Hot answers tagged mathematical-psychology
9
Given your background and interest in modeling, I would highly recommend The Cambridge Handbook of Computational Psychology. The book provides an overview for several of the prominent modeling paradigms in cogsci, including dynamical systems, as well as many concrete examples--albeit most using other computational paradigms.
Dynamical systems, to my ...
9
Here are a few options. I have not tried them yet personally.
LBA
Scott Brown has a copy of Donkin et al (2009) on his web page with some code in R, Excel, and WinBUGS for fitting the LBA model:
http://www.newcl.org/publications/DonkinAverellEtAl2009BRM.pdf
http://www.newcl.org/members/chris/fitLBA.zip
Diffusion model
The Diffussion model is ...
8
I would go with Physics.
Physicists study the world using mathematics, while mathematicians study mathematics itself which is a construct that does not necessarily exist in the real world (Albert Einstein once said: "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."). ...
7
Dehaene & Changeux (1991) made a neural-network model:
The coding units are clusters of neurons organized in layers, or assemblies. A sensonmotor loop enables the network to sort the input cards according to several criteria (color, form, etc.). A higher-level assembly of rule-coding clusters codes for the currently tested rule, which shifts when ...
7
I recently read a paper, which showed a mathematical model for performance scaling of research groups in different scientific branches. I'm aware you were originally asking for smaller "cognitive tasks" and project-like group-processes in the comments, but output and quality of publications/patents is probably anyway a better and more objective measure on a ...
7
It's a big topic. The relationship between group size and performance on a cognitive task is going to vary by several factors.
Here are a few thoughts:
The form of interdependence adopted by the group on the task will matter. When everyone can just work independently (e.g., taking calls in a call centre), then it makes sense that output would increase ...
6
This is a bit of a tangential answer, but hopefully still useful.
When we give humans noisy data, we can basically think of them as some sort of Bayesian inference machines that try to figure out what the function that data came from looks like. The important thing we then need to know, is how strong of a bias (prior) humans have towards expecting certain ...
6
You'd probably want to take a look at signal detection theory. This is a set of tools that you use to analyse how well a person (or an animal, or a machine) is able to discern trials where there is a signal present (e.g. a picture is shown that has been shown before, a tumour is present in an x-ray image, a dot on a radar is an enemy aircraft) from trials ...
6
I have a similar background to you, and have found a lot of interesting things in evolutionary game theory (you can follow links from my profile for more). But on the specific content of your question: I have come across to uses of dynamic systems on the opposite ends of cognition. Beer's work on modeling minimal cognition, and Busemeyer & Townsend's ...
6
Diederich & Busemeyer (2003) presented a diffusion model for three choice alternatives (p. 314). The paper is a tutorial for calculating diffusion models with (discrete) matrix methods. The extension to three choice alternatives is reached by defining a two-dimensional diffusion process on a triangular plane (state space).
Recently, Wollschläger & ...
6
Instead of having a single integrator with two bounds for two choices (symmetric random walk model), you can have many competing integrators each with a bound (race model). For example, see Fig 2. of Gold and Shadlen 2007 and references therein.
As for the continuous choices case, it is important to understand a limit of discrete choices can be very ...
5
Now that @ofri has presented a good argument for physics, I'll give a few arguments for the benefits of a course in maths, and particularly a math course that focuses heavily on statistics.
There are many areas of psychology where a good understanding of statistics is very helpful. Statistics is particularly useful in psychometrics, mathematical ...
5
Great to hear you're interested in applying your quantitative background to cognitive science; the field can definitely use more individuals like you!
I'm not sure to what degree these models might be meet your definition of "dynamical systems", but here are some off the top of my head:
stochastic models of human response time and accuracy in ...
4
I am pretty sure that you will not find a paper that tries to give purely behaviorist interpretations of decision field theory (or other similar models of decision making), because that would not make sense at all.
As you noted in your initial question, decision field theory is a cognitive model, i.e., it tries to explain overt behavior in terms of ...
4
The following are just my thoughts on what seems to make sense from first principles. I don't have a detailed understanding of what is standard practice in the wisdom of crowds literature. I've also only given what you've written a basic read. I.e., enough to understand the broad question, but not enough to follow exactly what you've done.
Let $y_i$ be the ...
4
Reading list
As @Jeff has mentioned Tom Griffiths has several useful resources. In particular Tom Griffiths has an extensive reading list that you might find relevant. To quote the summary of the content:
This list is intended to introduce some of the tools of Bayesian
statistics and machine learning that can be useful to computational
research in ...
4
+1 to Speldosa's suggestion. Griffiths and colleagues have written several primers on the use of Bayesian models in cogsci. Many of them can be found on Griffiths' website under 'Foundations':
http://cocosci.berkeley.edu/publications.php?topic=Foundations
e.g.
Perfors, A., Tenenbaum, J.B., Griffiths, T. L., & Xu, F. (2011). A
tutorial ...
4
For the diffusion model, there is also Eric-Jan Wagenmakers' "EZ-diffusion model", which you can find here.
This paper compares three different pieces of software for estimation of diffusion model parameters:
von Ravenzwaaij D., & Oberauer, K. (2009). How to use the diffusion
model: Parameter recovery of three methods: EZ, fast-dm, and DMAT.
...
3
Unfortunately, in psychology and cognitive sciences (and some parts of neuroscience) absolutely no mathematical training is given beyond the highschool level (intro stats, basics of linear algebra in $\mathbb{R}^2$ and $\mathbb{R}^3$, and intro calc). To make this relatable, I will compare understanding dynamics sytems to literature, where you have 3 levels: ...
3
Have you read this:
Fishbein, M., Middlestadt, S. (1995) Noncognitive Effects on Attitude Formation and Change: Fact or Artifact? Journal of Consumer Psychology, 4(2),181-202. [DOI]
Direct quote from page 187:
Note that the psychology of the double negative is an essential part of an expectancy-value formulation (Ajzen & Fishbein, 1980; Fishbein, ...
3
In the fairly recent book "The Cambridge Handbook of Computational Psychology", chapter three is devoted to bayesian modeling. It's written by Thomas Griffiths, Charles Kemp, and Joshua Tenenbaum.
I haven't read this chapter yet myself but will update this answer when I have.
3
Related to this is several works on the integration or non-integration of computational models in general to cognitive science. For instance, the Tractable Cognition Thesis basically says that we can improve cognitive modeling if we limit cognitive models to those tractably implementable on a Turing machine.
Van Rooij, I. 2008. The Tractable Cognition ...
3
This seems related to the literature on multiple-cue probability learning (MCPL). In this paradigm, a typical task presents subjects a list of cues and values, and asks them to predict the probability of certain outcomes. This paradigm has a decent amount of literature both in the JDM (judgment and decision making) community as well as the human factors ...
2
From my social psychology perspective, there has been some computational modelling work on things like attitudinal influence dynamics. See:
Nowak, A., Szamrej, J., & Latané, B. (1990). From private attitude to public opinion: a dynamic theory of social impact. Psychological Review, 97, 362-476.
Robin Vallacher and Andrzej Nowak crop up a lot in this ...
2
Recently Bayesian models of cognitive development have been very successful in at least formulating working hypotheses as to how abstract knowledge "regularizes" and guides learning and reasoning from sparse data. I was thinking for instance of the following paper:
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., and Goodman, N. D. (2011). How to Grow a Mind: ...
2
My colleagues have applied the COVIS model of category learning to the WCST. COVIS isn't a model of WCST performance per se, but can account for several known phenomena. See this Google Scholar search: http://scholar.google.com/scholar?hl=en&q=Helie+Paul+ashby&btnG=&as_sdt=1%2C5&as_sdtp=
2
Unless I'm mistaken, it sounds like you're actually interested in meta-cognition and type-2 signal detection theory (the form of SDT that Speldosa has pointed to is type-1 signal detection theory). It's used to study our ability to reflect on our own knowledge, or what we think about what we think.
This wikipedia article might get you started on ...
1
The problem is fundamentally due to the level of likelihood you allocate to an event, that is variable $e_i$, should not be measured using a bi-polar scale. Instead, likelihoods should be associated with a percentage, between 0 and 100%. This is a more natural unit, as a "low likelihood" result usually means that the respondent thinks the probability of ...
1
Bogacz et al. (2006) provide the most comprehensive overview of models in this domain. This includes comparisons of the Drift Diffusion Model (Ratcliff, 1978), Ornstein–Uhlenbeck (O-U) Model (e.g. Busemeyer & Townsend, 1993; "Decision Field Theory"), race models without inhibition (e.g. Vickers, 1970), and race models with inhibition (e.g. Usher & ...
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