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+sigma_temperature->inverse_temperature + + + + + +mu_volatility + +mu_volatility +~ +Normal + + + +volatility + +volatility +~ +Normal + + + +mu_volatility->volatility + + + + + +sigma_volatility + +sigma_volatility +~ +HalfNormal + + + +sigma_volatility->volatility + + + + + +mu_temperature + +mu_temperature +~ +Normal + + + +mu_temperature->inverse_temperature + + + + + +pointwise_loglikelihood + +pointwise_loglikelihood +~ +Deterministic + + + +inverse_temperature->pointwise_loglikelihood + + + + + +log_likelihood + +log_likelihood +~ +CustomDist_log_likelihood + + + +inverse_temperature->log_likelihood + + + + + +volatility->pointwise_loglikelihood + + + + + +volatility->log_likelihood + + + + + \ No newline at end of file diff --git a/dev/_images/814a296a3d5ba45eb453c55807a1b1430b18f7b7513122e9077e6b6d1af31c67.png b/dev/_images/814a296a3d5ba45eb453c55807a1b1430b18f7b7513122e9077e6b6d1af31c67.png deleted file mode 100644 index a9a952672..000000000 Binary files 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b/dev/_images/dc0d222dcfe1385508ef3f221b0fcd2d0ebc4f025f09569b9d250b27e018a7c2.png deleted file mode 100644 index ed99a908f..000000000 Binary files a/dev/_images/dc0d222dcfe1385508ef3f221b0fcd2d0ebc4f025f09569b9d250b27e018a7c2.png and /dev/null differ diff --git a/dev/_images/df04c50a598763e25214aadc382bbf9d014e1de10891f6614d13a1a5fa7c6257.png b/dev/_images/df04c50a598763e25214aadc382bbf9d014e1de10891f6614d13a1a5fa7c6257.png new file mode 100644 index 000000000..a49ce9766 Binary files /dev/null and b/dev/_images/df04c50a598763e25214aadc382bbf9d014e1de10891f6614d13a1a5fa7c6257.png differ diff --git a/dev/_images/e288043d732abf201db1bbb2866ad3378beee8f0f8a551a277a89997f4109245.png b/dev/_images/e288043d732abf201db1bbb2866ad3378beee8f0f8a551a277a89997f4109245.png deleted file mode 100644 index 328c02c59..000000000 Binary files a/dev/_images/e288043d732abf201db1bbb2866ad3378beee8f0f8a551a277a89997f4109245.png and /dev/null differ diff --git a/dev/_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg b/dev/_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg new file mode 100644 index 000000000..0a0877fe9 --- /dev/null +++ b/dev/_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg @@ -0,0 +1,35 @@ + + + + + + +%3 + + + +hgf_loglike + +hgf_loglike +~ +Potential + + + +tonic_volatility_2 + +tonic_volatility_2 +~ +Uniform + + + +tonic_volatility_2->hgf_loglike + + + + + \ No newline at end of file diff --git a/dev/_images/graph_network.svg b/dev/_images/graph_network.svg new file mode 100644 index 000000000..0218ad7b7 --- /dev/null +++ b/dev/_images/graph_network.svg @@ -0,0 +1,2578 @@ + + + +Update functionsUpdate sequencesPosterior updateAttributesEdgesPredictionPrediction errortt+1 diff --git a/dev/_sources/learn.md.txt b/dev/_sources/learn.md.txt index a18daa681..385388dca 100644 --- a/dev/_sources/learn.md.txt +++ b/dev/_sources/learn.md.txt @@ -67,7 +67,7 @@ How the generative model of the Hierarchical Gaussian filter can be turned into :::{grid-item-card} Creating and manipulating networks of probabilistic nodes :link: probabilistic_networks :link-type: ref -:img-top: ./images/graph_networks.svg +:img-top: ./images/graph_network.svg How to create and manipulate a network of probabilistic nodes for reinforcement learning? Working at the intersection of graphs, neural networks and probabilistic frameworks. ::: diff --git a/dev/_sources/notebooks/0.2-Creating_networks.ipynb.txt b/dev/_sources/notebooks/0.2-Creating_networks.ipynb.txt index a77d8f0b9..743923905 100644 --- a/dev/_sources/notebooks/0.2-Creating_networks.ipynb.txt +++ b/dev/_sources/notebooks/0.2-Creating_networks.ipynb.txt @@ -132,7 +132,7 @@ "\n", "This list describes the sequence of function-to-nodes instructions that are executed during the inference and update processes.\n", "\n", - "![graph_networks](../images/graph_networks.svg)\n", + "![graph_network](../images/graph_network.svg)\n", "\n", "```{tip} Compatibility with JAX transformations\n", "One of the advantages of reasoning this way is that it dissociates variables that are transparent to the JAX framework and can be expressed as \"PyTress\" from variables that should be filtered before transformations. The variable `attributes` ($\\theta$) is typically expressed as a PyTree while the other variables that contain parametrized functions are filtered. See [the documattion](https://jax.readthedocs.io/en/latest/notebooks/thinking_in_jax.html#jit-mechanics-tracing-and-static-variables) for further details on JAX transformations.\n", diff --git a/dev/learn.html b/dev/learn.html index ee5eb8f1e..784a9cef0 100644 --- a/dev/learn.html +++ b/dev/learn.html @@ -528,7 +528,7 @@

Theory#
- +
Creating and manipulating networks of probabilistic nodes
diff --git a/dev/notebooks/0.1-Theory.html b/dev/notebooks/0.1-Theory.html index 9a61d3f72..16d83c5ea 100644 --- a/dev/notebooks/0.1-Theory.html +++ b/dev/notebooks/0.1-Theory.html @@ -927,11 +927,11 @@

System configuration

diff --git a/dev/notebooks/0.2-Creating_networks.html b/dev/notebooks/0.2-Creating_networks.html index ba12bb19b..81f64745d 100644 --- a/dev/notebooks/0.2-Creating_networks.html +++ b/dev/notebooks/0.2-Creating_networks.html @@ -557,7 +557,7 @@

Theory and implementation details \[\Sigma = [f_1(n_1), ..., f_i(n_j), f \in \mathcal{F}, n \in 1, ..., k ]\]

This list describes the sequence of function-to-nodes instructions that are executed during the inference and update processes.

-

graph_networks

+

graph_network

Tip

Compatibility with JAX transformations @@ -754,7 +754,7 @@

Continuous value coupling -../_images/6ba51a89685df9218b30371921a00dac7688f5de6f9d278eb874564b67c5136a.png +../_images/4d7a8096e2f2372f704d28fc9e9b92e1c6c4ff9535432e9d14542bb869ccd5ee.png
@@ -967,7 +967,7 @@

Value coupling -
/tmp/ipykernel_2273/1724106460.py:6: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_2231/1724106460.py:6: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

@@ -1100,10 +1100,10 @@ 
System configuration
diff --git a/dev/notebooks/0.3-Generalised_filtering.html b/dev/notebooks/0.3-Generalised_filtering.html index 6a4731e18..8998744f9 100644 --- a/dev/notebooks/0.3-Generalised_filtering.html +++ b/dev/notebooks/0.3-Generalised_filtering.html @@ -994,12 +994,12 @@

System configuration

diff --git a/dev/notebooks/1.1-Binary_HGF.html b/dev/notebooks/1.1-Binary_HGF.html index 9d1cfa94d..4bfb3b889 100644 --- a/dev/notebooks/1.1-Binary_HGF.html +++ b/dev/notebooks/1.1-Binary_HGF.html @@ -776,7 +776,7 @@

Visualizing the model

-../_images/7d29572ae423fb4c8d4ea736f01dab651bf0ee09a3d53b5838bcf639ba2eaf01.svg +../_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg
@@ -814,10 +814,6 @@

Sampling "ipywidgets" for Jupyter support warnings.warn('install "ipywidgets" for Jupyter support') -
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
-"ipywidgets" for Jupyter support
-  warnings.warn('install "ipywidgets" for Jupyter support')
-

 

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.
@@ -835,7 +831,7 @@ 
Sampling
 

 

 

-../_images/a3c305ff27113cdffbd731a857652b2dd932a274e7b0c5bedeb3a0fe7b269fc5.png
+../_images/06334d74dea62d03736ed5ff69b1cbd6e5df290d314b5cbaf9bf5e3eae24452d.png
 

 
 
@@ -872,7 +868,7 @@ 
Using the learned parameters
-../_images/b33334f5c63409df2496cf92b0fc5fd94311d602dae2cb83ef4f1d0b6a1cbaf0.png
+../_images/3ac2ac56a5061c4dfe402ef793c1fa39ff840b69973563bb8e554a65772ed8e7.png
 
 
 

@@ -882,7 +878,7 @@ 
Using the learned parameters
-
Array(202.53, dtype=float32)
+
Array(202.53107, dtype=float32)
 

 

 

@@ -934,7 +930,7 @@ 
Visualizing the model
-../_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg
+../_images/69539e2739458d7218e514133841304a4e4b0eb711fc8054497123f2e226d095.svg
 

 

 
@@ -980,10 +976,6 @@ 
Sampling#
 "ipywidgets" for Jupyter support
   warnings.warn('install "ipywidgets" for Jupyter support')
 
-
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
-"ipywidgets" for Jupyter support
-  warnings.warn('install "ipywidgets" for Jupyter support')
-

 

 

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 9 seconds.
@@ -1003,7 +995,7 @@ 
Sampling#
 

 

 

-../_images/0564071d1880f558fc740741edd8ca2e61db996003f3f1edbcf0c91b0a39902e.png
+../_images/9ec896d2752649fcf664af855dd75db25e9c3c05294eea44a85d59f29f4d84b2.png
 

 
 
@@ -1041,7 +1033,7 @@ 
Using the learned parameters
-../_images/ae4f4840f241feb42ad3198f7dd2b8bcfae594202914db7daa6521070a721faa.png
+../_images/b57941e0d5c4edba1b42cd43e7413cee7aa938214f12d722746534a5c0d59112.png
 
 
 

@@ -1051,7 +1043,7 @@ 
Using the learned parameters
-
Array(203.0192, dtype=float32)
+
Array(203.01193, dtype=float32)
 

 

 

@@ -1079,11 +1071,11 @@ 
System configurationSimulating a dataset
 

 

-../_images/dc0d222dcfe1385508ef3f221b0fcd2d0ebc4f025f09569b9d250b27e018a7c2.png
+../_images/78ffd3a01762302291f05dad069b37af2710b6b55d7ad983a5a50e89733061d8.png
 

 

 

@@ -698,7 +698,7 @@ 
Fitting the model forwards
-../_images/814a296a3d5ba45eb453c55807a1b1430b18f7b7513122e9077e6b6d1af31c67.png
+../_images/df04c50a598763e25214aadc382bbf9d014e1de10891f6614d13a1a5fa7c6257.png
 

 
 
@@ -856,13 +856,13 @@ 
System configuration
diff --git a/dev/notebooks/1.3-Continuous_HGF.html b/dev/notebooks/1.3-Continuous_HGF.html
index 7ebe5e7d6..ed90ed090 100644
--- a/dev/notebooks/1.3-Continuous_HGF.html
+++ b/dev/notebooks/1.3-Continuous_HGF.html
@@ -873,10 +873,6 @@ 
Sampling
 "ipywidgets" for Jupyter support
   warnings.warn('install "ipywidgets" for Jupyter support')
 
-
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
-"ipywidgets" for Jupyter support
-  warnings.warn('install "ipywidgets" for Jupyter support')
-

 

 

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 7 seconds.
@@ -895,11 +891,11 @@ 
Sampling
 

 

 

-
/tmp/ipykernel_3137/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_3096/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/e288043d732abf201db1bbb2866ad3378beee8f0f8a551a277a89997f4109245.png
+../_images/d3114c8a6213cb146f6a8997c321bcd9973b364a8823e2aa3274328a72c66506.png
 

 

 
@@ -934,7 +930,7 @@ 
Using the learned parameters
-../_images/b1ebdbec5787b8c915620c04df80de2787306c989b8114b8f298fd93bff79efe.png
+../_images/04ba476165668d72a08c2a380fe6227dbbc0f7b1fb48247a858f2f14c37497d2.png
 

 
 

@@ -944,7 +940,7 @@ 
Using the learned parameters
-
Array(-1106.1144, dtype=float32)
+
Array(-1106.1195, dtype=float32)
 

 

 

@@ -1044,11 +1040,18 @@ 
Sampling#
 "ipywidgets" for Jupyter support
   warnings.warn('install "ipywidgets" for Jupyter support')
 
+
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
+"ipywidgets" for Jupyter support
+  warnings.warn('install "ipywidgets" for Jupyter support')
+

 

 

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 8 seconds.
 

 

+
There were 1 divergences after tuning. Increase `target_accept` or reparameterize.
+

+

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
 

 

@@ -1061,7 +1064,7 @@ 
Sampling#
 

 
 

-../_images/02d50512b4ae418f5375837aa92775400b80e4e22eb845907dd7168dcd7b0fb2.png
+../_images/3a0f76b6c4d871ca3fcc32a44a7a239e493649653bc8f7be5749ae0e5a7f3edc.png
 

 
 
@@ -1095,7 +1098,7 @@ 
Using the learned parameters
-../_images/dbab2b51169a1b91ae69e678f19a9e80cfc34b65b22d843517577420e2779bcb.png
+../_images/d1edc251cc2467c29958bb035ae47ad078dea8b3b408ed28d0fe452dd781005b.png
 
 
 

@@ -1105,7 +1108,7 @@ 
Using the learned parameters
-
Array(-1118.0496, dtype=float32)
+
Array(-1118.0265, dtype=float32)
 

 

 

@@ -1134,11 +1137,11 @@ 
System configuration

diff --git a/dev/notebooks/2-Using_custom_response_functions.html b/dev/notebooks/2-Using_custom_response_functions.html
index b93ae1e34..2185e65c9 100644
--- a/dev/notebooks/2-Using_custom_response_functions.html
+++ b/dev/notebooks/2-Using_custom_response_functions.html
@@ -967,19 +967,19 @@ 
Recovering HGF parameters from the observed behaviors
     
       tonic_volatility_2
-      -3.936
-      0.487
-      -4.844
-      -3.066
-      0.02
-      0.014
-      601.0
-      1217.0
-      1.01
+      -3.939
+      0.49
+      -4.829
+      -3.004
+      0.018
+      0.013
+      747.0
+      1359.0
+      1.0
     
   
 
-
../_images/89924152a56c33ccfa3204c63789e3f2f9eb919b53db59df63a698ae3fe1fe36.png
+../_images/25564f805e32fc7c22e4f64804c95fef19978c0e8b2a1c02e403155b1fa80863.png
 
 
 
The results above indicate that given the responses provided by the participant, the most likely values for the parameter \(\omega_2\) are between -4.9 and -3.1, with a mean at -3.9 (you can find slightly different values if you sample different actions from the decisions function). We can consider this as an excellent estimate given the sparsity of the data, and the complexity of the model.

@@ -1017,12 +1017,12 @@ 
System configurationPlot the computational graph
-../_images/14ce0fe48b4c42282a1f1418a319a9ecba80ec384cdb55da28354e40beca4ddf.svg
+../_images/7f83375f6bb4391f5e1312ee4a44e05aa4f48e556b396b42cb3261e32f9fb912.svg
 
 
 
@@ -831,6 +831,9 @@ 
Sampling
 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 45 seconds.
 

 

+
There were 1 divergences after tuning. Increase `target_accept` or reparameterize.
+

+

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
 

 

@@ -860,7 +863,7 @@ 
Visualization of the posterior distributions
-../_images/8db728f301bcd2082eef19d10e180d6e0a33ea2a3dfad6846cdff597346d9b2a.png
+../_images/25432f6d75602060a4bad305d793aca90494098794032fb1d2d1f394a706397c.png
 
 
 
The reference values on both posterior distributions indicate the mean of the distribution used for simulation.

@@ -887,16 +890,16 @@ 
Model comparison
Computed from 2000 posterior samples and 3200 observations log-likelihood matrix.
 
          Estimate       SE
-elpd_loo -1684.41    25.64
-p_loo       18.15        -
+elpd_loo -1684.38    25.64
+p_loo       18.10        -
 
 There has been a warning during the calculation. Please check the results.
 ------
 
 Pareto k diagnostic values:
                          Count   Pct.
-(-Inf, 0.70]   (good)     3185   99.5%
-   (0.70, 1]   (bad)         2    0.1%
+(-Inf, 0.70]   (good)     3187   99.6%
+   (0.70, 1]   (bad)         0    0.0%
    (1, Inf)   (very bad)   13    0.4%
 

 
@@ -924,14 +927,14 @@ 
System configuration
diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index b2dee6c81..07b0c71ba 100644
--- a/dev/notebooks/4-Parameter_recovery.html
+++ b/dev/notebooks/4-Parameter_recovery.html
@@ -685,9 +685,13 @@ 
Inference from the simulated behaviours
+
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
+"ipywidgets" for Jupyter support
+  warnings.warn('install "ipywidgets" for Jupyter support')
+

 

 

-
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 70 seconds.
+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 54 seconds.
 

 

 
There were 2000 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -760,7 +764,7 @@ 
Visualizing parameters recovery
-../_images/aa0fc414be4b661462a66791a6a06b32732f67982af09a7c9f8f8528079cf457.png
+../_images/7ac29c262916333d92fc28194fdceff517d3ecda9390770d8f16e9aeaa26f9d4.png
 

 

 
@@ -785,14 +789,14 @@ 
System configuration

diff --git a/dev/notebooks/5-Non_linear_value_coupling.html b/dev/notebooks/5-Non_linear_value_coupling.html
index 1ec4d542a..22ed12db8 100644
--- a/dev/notebooks/5-Non_linear_value_coupling.html
+++ b/dev/notebooks/5-Non_linear_value_coupling.html
@@ -932,12 +932,12 @@ 
System configuration
diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index 527cb40a8..41d5f2f8b 100644
--- a/dev/notebooks/Example_1_Heart_rate_variability.html
+++ b/dev/notebooks/Example_1_Heart_rate_variability.html
@@ -567,16 +567,16 @@ 
Loading and preprocessing physiological recording
Downloading ECG channel:   0%|          | 0/2 [00:00<?, ?it/s]
 

 
-
Downloading ECG channel:  50%|█████     | 1/2 [00:01<00:01,  1.03s/it]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:00<00:00,  1.15it/s]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:01<00:01,  1.03s/it]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  1.15it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.02it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.35it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.01it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.31it/s]
 

 

 

@@ -693,13 +693,9 @@ 
Model#<
 "ipywidgets" for Jupyter support
   warnings.warn('install "ipywidgets" for Jupyter support')
 

-
/opt/hostedtoolcache/Python/3.12.5/x64/lib/python3.12/site-packages/rich/live.py:231: UserWarning: install 
-"ipywidgets" for Jupyter support
-  warnings.warn('install "ipywidgets" for Jupyter support')
-

 

 

-
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 9 seconds.
+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 10 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -714,7 +710,7 @@ 
Model#<
 

 

 

-../_images/90685c5cae0e7b546798595c6eed168f1199cbb6dceb398a2aa1b47144491f9c.png
+../_images/22d404d3312dc67a4b50a6cd3767370913f0e81621739a6f7254902e6c5febfa.png
 

 

 

@@ -746,7 +742,7 @@ 
Model#<
 

 

 

-../_images/0ba65546358df322c0e9a37419861fdb72ea8464d7bce7f2793a2fd31f425acb.png
+../_images/766c9c1aca9edee0423e0175ef3997ee291e635c554f32931b03ade6df835a35.png
 

 

 
@@ -771,12 +767,12 @@ 
System configuration

diff --git a/dev/notebooks/Example_2_Input_node_volatility_coupling.html b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
index fed5c8649..909a33db4 100644
--- a/dev/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -698,11 +698,11 @@ 
System configuration

diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index c0ce6a6cc..e0b2969d6 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -1137,7 +1137,7 @@ 
Bayesian inference
-../_images/128d2d731899b9ac31c46042c08ac6493e2a74b7ec747afff2f129b4d49ba93c.png
+../_images/5601fc7000039a546a1148d8c43f5b57a8d0d2fa35dd6ce0aaa642757224dfa9.png
 

 

 
@@ -1162,14 +1162,14 @@ 
System configurationSystem configuration

diff --git a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
index a6cc3b571..40b6beeb9 100644
--- a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
+++ b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
@@ -729,7 +729,7 @@ 
Parameters optimization
 

 

-../_images/1e061dc0dd11f04e68a20b0f57a3087c2ad5d719eba4e38c5196874dbab3010e.png
+../_images/6c124353a22e3c8858a204cbb7ffe905b0b3cbd8c2fc72cbbcfe7e1b29bacd71.png
 

 

 

@@ -771,14 +771,14 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.567
-      0.388
-      -3.355
-      -1.889
-      0.016
-      0.012
-      620.0
-      557.0
+      -2.578
+      0.385
+      -3.282
+      -1.876
+      0.014
+      0.01
+      743.0
+      494.0
       1.0
     
   
@@ -843,7 +843,7 @@ 
Biased random
-../_images/4c4191b135346e26bfcee042f87e00916247057410c58490d37a3636fd237359.png
+../_images/51fda25b894f0eb9eab71d96d34d29d6af97801ce92b643e2c41fc605d59313b.png
 

 
 
Assess model fitting, here using leave-one-out cross-validation from the Arviz library.

@@ -924,7 +924,7 @@ 
Rescorla-Wagner

-
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 21 seconds.
+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 23 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -939,7 +939,7 @@ 
Rescorla-Wagner
-../_images/50863c50e8795cfc47856eebdc1f084072f8b46179f15a85128799dbc80ace09.png
+../_images/ad08c32d710aad4621155a93dc111666d613b308254d09a513a27ed9486be2ca.png
 

 

 
@@ -1059,7 +1059,7 @@ 
Two-level HGF
-../_images/914cd605f5f2a2a84217c9ef77c6dda6762bfbb9dd5ad944a12c60b531d034b2.png
+../_images/264883212d2563ab55e75af7697da9c922e4b5dbb4320c8edfe374a088736b43.png
 

 
 
We have saved the pointwise log probabilities as a variable, here we simply move this variable to the log_likelihoo field of the idata object, so Arviz knows that this can be used later for model comparison.

@@ -1178,7 +1178,7 @@ 
Three-level HGF
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 7 seconds.
 

 
-
There were 60 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 58 divergences after tuning. Increase `target_accept` or reparameterize.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1193,7 +1193,7 @@ 
Three-level HGF
-../_images/317c1c9786c818b7cd919671434f1449433afde1071f92cbdffd78499b4d457f.png
+../_images/3137124c3697d7d29702d87fef09593aaa269e8e7ad34ca6d6de35c76e712db2.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1266,11 +1266,11 @@ 
Model comparison
-../_images/b1c82bad5094f37ec32f6bddc01e212b07e88918256b787d213c4dc95c141476.png
+../_images/6a052e5f57f7ac6392ce614fb501095ae203a299bcc6e463d726f8366b226b23.png
 

 

 
Looking at the final result, we can see that the three-level HGF had the best predictive performance on the participant decision, suggesting that higher-level uncertainty is important here to understand the agent’s behaviour.

@@ -1439,7 +1439,7 @@ 
Beliefs trajectories
 
 

-../_images/9e9911d31fcdf444013d679b9fc0facd3e3be749fa6ec97fb72422c11217979b.png
+../_images/05d12e103eb7b1600b7a878baf77195ef9499447795dcb592d04dddfe437ad9f.png
 

 
 
The resulting samples show belief trajectories for 10 samples for each model (we are not depicting the biased random here for clarity). The trajectories are highly similar, but we can see that the two and three-level HGF are slightly adjusting their learning rates in a way that was more consistent with the observed behaviours.

@@ -1483,14 +1483,14 @@ 
System configuration
diff --git a/dev/searchindex.js b/dev/searchindex.js
index d38c3e12a..527bf9630 100644
--- a/dev/searchindex.js
+++ b/dev/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"": [[77, "exercise1"], [77, "exercise2"], [77, "exercise3"], [77, "exercise4"], [77, "exercise5"]], "API": [[0, "api"]], "Acknowledgments": [[62, "acknowledgments"]], "Add data": [[67, "add-data"], [67, "id4"], [69, "add-data"], [69, "id3"]], "Adding a drift to the random walk": [[64, "adding-a-drift-to-the-random-walk"]], "Application to reinforcement learning": [[78, null]], "Autoregressive processes": [[64, "autoregressive-processes"]], "Bayesian inference": [[76, "bayesian-inference"]], "Beliefs trajectories": [[78, "beliefs-trajectories"]], "Biased random": [[78, "biased-random"]], "Binary inputs": [[0, "binary-inputs"]], "Binary nodes": [[0, "binary-nodes"], [0, "id1"]], "Binary state nodes": [[0, "binary-state-nodes"]], "Bivariate normal distribution": [[66, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous inputs": [[0, "continuous-inputs"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id2"]], "Continuous state nodes": [[0, "continuous-state-nodes"]], "Continuous value coupling": [[65, "continuous-value-coupling"]], "Continuous volatility coupling": [[65, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[65, "coupling-with-binary-nodes"]], "Create the model": [[67, "create-the-model"], [67, "id3"], [69, "create-the-model"], [69, "id2"]], "Creating a new response function": [[70, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[70, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[65, null]], "Creating custom update functions": [[65, "creating-custom-update-functions"]], "Creating custom update sequences": [[65, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[65, "creating-probabilistic-nodes"]], "Creating the decision rule": [[70, "creating-the-decision-rule"]], "Creating the model": [[67, "creating-the-model"], [67, "id7"], [69, "creating-the-model"], [69, "id5"]], "Creating the probabilistic network": [[68, "creating-the-probabilistic-network"]], "Decision rule": [[76, "decision-rule"]], "Dirichlet processes": [[0, "dirichlet-processes"], [0, "id3"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[65, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[64, "dynamic-beliefs-updating"]], "Example 1: Bayesian filtering of cardiac volatility": [[74, null]], "Example 2: Estimating the mean and precision of an input node": [[75, null]], "Example 3: A multi-armed bandit task with independent rewards and punishments": [[76, null]], "Exercises": [[63, "exercises"]], "Exponential family": [[0, "exponential-family"]], "Filtering the Sufficient Statistics of a Non-Stationary Distribution": [[66, "filtering-the-sufficient-statistics-of-a-non-stationary-distribution"]], "Filtering the Sufficient Statistics of a Stationary Distribution": [[66, "filtering-the-sufficient-statistics-of-a-stationary-distribution"]], "Fitting behaviours to different RL models": [[78, "fitting-behaviours-to-different-rl-models"]], "Fitting the binary HGF with fixed parameters": [[67, "fitting-the-binary-hgf-with-fixed-parameters"]], "Fitting the continuous HGF with fixed parameters": [[69, "fitting-the-continuous-hgf-with-fixed-parameters"]], "Fitting the model forwards": [[68, "fitting-the-model-forwards"]], "Frequency tracking": [[73, "frequency-tracking"]], "From Reinforcement Learning to Generalised Bayesian Filtering": [[66, null]], "Gaussian Random Walks": [[64, "gaussian-random-walks"], [77, "gaussian-random-walks"]], "Generic input": [[0, "generic-input"]], "Getting started": [[62, "getting-started"]], "Glossary": [[64, "glossary"], [70, "glossary"]], "Group-level inference": [[71, "group-level-inference"]], "Hierarchical Bayesian modelling with probabilistic neural networks": [[71, null]], "How does it work?": [[62, "how-does-it-work"]], "How to cite?": [[1, null]], "Imports": [[67, "imports"]], "Inference from the simulated behaviours": [[72, "inference-from-the-simulated-behaviours"]], "Inference using MCMC sampling": [[68, "inference-using-mcmc-sampling"]], "Inputs": [[0, "inputs"]], "Installation": [[62, "installation"]], "Introduction to the Generalised Hierarchical Gaussian Filter": [[64, null]], "Introduction to the generalised Hierarchical Gaussian Filter": [[77, null]], "Kown mean, unknown precision": [[75, "kown-mean-unknown-precision"]], "Learn": [[63, null]], "Learning parameters with MCMC sampling": [[67, "learning-parameters-with-mcmc-sampling"], [69, "learning-parameters-with-mcmc-sampling"]], "Loading and preprocessing physiological recording": [[74, "loading-and-preprocessing-physiological-recording"]], "Math": [[0, "math"]], "Model": [[0, "model"], [74, "model"]], "Model comparison": [[71, "model-comparison"], [78, "model-comparison"]], "Model fitting": [[62, "model-fitting"]], "Model inversion: the generalized Hierarchical Gaussian Filter": [[77, "model-inversion-the-generalized-hierarchical-gaussian-filter"]], "Modifying the attributes": [[65, "modifying-the-attributes"]], "Modifying the edges": [[65, "modifying-the-edges"]], "Multivariate coupling": [[65, "multivariate-coupling"]], "Non-linear predictions": [[73, "non-linear-predictions"]], "Non-linear value coupling": [[73, null]], "Parameter recovery": [[76, "parameter-recovery"]], "Parameters optimization": [[78, "parameters-optimization"]], "Plot correlation": [[69, "plot-correlation"]], "Plot the computational graph": [[71, "plot-the-computational-graph"]], "Plot the signal with instantaneous heart rate derivations": [[74, "plot-the-signal-with-instantaneous-heart-rate-derivations"]], "Plot trajectories": [[67, "plot-trajectories"], [67, "id5"], [69, "plot-trajectories"], [69, "id4"]], "Plots": [[0, "plots"]], "Posterior predictive sampling": [[78, "posterior-predictive-sampling"]], "Posterior updates": [[0, 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"sampling"], [69, "id7"], [71, "sampling"]], "Simulate a dataset": [[71, "simulate-a-dataset"], [76, "simulate-a-dataset"]], "Simulate behaviours from a one-armed bandit task": [[72, "simulate-behaviours-from-a-one-armed-bandit-task"]], "Simulate responses from a participant": [[76, "simulate-responses-from-a-participant"]], "Simulating a dataset": [[68, "simulating-a-dataset"]], "Solution to Exercise 1": [[77, "solution-exercise1"]], "Solution to Exercise 2": [[77, "solution-exercise2"]], "Solution to Exercise 3": [[77, "solution-exercise3"]], "Solution to Exercise 4": [[77, "solution-exercise4"]], "Solutions": [[77, "solutions"], [78, "solutions"]], "State nodes": [[0, "state-nodes"]], "Static assignation of update sequences": [[65, "static-assignation-of-update-sequences"]], "Surprise": [[67, "surprise"], [67, "id6"], [69, "surprise"]], "System configuration": [[64, "system-configuration"], [65, "system-configuration"], [66, "system-configuration"], [67, "system-configuration"], 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