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# Cognitive Models with Julia

[![](https://img.shields.io/badge/status-looking_for_collaborators-orange)](https://github.com/DominiqueMakowski/CognitiveModels/issues)
[![](https://img.shields.io/badge/access-open-green)](https://dominiquemakowski.github.io/CognitiveModels/)

The project is to write an open-access book on **cognitive models**, i.e., statistical models that best fit **psychological data** (e.g., reaction times, scales from surveys, ...).
This framework aims at moving away from a mere description of the data, to make inferences about the underlying cognitive processes that led to its generation.
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{"title":"Pieces of Puzzle","markdown":{"headingText":"Pieces of Puzzle","containsRefs":false,"markdown":"\n1. Very quick intro to Julia and Turing\n\n```{julia}\nusing Plots\n\nplot(1:10)\n```\n\n\n\n\n2. Linear Regression: understand what the parameters mean (intercept, slopes, sigma)\n3. Boostrapping: Introduce concepts related to pseudo-posterior distribution description\n4. Hierarchical Models: Simpson's paradox, random effects, how to leverage them to model interindividual differences\n5. Bayesian estimation: introduce Bayesian estimation and priors over parameters\n6. 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{"title":"Fundamentals of Bayesian Modeling in Julia","markdown":{"headingText":"Fundamentals of Bayesian Modeling in Julia","containsRefs":false,"markdown":"\n![](https://img.shields.io/badge/status-not_started-red)\n\n\n## Very quick intro to Julia and Turing\n\nGoal is to teach just enough so that the reader understands the code.\n\n### Generate Data from Normal Distribution\n\n```{julia}\nusing Turing, Distributions, Random\nusing Makie\n\n# μ=100, σ=15\niq = rand(Normal(100, 15), 500)\n```\n\n```{julia}\nfig = Figure()\nax = Axis(fig[1, 1], title=\"Distribution\")\ndensity!(ax, iq)\nfig\n```\n\n### Recover Distribution Parameters with Turing\n\n```{julia}\n@model function model_gaussian(x)\n # Priors\n μ ~ Uniform(0, 200)\n σ ~ Uniform(0, 30)\n\n # Check against data\n for i in 1:length(x)\n x[i] ~ Normal(μ, σ)\n end\nend\n\nmodel = model_gaussian(iq)\nsampling_results = sample(model, NUTS(), 400)\n\n# Summary (95% CI)\nsummarystats(sampling_results)\n```\n\n\n## Linear Models\n\nUnderstand what the parameters mean (intercept, slopes, sigma).\n\n3. 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