Autocorrelated Sampling in Cognition

Implementing MCMC Algorithms as Cognitive Models and Fitting Them Without Likelihoods

A fundamental question in cognitive science is how people achieve such high levels of performance given the limited resources they have access to. Human behaviour is similar to the Bayesian ideal, but implementing Bayes’ rule is intractable but for the simplest problems.

To circumvent this problem, computer scientists have developed a family of algorithms, Markov Chain Monte Carlo (Brooks et al., 2011), which operate by drawing samples directly from the posterior distribution (thus avoiding distribution multiplication), which make the inference task possible. An exciting development in cognitive science has been to show that these inference algorithms describe human behaviour remarkably well: in perception (Gershman et al., 2012), causal reasoning (Bramley et al., 2017; Davis & Rehder, 2020), forecasting (Spicer et al., 2024), numerical estimates (Lieder et al., 2018) and probability judgments (Dasgupta et al., 2017) among others ¹.

In this workshop, we will:

discuss approaches to cognition using MCMC,
show how to use the samplr package, an R package that implements these models, and
show how to go from simulated data to model and parameter inference

No previous experience with MCMC algorithms is needed.

In this website, you will find a schedule for the workshop as well as workshop materials and slides.

Workshop Prerequisites

Before the workshop, please install the R programming language in your machine. An IDE such as RStudio is recommended but not necessary.

The workshop will make use of the following packages for computations: samplr, abc; and these packages for plotting purposes: tidyverse, patchwork. You can install them by running:

install.packages(c("samplr", "abc", "tidyverse", "patchwork"))

on your R console.

If you have issues installing these, please email Lucas Castillo (lucas.castillo@warwick.ac.uk).

References

Bramley, N. R., Dayan, P., Griffiths, T. L., & Lagnado, D. A. (2017). Formalizing Neurath’s ship: Approximate algorithms for online causal learning. Psychological Review, 124(3), 301–338. https://doi.org/10.1037/rev0000061

Brooks, S., Andrew Gelman, Jones, G., & Meng, X.-L. (Eds.). (2011). Handbook for Markov chain Monte Carlo. Taylor & Francis.

Dasgupta, I., Schulz, E., & Gershman, S. J. (2017). Where do hypotheses come from? Cognitive Psychology, 96, 1–25. https://doi.org/10.1016/j.cogpsych.2017.05.001

Davis, Z. J., & Rehder, B. (2020). A process model of causal reasoning. Cognitive Science, 44(5), e12839.

Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012). Multistability and Perceptual Inference. Neural Computation, 24(1), 1–24. https://doi.org/10.1162/NECO_a_00226

Lieder, F., Griffiths, T. L., M. Huys, Q. J., & Goodman, N. D. (2018). The anchoring bias reflects rational use of cognitive resources. Psychonomic Bulletin & Review, 25(1), 322–349. https://doi.org/10.3758/s13423-017-1286-8

Spicer, J., Zhu, J.-Q., Chater, N., & Sanborn, A. N. (2024). How do people predict a random walk? Lessons for models of human cognition. Psychological Review, 131(5), 1069–1113. https://doi.org/10.1037/rev0000493

Footnotes

We have compiled a list of papers using sampling approaches to cognition here ↩︎