Author: Andi

Individual differences (continued)

“I am surprised that the author has used this data set. In my lab, when we collect data with such large individual differences, we refer to the data as ‘junk’. We then redesign our stimuli and/or experimental procedures, and run a new experiment. The junk data never appear in publications”

—An anonymous reviewer in 2005, commenting on research that sought to model individual differences in cognition.

From the intro to Navarro, D. J.; Griffiths, T. L.; Steyvers, M. & Lee, M. D. Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology, 2006, 50, 101-122

Death and furniture

Found this paper by Edwards, Ashmore, and Potter (1995) amusing as recently I tapped a table to make a point about different levels of analysis. From the intro:

“When relativists talk about the social construction of reality, truth, cognition, scientific knowledge, technical capacity, social structure, and so on, their realist opponents sooner or later start hitting the furniture, invoking the Holocaust, talking about rocks, guns, killings, human misery, tables and chairs. The force of these objections is to introduce a bottom line, a bedrock of reality that places limits on what may be treated as epistemologically constructed or deconstructible. There are two related kinds of moves: Furniture (tables, rocks, stones, etc. — the reality that cannot be denied), and Death (misery, genocide, poverty, power — the reality that should not be denied). Our aim is to show how these “but surely not this” gestures and arguments work, how they trade off each other, and how unconvincing they are, on examination, as refutations of relativism.”

And the point about levels is made:

“It is surprisingly easy and even reasonable to question the table’s given reality. It does not take long, in looking closer, at wood grain and molecule, before you are no longer looking at a “table”. Indeed, physicists might wish to point out that, at a certain level of analysis, there is nothing at all “solid” there, down at the (most basic?) levels of particles, strings and the contested organization of sub-atomic space. Its solidity is then, ineluctably, a perceptual category, a matter of what tables seem to be like to us, in the scale of human perception and bodily action. Reality takes on an intrinsically human dimension, and the most that can be claimed for it is an ‘experiential realism'”

Reference

Edwards, D., Ashmore, M., & Potter, J. (1995). Death and furniture: The rhetoric, politics and theology of bottom line arguments against relativism, History of the Human Sciences, 8, 25-49.

Maximum likelihood

From an old post to the R mailing list by Peter Dalgaard:

“the possibility of finding maximum likelihood estimates by writing up the likelihood and maximizing it is often overlooked…”

R really is magical sometimes. Suppose you want to fit a distribution, M. All you need is to maximise \(\prod_{i=1}^N P(x_i | M)\), or equivalently, \(\sum_{i=1}^N \log P(x_i | M)\). Here’s an example of fitting a Gaussian, starting by breaking a fairly good first guess…

> x = rnorm(1000, 100, 15)
> f = function(p) -2*sum(dnorm(x, p[1], p[2], log=T))
> optim(c(mean(x)-50, sd(x)+15), f)
$par
[1] 100 15

$value
[1] 8193

$counts
function gradient
69 NA

$convergence
[1] 0

$message
NULL

(Well actually -2 times the log-likelihood.) Now to have a look at your estimate:

hist(x, probability=T)
curve(dnorm(x,100,15), min(x), max(x), add=T)

Psychological assessment at NSA

The Memory Hole managed to obtain all non-classified forms used at the NSA (claims NSA). Two nice finds:

If you got here via Google because you’re applying to work for NSA, probably best not to email me about the assessment, eh? (Yes, some people have.)

Robin Cook’s resignation speech (17 Mar 2003)

(Full text over here.)

… It is not France alone that wants more time for inspections. Germany wants more time for inspections; Russia wants more time for inspections; … The reality is that Britain is being asked to embark on a war without agreement in any of the international bodies of which we are a leading partner—not NATO, not the European Union and, now, not the Security Council.

…

The threshold for war should always be high. None of us can predict the death toll of civilians from the forthcoming bombardment of Iraq, but the US warning of a bombing campaign that will “shock and awe” makes it likely that casualties will be numbered at least in the thousands…

Iraq probably has no weapons of mass destruction in the commonly understood sense of the term—namely a credible device capable of being delivered against a strategic city target. It probably still has biological toxins and battlefield chemical munitions, but it has had them since the 1980s when US companies sold Saddam anthrax agents and the then British Government approved chemical and munitions factories. Why is it now so urgent that we should take military action to disarm a military capacity that has been there for 20 years, and which we helped to create? …

… I have heard it said that Iraq has had not months but 12 years in which to complete disarmament, and that our patience is exhausted. Yet it is more than 30 years since resolution 242 called on Israel to withdraw from the occupied territories. We do not express the same impatience with the persistent refusal of Israel to comply.

… Nor is our credibility helped by the appearance that our partners in Washington are less interested in disarmament than they are in regime change in Iraq. That explains why any evidence that inspections may be showing progress is greeted in Washington not with satisfaction but with consternation: it reduces the case for war.

… On Iraq, I believe that the prevailing mood of the British people is sound. They do not doubt that Saddam is a brutal dictator, but they are not persuaded that he is a clear and present danger to Britain. They want inspections to be given a chance, and they suspect that they are being pushed too quickly into conflict by a US Administration with an agenda of its own. Above all, they are uneasy at Britain going out on a limb on a military adventure without a broader international coalition and against the hostility of many of our traditional allies.

… It has been a favourite theme of commentators that this House no longer occupies a central role in British politics. Nothing could better demonstrate that they are wrong than for this House to stop the commitment of troops in a war that has neither international agreement nor domestic support…

Box Of Rain, by the Grateful Dead

Look out of any window
Any morning, any evening, any day
Maybe the sun is shining
Birds are winging, no rain is falling from a heavy sky
What do you want me to do
To do for you to see you through?
For this is all a dream we dreamed one afternoon long ago

Walk out of any doorway
Feel your way like the day before
Maybe you’ll find direction
Around some corner where it’s been waiting to meet you
What do you want me to do
To watch for you while you’re sleeping?
Then please don’t be surprised when you find me dreaming too

Look into any eyes
You find by you; you can see clear to another day
Maybe been seen before
Through other eyes on other days while going home
What do you want me to do
To do for you to see you through?
It’s all a dream we dreamed one afternoon long ago

Walk into splintered sunlight
Inch your way through dead dreams to another land
Maybe you’re tired and broken
Your tongue is twisted with words half spoken and thoughts unclear
What do you want me to do
To do for you, to see you through?
A box of rain will ease the pain and love will see you through

Just a box of rain, wind and water
Believe it if you need it, if you don’t just pass it on
Sun and shower, wind and rain
In and out the window like a moth before a flame

And it’s just a box of rain, I don’t know who put it there
Believe it if you need it or leave it if you dare
And it’s just a box of rain, or a ribbon for your hair
Such a long, long time to be gone and a short time to be there

Competence vs. performance

It’s all Chomsky’s fault (Chomsky 1965, p. 4):

“We thus make a fundamental distinction between competence (the speaker-hearer’s knowledge of his language) and performance (the actual use of language in concrete situations). […] A record of natural speech will show numerous false starts, deviations from rules, changes of plan in mid-course, and so on. The problem for the linguist, as well as for the child learning the language, is to determine from the data of performance the underlying system of rules that have been mastered by the speaker-hearer and that he puts to use in actual performance.”

So the idea is that people are trying to do C but only manage to do P, because of various constraints. We (children, adults, theorists) see (imperfect) P, and want to infer C. We go to school and go through various rigmaroles to better approximate C. The same distinction is applied in reasoning. Various options: people are irrational (with respect to C); maybe C = P, if we look hard enough to see it. Or bright people have P = C. Or bright people want P = C.

What fascinates me in reasoning is the role played by small groups of experts who produce particular systems of reasoning – logical calculi, probabilistic machinery – along with proofs that they have properties which they argue are reasonable properties to have. Then others come along to use the systems. Hey, this looks like a good logic to know; maybe it’ll help make my arguments better if I use it. Maybe this probability calculus will make it easier to diagnose illness in my patients. And so on. Then somebody else comes along and decides whether or not we’re consistent with a competence theory’s judgements, or whether we’re interpreting things a different way; whether another competence theory (application thereof) might be more appropriate for a given situation or a different psychological model of the situation.

Easy to get tied up in knots.

References

Chomsky, N. (1965). Aspects of the Theory of Syntax. MIT Press.

disorder

It may be taken for granted that any attempt at defining disorder in a formal way will lead to a contradiction. This does not mean that the notion of disorder is contradictory. It is so, however, as soon as I try to formalize it.

–Hans Freudenthal, cited in Michiel van Lambalgen’s PhD thesis