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LegrandNico committed Jul 18, 2023
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41 changes: 23 additions & 18 deletions docs/source/notebooks/3-Using_custom_response_functions.ipynb

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11 changes: 8 additions & 3 deletions docs/source/notebooks/3-Using_custom_response_functions.md
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Expand Up @@ -20,7 +20,7 @@ kernelspec:
editable: true
slideshow:
slide_type: ''
tags: [hide-input]
tags: [hice-cell]
---
%%capture
import sys
Expand Down Expand Up @@ -168,15 +168,20 @@ In [pyhgf](https://github.com/ilabcode/pyhgf), the {term}`Perceptual model` is t
```{important}
A *response function* should not return the actions $y$ (this is what the {term}`Decision rule` does), but the [surprise](https://en.wikipedia.org/wiki/Information_content) $S$ associated with the observation $x$, which is defined by:
$$S(x) = -\log[Pr(x)]$$
$$
\begin{align}
S(x) = -\log[Pr(x)]
\end{align}
$$
```
If you are already familiar with using HGFs in the Julia equivalent of pyhgf, you probably noted that the toolbox is split into a **perceptual** package [HierarchicalGaussianFiltering.jl](https://github.com/ilabcode/HierarchicalGaussianFiltering.jl) and a **response** package [ActionModels.jl](https://github.com/ilabcode/ActionModels.jl). This was made to make the difference between the two parts of the HGF clear and be explicit that you can use a perceptual model without any action model. In [pyhgf](https://github.com/ilabcode/pyhgf) however, everything happens in the same package, the response function is merely an optional, additional argument that can be passed to describe how surprise is computed.
````

+++ {"editable": true, "slideshow": {"slide_type": ""}}

Therefor, ee want a {term}`Response function` that returns the surprise for observing the response $y$, which is:
Therefore, we want a {term}`Response function` that returns the surprise for observing the response $y$, which is:

$$
\begin{align}
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