A bit like in the previous entry, a while ago I came across an edition of the journal Developmental Science which was dedicated to a single topic. In this case it was using modelling techniques to try and gain insight into the way that infants think. The papers were really interesting and I need to go back to them to properly understand what they were saying. However, just recently I picked up this paper by Shultz (2007) which sat at the end of the journal and provided an overview of the preceding papers.
The first comments pointed out some nuances in different modelling approaches that had eluded me the first time I read the papers themselves and the insight is very helpful….
“In the Bayesian models that I have seen, Bayes’ rule does not generate abstract structures – rather it computes statistics over structures designed by modelers. In contrast, connectionist approaches sometimes show how structures are created , as when a linear structure is created by a network learning a collection of weights of systematically increasing strength.”
“Kemp et al. note that a common reservation about Bayesian models is that their success depends on the modelers ability to choose the correct prior probabilities. Interestingly, hierarchical models solve this problem in that abstract knowledge need not be specified in advance but can be learnt from the data.”
“Interestingly, probability estimation and model building seem analogous to quantitative and qualitative developmental mechanisms, respectively, in constructive neural networks. Constructive networks start with minimal structure and recruit single hidden units or previously learned networks as needed to reduce network error. Change occurs through quantitative adjustment of connection weights within a particular network structure or, when that fails to solve the current problem, through qualitative recruitment of additional computational devices. This recurring cycle of adjustments and recruitments creates novel representational structures that the network could not previously express. Perhaps there are computational lessons in these mechanisms that could be of use to Bayesian modelers of psychological development.”
This helped to clarify what the different modellers were doing and what the value of their approaches were. However, Shultz made some other comments about whether these approaches can be taken and applied to adult thinking as well…
“The resurrgence of interest in Bayesian methods is somewhat surprising given the Nobel Prize-winning work showing that people are rather poor Bayesians, subject to such biases as the base-rate fallacy and the representativeness heuristic. There is also evidence that people confuse the direction of conditional probabilities, e.g. the probability of a symptom given a disease vs. the probability of a disease given a symptom. Even experienced medical professionals deviate from Bayes in these ways, creating medical inefficiencies and sometimes disastrous outcomes.”
“Clearly, the new evidence that people are Bayesian optimizers needs to be reconciled with this older work suggesting that people routinely ignore prior probabilities and confuse the direction of conditional probabilities. [Shultz goes on to discuss various hypotheses being explored to explain this phenomenon.]
So the answer there is… not really (?) or, at least, not very well. This is all very vexing as it would be really useful to gain insight into adult cognitive processes when faced with, say, an unfamiliar object. Also, if adults do think differently to children, then when and how does that transition take place?
ReferenceShultz, T.R. (2007) ‘The Bayesian Revolution approaches psychological development’, Developmental Science, 10, 3, 357-364