.

I suggest using the phrase “additive utilitarianism” rather than “aggregative utilitarianism”. It was entirely my fault for saying aggregative utilitarianism in my comment, which was a misnomer; I got it mixed up with aggregative consequentialism. (All flavors of utilitarianism are by definition aggregative because they take into account the utilities from some collection of beings, but not all flavors are additive.)

Note: VincentYu has pointed out in the comments below that VNM utility may be able to deal with the infinites in this problem without taking limits.

Unfortunately, I think that ascribes too much power to VNM utility functions (that term itself is a LessWrongism; elsewhere, they would be called cardinal utility functions or just utility functions). If we had our hands on a VNM utility function, we would be okay (we simply ask it which option it prefers!), but the VNM theorem simply asserts the existence of a utility function given certain basic axioms, and it doesn’t give us the utility function! So, unfortunately, VNM utility also falls flat on its face unless we already know what we prefer. (An important point is that VNM utility functions cannot work with the “utility” described in the problem. It’s an unfortunate historical accident that the word “utility” is overloaded, because VNM utility requires careful handling.)

If we fail to specify the exact type of decision theory we’re using, it is entirely unclear whether taking infinite limits would lead to a self-consistent solution.

If we want to make a decision based on [additive] utility, the infinite problem is ill posed; it has no unique solution unless we take on additional assumptions.

Great, I think these are good clarifications!

VincentYu Oct 13, 2013, 9:46 PM
2 points
in reply to: aspera’s comment on: On the importance of taking limits: Infinite Spheres of Utility
Tell me if this is right:

It is possible mathematically to represent a countably infinite number of immortal people, as well as the process of moving them between spheres. Further, we should not expect a priori that a problem involving such infinities would have a solution equivalent to those solutions reached by taking infinite limits of an analogous finite problem.

That’s an accurate interpretation of my comment.

Some confusion arises when we introduce the concept of “utility” to determine which of the two choices is better, since utility only serves as a basis on which to make decision for finite problems.

I do think that confusion arises in this context from the concept of “utility”, but not because “utility only serves as a basis on which to make decision for finite problems.” The “utility” in the problem is clearly not that of VNM-utility (of which I previously gave a brief explanation) because we not assigning utility to actions, decisions, or choices (a VNM-utility function U would generally have no problem responding to an infinite set of choices, as it simply says: do argmax_{choice}(U(choice))). This severely undermines what we can do with the “utility” in the problem because we are left with the various flavors of aggregative utilitarianism, which suffer from intractable problems even in finite situations! Attempting to extend them to the situation at hand is problematic (and, as Kaj_Sotala remarked, dealing with infinities in aggregative consequentialism is the topic of one of Bostrom’s papers).
1. Do you view the paradox as therefore unresolvable as stated, or would you claim that a different resolution is correct?
I think that the appearance of the paradox is a consequence of unfamiliarity with infinite sets, and that it is not too surprising that our intuition appears to contradict itself in this context (by presenting each option as better than the other). The contradictory intuitions don’t correspond to a logical contradiction, so the apparent paradox needs no resolution. The actual problem (choosing between the two options) is a matter of preference, just as the choice between strawberry and chocolate is a matter of preference.

2. If I carefully restricted my claim about ill-posedness to the question of which choice is better from a utilitarian sense, would you agree with it?

Absolutely. I think aggregative utilitarianism (as a moral theory) is screwed even in finite scenarios, much less infinite scenarios. (But I also think aggregative utilitarianism is a good but ill-defined general standard for comparing consequences in real life.)

VincentYu Oct 13, 2013, 6:27 PM
4 points
in reply to: protest_boy’s comment on: LessWrong help desk—free paper downloads and more
Here.

VincentYu Oct 13, 2013, 6:26 PM
3 points
in reply to: gwern’s comment on: LessWrong help desk—free paper downloads and more
Here.

VincentYu Oct 13, 2013, 4:54 PM
11 points
on: On the importance of taking limits: Infinite Spheres of Utility

The answer [edited Oct 13, 2013]

As several commenters have pointed out, the original problem does not supply a method for taking limits. Our analysis shows that the problem is ill posed: it has no unique solution unless we take on additional assumptions.

I disagree that the mathematics of original problem is ill-posed, and I think DanielLC made the same point. The point of contention seems to center on the use of infinities in the original problem, which is indeed an issue if they were manipulated as real numbers, but they were not. It is perfectly acceptable and mathematical to have a countably infinite set of objects, and to define a sequence of subsets corresponding to the time evolution of that set. Infinite sets are not defined as the limit of some sequence of finite sets! There is no ambiguity in the mathematics of original problem.*

Because the use of infinity in the original problem is not in the sense of a limit, there is no good reason to think that we should take limits, or that the limits of the solutions to the finite problems should correspond in any way to the solutions of the original problem.

Where there are ambiguities are in the use of the word “utility” and similar concepts as though they were well-defined in this context. And in this sense, I agree that the original problem is ill-posed.

* There are mathematical ambiguities in an unfavorable reading of the original problem, but the following steelman removes them: Biject the people with the natural numbers, and then transfer the nth person on day n.

VincentYu Oct 13, 2013, 12:59 AM
1 point
in reply to: aspera’s comment on: On the importance of taking limits: Infinite Spheres of Utility
Another small typo: Under “The Finite Problem”, n_{A,s} and n_{B,s} should be n_{A,t} and n_{B,t} instead.