# Tag Info

17

Here are a few options. I have not tried them yet personally. As mentioned below, the rtdists package in R is able to fit both LBA and diffusion models. Other Options 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/...

13

It seems like there is a fairly big literature on this topic. Wagenaar (1972) provides an early review of research. The author summarises around 15 studies. The studies involved generated random elements including letters and numbers of varying lengths. In all but one study, participants were deemed to be not good at randomising. As part of their review ...

12

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 ...

11

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 ...

11

The question which of these two descriptions is correct? is perhaps natural in the context of, say, someone studying for an examination. Epistemologists might suggest that a better formulation would be is either of these correct? However, as stated here there are clear reasons for preferring the first formulation to the second. I shall first explain why, ...

11

Very many references may easily be found with a Google search for "mathematical model memory". Probably the most classic and iconic reference is Atkinson and Shiffrin (1965), which is also described on Wikipedia. Its three components and their relationships are nicely encapsulated in this figure: Many other, lesser-known mathematical models of memory exist, ...

10

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 ...

10

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."). ...

9

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 ...

9

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. ...

9

Here's my list of math subjects that support the study of brain (from a computational neuroscientist's perspective): Linear algebra to understand high dimensions, to compute things quickly, foundation for other math Calculus basics for everything continuous valued Statistics to analyze any data, you need stats! basis for modeling, regression, ...

9

I will deviate from the other answers and give more pessimistic response based on my experience as a mathematician and theoretical computer scientist that spends some of his time in a psychology department. In cognitive science, neuroscience, and psychology (like in most sciences) you will never do mathematics in the definition, lemma, theorem, proof sense....

8

In general, there are two types of 'complexity' that are studied. Usually, when people talk about 'complexity', especially on the internet, they mean Santa Fe Institute style complexity. This is a vague and poorly defined concept that has struggled for a number of years without making significant progress. It uses pretty words, but has yet to deliver on any ...

8

To calculate $d'$ you need to know two things: the hit rate and the false alarm rate. The hit rate is the proportion of trials where the stimulus was present and the subject responded that the stimulus was present. The false alarm rate is the proportion of trials where the stimulus was not present, and the subject responded that the stimulus was present. ...

7

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; see also this answer). To make this relatable, I will compare understanding dynamics sytems to literature, ...

7

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

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 ...

6

+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 ...

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

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 2-alternative ...

6

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 psychology,...

6

Thoughts on the paper The paper appears to provide a high level overview of the role of mathematics in cognitive science. I'm not a sufficient expert in the overall field of cognitive science where I'd feel comfortable to truly judge the accuracy of the overall synthesis that Andler (2012) provides. That said, much of the paper is about providing examples ...

6

Note: This is not intended to set a verbosity standard for answers, but to give a comprehensive example of what kind of information I am looking in order to further clarify the question. An answer including only a parallel of the principles of ecological psychology subsection would be sufficient, for example. Ecological psychology Ecological Psychology (EP)...

6

I think the key concept to tackle this question is to consider the concept of abstraction. Abstract models are generalized models of some kind "reality" that we are interested in, with the aim to describe some behavior of the system in question reasonably well. Often the abstraction should also be relevant to many instances of the entity that we would like ...

5

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 ...

5

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 ...

5

The R package diffIRT (http://www.dylanmolenaar.nl/jss1265.pdf) estimates both the Q and the D diffusion models (see his website for the van der Maas et al. paper discussing the differences between these models). R code for the EZ2 approach, which is much faster if that is important for your applications, is http://raoul.socsci.uva.nl/EZ2/.

5

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 ...

5

For a review of how this question is debated in Cognitive Science, search for Searle's Chinese Room Thought Experiment. In the Chinese Room Thought Experiment, Searle argues there is something fundamentally meaningful (semantic-holding-preserving) about the internal state of a living being. Additionally, this meaning cannot be approximated by a computer. ...

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