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README.md

@@ -14,7 +14,7 @@ Importantly, it is currently the only language in which we can fit all the cogni
 ## Why Bayesian?
 
 Unfortunately, cognitive models often involve distributions for which Frequentist estimations are not yet implemented, and usually contain a lot of parameters (due to the presence of **random effects**), which makes traditional algorithms fail to converge.
-Simply put, the Bayesian approach is the only one currently robust enough to fit these somewhat complex models.
+Simply put, the Bayesian approach is the only one currently robust enough to fit these complex models.
 
 ## The Plan
 

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-    "markdown": "# Fundamentals of Bayesian Modeling in Julia\n\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::: {#86de7312 .cell execution_count=1}\n``` {.julia .cell-code}\nusing Turing, Distributions, Random\nusing Makie\n\n# Random sample from a Normal(μ=100, σ=15)\niq = rand(Normal(100, 15), 500)\n```\n:::\n\n\n::: {#8df07ece .cell execution_count=2}\n``` {.julia .cell-code}\nfig = Figure()\nax = Axis(fig[1, 1], title=\"Distribution\")\ndensity!(ax, iq)\nfig\n```\n\n::: {.cell-output .cell-output-stderr}\n```\n┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.\n└ @ Makie C:\\Users\\domma\\.julia\\packages\\Makie\\VRavR\\src\\scenes.jl:220\n```\n:::\n\n::: {.cell-output .cell-output-display execution_count=3}\n![](1_introduction_files/figure-html/cell-3-output-2.svg){}\n:::\n:::\n\n\n### Recover Distribution Parameters with Turing\n\n::: {#3276026a .cell execution_count=3}\n``` {.julia .cell-code}\n@model function model_gaussian(x)\n    # Priors\n    μ ~ Uniform(0, 200)\n    σ ~ Uniform(0, 30)\n\n    # Check against each datapoint\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::: {.cell-output .cell-output-stderr}\n```\n┌ Info: Found initial step size\n└   ϵ = 0.05\n\rSampling:   0%|█                                        |  ETA: 0:00:29\rSampling: 100%|█████████████████████████████████████████| Time: 0:00:00\n```\n:::\n\n::: {.cell-output .cell-output-display execution_count=4}\n\n::: {.ansi-escaped-output}\n```{=html}\n<pre>Summary Statistics\n <span class=\"ansi-bold\"> parameters </span> <span class=\"ansi-bold\">    mean </span> <span class=\"ansi-bold\">     std </span> <span class=\"ansi-bold\">    mcse </span> <span class=\"ansi-bold\"> ess_bulk </span> <span class=\"ansi-bold\"> ess_tail </span> <span class=\"ansi-bold\">    rhat </span> <span class=\"ansi-bold\"> e</span> ⋯\n <span class=\"ansi-bright-black-fg\">     Symbol </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\">  Float64 </span> <span class=\"ansi-bright-black-fg\">  Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\">  </span> ⋯\n           μ   99.7082    0.6935    0.0367   349.6040   232.8456    1.0045     ⋯\n           σ   15.2626    0.4713    0.0255   337.7052   265.8666    1.0002     ⋯\n<span class=\"ansi-cyan-fg\">                                                                1 column omitted</span>\n</pre>\n```\n:::\n\n:::\n:::\n\n\n## Linear Models\n\nUnderstand what the parameters mean (intercept, slopes, sigma).\n\n## Boostrapping\n\nIntroduce concepts related to pseudo-posterior distribution description\n\n## Hierarchical Models\n\nSimpson's paradox, random effects, how to leverage them to model interindividual differences\n\n## Bayesian estimation\n\nintroduce Bayesian estimation and priors over parameters\n\n## Bayesian mixed linear regression\n\nput everything together\n\n",
+    "markdown": "# Fundamentals of Bayesian Modeling in Julia\n\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::: {.callout-important}\n\n### Notable Differences with Python and R\n\nThese are the most common sources of confusion and errors for newcomers to Julia:\n\n- **1-indexing**: Similarly to R, Julia uses 1-based indexing, which means that the first element of a vector is `x[1]` (not `x[0]` as in Python).\n- **Positional; Keyword arguments**: Julia functions makes a clear distinction between positional and keyword arguments, and both are often separated by `;`. Positional arguments are typically passed without a name, while keyword arguments must be named (e.g., `scatter(0, 0; color=:red)`). Some functions might look like `somefunction(; arg1=val1, arg2=val2)`.\n- **Symbols**: Some arguments are prefixed with `:` (e.g., `:red` in `scatter(0, 0; color=:red)`). These **symbols** are like character strings that are not manipulable (there are more efficient).\n- **Explicit vectorization**: Julia does not vectorize operations by default. You need to use a dot `.` in front of functions and operators to have it apply element by element. For example, `sin.([0, 1, 2])` will apply the `sin()` function to each element of its vector.\n- **In-place operations**: Julia has a strong emphasis on performance, and in-place operations are often used to avoid unnecessary memory allocations. When functions modify their input \"in-place\" (without returns), a band `!` is used. For example, assuming `x = [0]` (1-element vector containing 0), `push!(x, 2)` will modify `x` in place (it is equivalent to `x = push(x, 2)`).\n:::\n\n\n### Generate Data from Normal Distribution\n\n::: {#0c15ea13 .cell execution_count=1}\n``` {.julia .cell-code}\nusing Turing, Distributions, Random\nusing Makie\n\n# Random sample from a Normal(μ=100, σ=15)\niq = rand(Normal(100, 15), 500)\n```\n:::\n\n\n::: {#6de958d5 .cell execution_count=2}\n``` {.julia .cell-code}\nfig = Figure()\nax = Axis(fig[1, 1], title=\"Distribution\")\ndensity!(ax, iq)\nfig\n```\n\n::: {.cell-output .cell-output-stderr}\n```\n┌ Warning: Found `resolution` in the theme when creating a `Scene`. The `resolution` keyword for `Scene`s and `Figure`s has been deprecated. Use `Figure(; size = ...` or `Scene(; size = ...)` instead, which better reflects that this is a unitless size and not a pixel resolution. The key could also come from `set_theme!` calls or related theming functions.\n└ @ Makie C:\\Users\\domma\\.julia\\packages\\Makie\\VRavR\\src\\scenes.jl:220\n```\n:::\n\n::: {.cell-output .cell-output-display execution_count=3}\n![](1_introduction_files/figure-html/cell-3-output-2.svg){}\n:::\n:::\n\n\n### Recover Distribution Parameters with Turing\n\n::: {#76fbbced .cell execution_count=3}\n``` {.julia .cell-code}\n@model function model_gaussian(x)\n    # Priors\n    μ ~ Uniform(0, 200)\n    σ ~ Uniform(0, 30)\n\n    # Check against each datapoint\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::: {.cell-output .cell-output-stderr}\n```\n┌ Info: Found initial step size\n└   ϵ = 0.05\n\rSampling:   0%|█                                        |  ETA: 0:00:32\rSampling: 100%|█████████████████████████████████████████| Time: 0:00:01\n```\n:::\n\n::: {.cell-output .cell-output-display execution_count=4}\n\n::: {.ansi-escaped-output}\n```{=html}\n<pre>Summary Statistics\n <span class=\"ansi-bold\"> parameters </span> <span class=\"ansi-bold\">     mean </span> <span class=\"ansi-bold\">     std </span> <span class=\"ansi-bold\">    mcse </span> <span class=\"ansi-bold\"> ess_bulk </span> <span class=\"ansi-bold\"> ess_tail </span> <span class=\"ansi-bold\">    rhat </span> <span class=\"ansi-bold\"> </span> ⋯\n <span class=\"ansi-bright-black-fg\">     Symbol </span> <span class=\"ansi-bright-black-fg\">  Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\">  Float64 </span> <span class=\"ansi-bright-black-fg\">  Float64 </span> <span class=\"ansi-bright-black-fg\"> Float64 </span> <span class=\"ansi-bright-black-fg\"> </span> ⋯\n           μ   101.0966    0.6163    0.0285   464.5397   331.0063    1.0010    ⋯\n           σ    14.5905    0.4758    0.0221   504.1965   231.1654    1.0362    ⋯\n<span class=\"ansi-cyan-fg\">                                                                1 column omitted</span>\n</pre>\n```\n:::\n\n:::\n:::\n\n\n## Linear Models\n\nUnderstand what the parameters mean (intercept, slopes, sigma).\n\n## Boostrapping\n\nIntroduce concepts related to pseudo-posterior distribution description\n\n## Hierarchical Models\n\nSimpson's paradox, random effects, how to leverage them to model interindividual differences\n\n## Bayesian estimation\n\nintroduce Bayesian estimation and priors over parameters\n\n## Bayesian mixed linear regression\n\nput everything together\n\n",
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