small fixes in the documentation (#111)

* fix error in equation in the exercise

* remove unecessary config from docs setup.py

docs/source/conf.py

@@ -72,9 +72,6 @@
 # The master toctree document.
 master_doc = "index"
 
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ["_templates"]
-
 # List of patterns, relative to source directory, that match files and
 # directories to ignore when looking for source files.
 # This pattern also affects html_static_path and html_extra_path.
@@ -120,9 +117,6 @@
   "changelog": [],
 }
 
-def setup(app):
-    app.add_css_file('style.css')
-
 # -- Intersphinx ------------------------------------------------
 
 intersphinx_mapping = {

docs/source/notebooks/Exercise_1_Using_the_HGF.ipynb

@@ -127,11 +127,11 @@
     "\n",
     "The HGF hierarchically generalize this process by making the parameters of a stochastic process depend on another GRW at a different level. In [PyHGF](https://github.com/ilabcode/pyhgf) we use a *nodalized* version of this framework {cite:p}`weber:2023`, and consider that each stochastic process is a node in a network, connected with other nodes through probabilistic dependencies: **value coupling** (targetting the value $\\mu$ of the child node) or **volatility coupling** (targetting the volatility $\\sigma^2$ of the child node).\n",
     "\n",
-    "Let's consider for example a network constituted of two nodes $x_1$ and $x_2$, as it is found in the continuous HGF {cite:p}`2014:mathys`. The node $x_1$ is performing a GRW as previously described. We can add a dependency on the mean of the distribution (**value coupling**) by assuming that $x_1$ inherits this value directly from $x_2$, instead of using its own previous value. Mathematically, this would write:\n",
+    "Let's consider for example a network constituted of two nodes $x_1$ and $x_2$, as it is found in the continuous HGF {cite:p}`2014:mathys`. The node $x_1$ is performing a GRW as previously described. We can add a dependency on the mean of the distribution (**value coupling**) by assuming that $x_1$ inherits the difference step from $x_2$, instead of using only its own previous value. Mathematically, this would write:\n",
     "\n",
     "$$\n",
     "x_2^{(k)} \\sim \\mathcal{N}(x_2^{(k-1)}, \\, \\sigma_2^2) \\\\\n",
-    "x_1^{(k)} \\sim \\mathcal{N}(x_2^{(k)}, \\, \\sigma_1^2) \\\\\n",
+    "x_1^{(k)} \\sim \\mathcal{N}(x_1^{(k-1)} + \\alpha_{1} x_2^{(k)}, \\, \\sigma_1^2) \\\\\n",
     "$$\n",
     "\n",
     "Note that this generative process reads top-down: the node higher in the hierarchy ($x_2$) generates new values and passes them to the child nodes.\n",

docs/source/notebooks/Exercise_1_Using_the_HGF.md

@@ -87,11 +87,11 @@ We have simulated above a simple GRW. At each time point, this process is fully
 
 The HGF hierarchically generalize this process by making the parameters of a stochastic process depend on another GRW at a different level. In [PyHGF](https://github.com/ilabcode/pyhgf) we use a *nodalized* version of this framework {cite:p}`weber:2023`, and consider that each stochastic process is a node in a network, connected with other nodes through probabilistic dependencies: **value coupling** (targetting the value $\mu$ of the child node) or **volatility coupling** (targetting the volatility $\sigma^2$ of the child node).
 
-Let's consider for example a network constituted of two nodes $x_1$ and $x_2$, as it is found in the continuous HGF {cite:p}`2014:mathys`. The node $x_1$ is performing a GRW as previously described. We can add a dependency on the mean of the distribution (**value coupling**) by assuming that $x_1$ inherits this value directly from $x_2$, instead of using its own previous value. Mathematically, this would write:
+Let's consider for example a network constituted of two nodes $x_1$ and $x_2$, as it is found in the continuous HGF {cite:p}`2014:mathys`. The node $x_1$ is performing a GRW as previously described. We can add a dependency on the mean of the distribution (**value coupling**) by assuming that $x_1$ inherits the difference step from $x_2$, instead of using only its own previous value. Mathematically, this would write:
 
 $$
 x_2^{(k)} \sim \mathcal{N}(x_2^{(k-1)}, \, \sigma_2^2) \\
-x_1^{(k)} \sim \mathcal{N}(x_2^{(k)}, \, \sigma_1^2) \\
+x_1^{(k)} \sim \mathcal{N}(x_1^{(k-1)} + \alpha_{1} x_2^{(k)}, \, \sigma_1^2) \\
 $$
 
 Note that this generative process reads top-down: the node higher in the hierarchy ($x_2$) generates new values and passes them to the child nodes.