Thinking when you think you’re not thinking—again

I really enjoyed the 2006 Science paper by Dijksterhuis, Bos, Nordgren and van Baaren on deliberation without attention.  Then came Acker (2008) with a meta-review and the suggestion that there is “little evidence” of an advantage of deliberation without attention.

Today, from the latest issue of Judgment and Decision Making: Are complex decisions better left to the unconscious? Further failed replications of the deliberation-without-attention effect by Dustin P. Calvillo and Alan Penaloza.

The summary seems to be that deciding without deliberation, immediately after the stimulus is presented, might sometimes be better than deliberation.  But not with distraction post stimulus.

The moderators of the effect—there seems to be something going on in a few studies!—are still not well understood.

Reasoning to an interpretation before applying Bayes’ rule

What’s the point of Bayes’ rule?  This web page by Eliezer S. Yudkowsky gives a long intuitive explanation (thanks to Keith Frankish for pointing to it).  This blog post is an attempt at a slightly shorter version with a bit more maths, and a bit of rambling about interpretation.

The information in the example problem given there is as follows:

1. 1% of women at age forty who participate in routine screening have breast cancer.
2. 80% of women with breast cancer will get positive mammographies.
3. 9.6% of women without breast cancer will also get positive mammographies.

The task: A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

The general problem solved by Bayes’ rule is that if you know the probability of if A, then B, how do you work out the probability of if B, then A?  More precisely if you know P(B|A), what is P(A|B)?

Here B|A denotes the conditional event, a simultaenously easy and difficult concept.  One way to think of it is as follows.

Consider a fair die with six sides.  It’s thrown.  What’s the probability of a six given that a side showing an even number lands upwards? (Van Frassen, 1976 used an example like this to explain the conditional event interpretation of the natural language if-then.)  This is P(lands six|lands even).  The idea is that you only consider cases where it’s showing an even number (2, 4, or 6). Assuming they’re all equally probable, then P(lands six|lands even) = 1/3.

Interpretation

The first stage of solving problems like that above is interpretating the problem in the language of the mathematical theory you want to use.

Let denote “has cancer”, denote “does not have cancer”, denote “shows a positive test result”, and denote “shows a negative test result”.

Let’s take each item of information individually.

1% of women at age forty who participate in routine screening have breast cancer.

There’s a mix of information here: a percentage of people (1%), from a particular sub-population (women, aged 40, who participate in routine screening), and a property they have.  From the problem it is clear that the interpretation is supposed to be:

But one can imagine a more complicated formalisation, for instance if the population of interest contains women of many different ages, some, but not all, of whom were screened because they had some worry about their health.

Next sentence:

80% of women with breast cancer will get positive mammographies.

This is an instance of

X% of people with property A have property B

The intended interpretation is P(B|A) = X%, but this might not be obvious to all readers.  Take some:

Some people with property A have property B

If this is interpreted as an existential quantifier, then it also follows that some people with property B have property A.  The conditional event, B|A, is in general not reversable in this way, so would not be suitable for the interpretation of an existential “some”.  Consider the following statement:

All people with property A have property B

This is not (in general) reversable. The percentage quantifier (used in the problem description) is also not reversible.  So there’s quite a lot of trickiness involved in interpreting this innocent looking statement. Given some background knowledge (we know the article is about Bayes’ rule, and about conditional probabilities), the intended interpretation of the original information is:

The idea is that if we choose a person at random from the population of interest, who has cancer (i.e., we know for sure she has cancer), then the probability of her having a positive test result is .8.

Then similarly for the last sentence:

9.6% of women without breast cancer will also get positive mammographies.

The formalisation is:

Here is the summary:

Now the problem statement:

A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

We have to infer . Note how this is a reversal of the conditional statements we encounted in the information given about the test.

Calculation

Now comes the calculation. A good place to start when thinking about conditional probability is the ratio formula for the probability of a condititional event:

Take an interpretatation of “If it is raining, then I have an umbrella” as the conditional event expression:

I have an umbrella  |  it is raining

The probability of this is the probability that I have an umbrella and it is raining, divided by the probability that it is raining.

This can easily be rewritten to

So if you know the probability of rain, and the probability that I have an umbrella when it rains, then you can multiply them to infer the probability that it is raining and I have an umbrella.

One step towards Bayes’ rule begins with:

1. 
2. [ in (this) probability theory, so it does not matter what order you write them]

From 2 we can infer , which slots into 1 to give

Now use the same variables as in the original problem

We can already fill in the numerator (top row) with and , but not yet the denominator (bottom row).

Let’s work a bit further then. We can infer as follows:

Which is easily calculated from the rewrite of the conditional probability above:

One more thing: .  So this gives:

Now we have everything we need:

.

Ben R. Slugoski on why he became a psychologist

When the desire to study psychology began:

“If my developmental psychology colleagues are right, I began formulating conceptions of human psychological states and processes at about the age of three.”

On the shift of study emphasis from English to Psychology:

“… there was no antidote to a few hours deconstructing Coleridge or Blake like working out the expected mean squares for a tricky experimental design (a rakish sex-life not otherwise being in the cards!). [...]

“[...] Erudite though my English professorss were, they were only vessels for conveying the brilliance of the ‘Greats’ and as such were never particularly good models for an aspiring player. What ultimately determined my allegiance to psychology was the brilliance personified in my psychology lecturers [...] the late Kenneth Burstein, old school rat-runner, unabashed liberal, and the person whom you would least want as a relationship counsellor [...]“

Teaching styles:

“It is probably worthy of note in these days of multimedia, dot point-driven instruction that my beacons were invariably Socratic minimalists for whom the take-home message was quite subsidiary to the intellectual journey (seemingly) constructed in situ. Thus, I recall Burstein leading us from eye-blink conditioning with rabbits to human divorce statistics via a little sociobiology, Koopman had the class reinvent the correlation coefficient, and Marcia … well, Marcia had us ruminating about the conditions and consequences of sleeping with ones’ clients.”

(From over here.)

The psychologists behind the torture

“They had never carried out a real interrogation, only mock sessions in the military training they had overseen. They had no relevant scholarship; their Ph.D. dissertations were on high blood pressure and family therapy. They had no language skills and no expertise on Al Qaeda.

“But they had psychology credentials and an intimate knowledge of a brutal treatment regimen used decades ago by Chinese Communists. For an administration eager to get tough on those who had killed 3,000 Americans, that was enough.”

From the NYT article on Jim Mitchell and Bruce Jessen.

I see little evidence that they used psychological research and a lot of evidence of just plain brutality.

Bentall on the “Kraepelinian paradigm”

Bentall, R. Madness explained: why we must reject the Kraepelinian paradigm and replace it with a `complaint-orientated’ approach to understanding mental illness. Medical Hypotheses, 2006, 66, 220-233:

“Instead of attempting to explain mythical diagnostic entities, we should try and explain the actual complaints that patients bring to the clinic, such as hallucinations, delusions, disordered communication and mania. This strategy assumes that, once these complaints have each been explained in turn, there will be no ’schizophrenia’ or ‘bipolar disorder’ leftover to account for.”

…

“a simple list of a patient’s complaints contains much more useful information than a Kraepelinian diagnosis, and takes less effort (because complaints have to be assessed in order to generate a diagnosis). In fact, cognitive-behaviour therapists have long argued that lists of this kind – the ‘problem list’ in the jargon of the approach – is the best starting point for clinical intervention… A complaint-orientated approach implies that treatments should be delivered according to patients’ needs.”

Create your own economy (updated some more)

Recently I read Create your own economy by Tyler Cowen (thanks Michelle for the tip-off!). Interesting page-turner discussing autism, autistic(-like) traits in non-autistics, and implications for society.

Cowen points out (what is thankfully becoming more familiar) that although autism is often associated with tragedy, many autistics and not only savants have cognitive strengths, e.g., being infovores for their preferred areas of interest, better perceptual skills than non-autistics, less suspectiblity to false memories.  He argues that technological tools available today such as iTunes and Facebook allow non-autistics to have the same abilities.  Non-autistics are driven to do the same sort of organisation and searching for information as autistics are, and this is being made possible by technology. He argues that education is even designed to teach non-autistics some of the cognitive strengths of autism.

One side of autism mentioned in the book and not frequently discussed is that autistics are more likely to talk about feelings than make small talk (has this been studied? Is it true? I would like to know more). The emotional experience of autistics is rarely acknowledged.  Cowan gives examples of people who despite appearing outwardly aloof are deeply sensitive, caring, and who are shocked when they’re told otherwise.

There are plenty of examples in the book of people, real and fictional, who appear(ed) to have autistic traits. I found this a tad tiresome (there has been a lot of it about elsewhere), especially when suffixed with hedges saying that of course we don’t know whether they were autistic. The key point is that “what-we-call-what-it-is-that-I-am-talking-about” (to quote Cowan) probably ought not be derived from a name for a disorder. So viewed this way, most of the book is not about autism, but about a cognitive and emotional profile which many people in society have. This is not to say that autistics do not have cognitive strengths—and he discusses some examples in the book—but I do not see what is to be gained by conjecturing that people are/were autistic. What does this explain?  The details matter, not a one word label. (However this could be because I am deeply suspicious of labels in general!)

Lots of good stuff in the book. In general I think it does a great job of defending the eccentric, and argues successfully that many of the traits eccentrics possess are desirable. Good news for academics!

There are plenty of important points on respecting the individual. I like this of course, and am a big fan of positive individual differences research, e.g., discovering the strengths of people diagnosed with various developmental and psychiatric conditions. But I think my favourite sentence in the book is this (relatively unimportant) one:

“In June 2009, a group of Norwegian astronomers broadbast a Doritos ad to a distant star, forty-two light years away.”

This is genius, and I think it’s a good author indeed who can spot and report such facts. It’s these kinds of things that make society fun.

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

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.

Level of analysis again

(From explodingdog.)