For those of you sucking on my RSS feed

You may have noticed some silence from this end.  That is because I finished my PhD and successfully defended it mid-Novemeber, and a few days later moved to (the very pretty) Salzburg, Austria, to begin a post-doc.

In other news: first appearance in the Reasoner over here, a summary of a workshop recently organised here in Salzburg.

More posts soon…

The Wisdom of Many in One Mind

Averaging many people’s estimates of, e.g., when a famous event occurred tend to be better than asking any one arbitrary person.   Herzog and Hertwig (2009) investigated whether the average of two estimates from one person tended to be better than their first estimate, using the years of 40 historical events, e.g., when electricity was invented.

There were three conditions:

1. Repeated sampling: just giving an estimate twice.
2. So-called “dialectical” sampling (they cite Hegel here), where participants were told: “First, assume that your first estimate is off the mark. Second, think about a few reasons why that could be. Which assumptions and considerations could have been wrong? Third, what do these new considerations imply? Was the first estimate rather too high or too low? Fourth, based on this new perspective, make a second, alternative estimate.”
3. Pairing each participant’s guess with a random other participant.

Results are below:

The instruction to consider you were wrong increases accuracy beyond that with simple repeated measurement.  Best of all is averaging with another person.

Reference

Herzog, S. M. & Hertwig, R. (2009). The Wisdom of Many in One Mind: Improving Individual Judgments With Dialectical Bootstrapping. Psychological Science, 20, 231-237

Sample size computation for GLMMs

MLPowSim is a piece of software for estimating sample size by simulation for data to be modelled using GLMMs, including for instance logistic regression with crossed random effects.  It spews out R (and MLwiN) code for doing the simulations.  Screenshot below:

Haven’t had time to play much yet, but you answer a load of questions, e.g., what sort of model, how many predictors, what random effects, estimate for slope, etc, etc.  Looks useful!  I suspect it might be easiest to generate a few example R scripts using the package and then hack them by hand.  I stopped when it asked  me, “There are more than one random effects associated by the first factor in your model and so you need to enter variance and covaraince matrix.”

Journal of Articles in Support of the Null Hypothesis

“In the past other journals and reviewers have exhibited a bias against articles that did not reject the null hypothesis. We seek to change that by offering an outlet for experiments that do not reach the traditional significance levels (p < .05). Thus, reducing the file drawer problem, and reducing the bias in psychological literature.”

(Over here; hat-tip: Andrew Gelman’s blog.)

Prover9 and Mace4

Just found two fantastic programs and a GUI for exploring first-order classical models and also automated proof, Prover9 and Mace4.  There are many other theorem provers and model checkers out there.  This one is special as it comes as a self-contained and easy to use package for Windows and Macs.

There are many impressive examples built in which you can play with.  To start easy, I gave it a little syllogism:

all B are A
no B are C

with existential presupposition, which is expressed simply:

exists x a(x).
exists x b(x).
exists x c(x).
all x (b(x) -> a(x)).
all x (b(x) -> -c(x)).

and asked it to find a model. Out popped a model with two individuals, named 0 and 1:

a(0).
- a(1).

b(0).
- b(1).

- c(0).
c(1).

So individual 0 is an A, a B, but not a C. Individual 1 is not an A, nor a B, but is a C.

Then I requested a counterexample to the conclusion no C are A:

a(0).
a(1).

b(0).
- b(1).

- c(0).
c(1).

The premises are true in this model, but the conclusion is false.

Finally, does the conclusion some A are not C follow from the premises?

2 (exists x b(x)) [assumption].
4 (all x (b(x) -> a(x))) [assumption].
5 (all x (b(x) -> -c(x))) [assumption].
6 (exists x (a(x) & -c(x))) [goal].
7 -a(x) | c(x). [deny(6)].
9 -b(x) | a(x). [clausify(4)].
10 -b(x) | -c(x). [clausify(5)].
11 b(c2). [clausify(2)].
12 c(x) | -b(x). [resolve(7,a,9,b)].
13 -c(c2). [resolve(10,a,11,a)].
16 c(c2). [resolve(12,b,11,a)].
17 $F. [resolve(16,a,13,a)].

Indeed it does. Unfortunately the proofs aren’t very pretty as everything is rewritten in normal forms.  One thing I want to play with is how non-classical logics may be embedded in this system.

A shockingly bad characterisation of autistic-like traits

Have a look at the article by Stewart Dakers in the Guardian (October 22).

He begins with a description of a violent young man named Bender, who smashes another young man’s face against the protective grill on a shop front. Dakers’ diagnosis of Bender and co:

This disaffection is characterised by indifference to the interests of others, self-preoccupation, by behaviours that are aloof or aggressive. They are “extreme blokes”, endlessly competitive, combative, techno-whizzes, system obsessed, vocabulary-lite, emotional and social misfits. Top-gear masculinity.

There is an uncomfortable resonance in this hypermaleness with a condition that has begun to assume epidemic proportions. Indeed, those mates of Bender’s fortunate enough to be assessed for special educational needs all have an autistic spectrum diagnosis. Autism has most recently been rebranded as AQ, the autistic quotient, implying that it is an inherent human condition, like IQ. As such, it surely affects us all, capable of being excited, both chronically and anecdotally, by experience of trauma.

It is still open for debate whether Autism Spectrum Condition (ASC) is actually on the increase, or whether diagnostic criteria are weakening or more cases are being spotted.

I am aware of no work connecting ramming peoples’ faces into shop fronts and ASC, and it’s downright irresponsible to suggest there is a connection.

ASC has not been “rebranded” AQ.  There is a self-report screening questionnaire named AQ which is used by some researchers.  AQ may be used to predict whether someone has Asperger’s Syndrome or High Functioning Autism, but it also detects traits which are not specific to these conditions.

I can’t bring myself to quote from Dakers’ causal explanation.

There is more info about the autism spectrum at the National Autistic Society’s website.

A quick poll

The meaning of meaning?

(Made with SpringNet.)

Level of analysis again

(From explodingdog.)

A non-judgmental reconstruction of drunken logic

Simmons (2007) makes a helpful contribution to the logical modelling of real arguments by an addition of the shot glass modality to intuitionist logic.  A snippet:

Per Per Martin-Löf [7], something is true when witnessed by an object of knowledge, which lends itself to an obvious question of whether the truth of a proposition can be obviated by the presence of alcohol, seeing as alcohol has an clearly negative impact on one’s knowledge [1]. The possibility of the analytical truth of a proposition becoming questionable under the influence is also evidenced by discussion as to whether conference submissions that can be understood while drunk are novel enough to be worth accepting.

I think the following inference rule which I discovered while living in the homeland of Martin-Löf still requires further investigation:

Reference

Robert J. Simmons.  A non-judgmental reconstruction of drunken logic.  Presented at SIGBOVIK 2007, April 1, 2007. Winner of the Best Paper raffle. [PDF]