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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 ...

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 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

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

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....

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

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. ...

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 ...

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, ...

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

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

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

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

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

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. ...

5

In my opinion as a computational neuroscience researcher, graph theory has not made major inroads into computational neuroscience because we don't have good evidence for what graphs characterise brains. For example, my research revolves around how patterns of connections between neurons within local cortical circuits relate to information processing ...

5

I also like https://bayesmodels.com/. I posted the question on twitter, you could check out the responses. Joachim Vandekerckhove suggested: Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Sage Publications. https://www.amazon.com/Computational-Modeling-Cognition-Principles-Practice/dp/1412970768 ...

4

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 ...

4

I don't think anyone has ever bothered (though Ralph Miller might disagree), since many of the 'failures' are outside of the model's purview. The model expresses as simply as possible the profound insight that we learn most when our expectations are not met. Many features of learning won't conform to this general principle (spontaneous recovery) but it doesn'...

4

Thanks for sharing the article. I read the paper and what I take from it is a rather pessimistic view. He suggests that there is a crucial need for overarching proper mathematical modeling, but he makes it sound this is also a huge obsticle and we must wait (longer than a young persons academic career) to see the fruits of it. I'm coming from a theoretical ...

4

If you have a physics background, you may be particularly interested in Sparse Distributed Memory, a model that provides a number of psychologically plausible characteristics, and is also neuroscientifically plausible. The model and some of its characteristics are summarized in this paper. Many great references have been provided by Nick Stauner, but ...

4

The index of sensitivity $d'$ is typically defined in terms of two equal variance normally distributed random variables with means $\mu_s$ and $\mu_n$ and standard deviation $\sigma$: $$d'=\frac{\mu_s-\mu_n}{\sigma}$$ In behavioural experiments, the probability that the subjects responded correctly (either saying 'yes' when the signal was present or saying ...

3

I would say that the maths that are most useful in cognitive science are the ones that have to do with decision theory. So I would include linear algebra (with its matrixes, and "transition" or changes of state analysis), as well as probability and statistics, with their "expected values" and resulting decision trees. Computational and information analysis, ...

3

Semantic foraging in memory is another nice example: concepts in memory can be represented spatially as locations in multidimensional space, and the route we travel in that 'space' has a lot in common with the optimal foraging movements animals adopt. http://www.indiana.edu/~clcl/Papers/HTJ_Foraging.pdf

3

Here are a few off the top of my head from neuroscience: neural activity may primarily exist on low dimensional attractors. reconstructing PET signal origins from emitted gamma rays It's widely believed our brains are gyrencephalic (wrinkly) to maximize surface area. Various distance metrics (Euclidean, Mahalanobis) are common tools for clustering data, for ...

3

It's a little unclear what you're asking. In general, psychologists try to build models that are parsimonious; this often means only introducing new parameters (particularly free parameters) into a model when they are absolutely necessary. You are right that with a sufficient number of free parameters, one can build a model that fits the data perfectly. But ...

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