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tonic_volatility_2 tonic_volatility_2 ~ Uniform + + +hgf_loglike + +hgf_loglike +~ +Potential + tonic_volatility_2->hgf_loglike diff --git a/dev/_images/80b5037552fce7ba1519f75d844f096365f88a5a4fed9c435e1162142e6289ff.png b/dev/_images/80b5037552fce7ba1519f75d844f096365f88a5a4fed9c435e1162142e6289ff.png deleted file mode 100644 index 73ea80023..000000000 Binary files a/dev/_images/80b5037552fce7ba1519f75d844f096365f88a5a4fed9c435e1162142e6289ff.png and /dev/null differ diff --git a/dev/_images/4e0668e9782a5934896508a7172b853db66596f0d46a9e048d24b9f15823d9ee.svg b/dev/_images/80eb33bae911dfeb334d2afc621d8f0cc12934a6af7a5dcf1d05fddd43719a4c.svg similarity index 100% rename from dev/_images/4e0668e9782a5934896508a7172b853db66596f0d46a9e048d24b9f15823d9ee.svg rename to dev/_images/80eb33bae911dfeb334d2afc621d8f0cc12934a6af7a5dcf1d05fddd43719a4c.svg index 4e83bc9d2..ad950c2df 100644 --- a/dev/_images/4e0668e9782a5934896508a7172b853db66596f0d46a9e048d24b9f15823d9ee.svg +++ 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100644 index 000000000..71b122f11 Binary files /dev/null and b/dev/_images/e1fe190e0657ca858d27c49ba18dd490cbb71ae3d47767dfd05f14ed26689b5d.png differ diff --git a/dev/_images/906f003ac3c62510821da40b51513f921c716a616f423184ce543353e719929c.svg b/dev/_images/e23b939a310486df3afa5ada7aac1a37266da7c16855b27f94e2ecf820ea7441.svg similarity index 93% rename from dev/_images/906f003ac3c62510821da40b51513f921c716a616f423184ce543353e719929c.svg rename to dev/_images/e23b939a310486df3afa5ada7aac1a37266da7c16855b27f94e2ecf820ea7441.svg index 3357dc509..4dfa88bea 100644 --- a/dev/_images/906f003ac3c62510821da40b51513f921c716a616f423184ce543353e719929c.svg +++ b/dev/_images/e23b939a310486df3afa5ada7aac1a37266da7c16855b27f94e2ecf820ea7441.svg @@ -9,13 +9,13 @@ %3 - + -tonic_volatility_3 +tonic_volatility_2 -tonic_volatility_3 +tonic_volatility_2 ~ -Normal +Uniform @@ -25,23 +25,23 @@ ~ Potential - + -tonic_volatility_3->hgf_loglike +tonic_volatility_2->hgf_loglike - + -tonic_volatility_2 +tonic_volatility_3 -tonic_volatility_2 +tonic_volatility_3 ~ -Uniform +Normal - + -tonic_volatility_2->hgf_loglike +tonic_volatility_3->hgf_loglike diff --git a/dev/_images/e3167d393c55fb41be0e52818d3ef41370d0a22206ee5f3200044c3e96e06459.png b/dev/_images/e3167d393c55fb41be0e52818d3ef41370d0a22206ee5f3200044c3e96e06459.png new file mode 100644 index 000000000..61369bd3d Binary files /dev/null and b/dev/_images/e3167d393c55fb41be0e52818d3ef41370d0a22206ee5f3200044c3e96e06459.png differ diff --git a/dev/_images/f343c3431b7c69c62a3e7bc181951ac90beafdfccc9d74b57a88a04f3520486f.png b/dev/_images/f343c3431b7c69c62a3e7bc181951ac90beafdfccc9d74b57a88a04f3520486f.png deleted file mode 100644 index dde96eefd..000000000 Binary files a/dev/_images/f343c3431b7c69c62a3e7bc181951ac90beafdfccc9d74b57a88a04f3520486f.png and /dev/null differ diff --git a/dev/_images/fa5c9ef313501f5221c5ef956cab0158eb941917cc2e7bc532ef953e4ad297de.png 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b/dev/notebooks/0.1-Theory.html index 6d5e1bbdf..122c64841 100644 --- a/dev/notebooks/0.1-Theory.html +++ b/dev/notebooks/0.1-Theory.html @@ -921,19 +921,19 @@

System configuration
-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 IPython   : 8.29.0
 matplotlib: 3.9.2
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 numpy     : 1.26.0
 seaborn   : 0.13.2
 
diff --git a/dev/notebooks/0.2-Creating_networks.html b/dev/notebooks/0.2-Creating_networks.html
index 13f60e597..72d416a7d 100644
--- a/dev/notebooks/0.2-Creating_networks.html
+++ b/dev/notebooks/0.2-Creating_networks.html
@@ -778,7 +778,7 @@ 
Continuous value coupling
-../_images/650babe98f5eb4eaafa530aa26750f4f8eba7442313584a1628ceef30ad00d68.png
+../_images/170ebe24a2af59403c14f18564b3278f8fb6da5377d67508464bc4ec7548d147.png
 

 

 

@@ -1125,22 +1125,22 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-numpy     : 1.26.0
-IPython   : 8.29.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-matplotlib: 3.9.2
+IPython   : 8.29.0
 seaborn   : 0.13.2
-pyhgf     : 0.0.0.post1.dev0+388c79c
+numpy     : 1.26.0
+matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/0.3-Generalised_filtering.html b/dev/notebooks/0.3-Generalised_filtering.html
index 97cc97338..c8324cf04 100644
--- a/dev/notebooks/0.3-Generalised_filtering.html
+++ b/dev/notebooks/0.3-Generalised_filtering.html
@@ -984,23 +984,23 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-seaborn   : 0.13.2
-matplotlib: 3.9.2
-pyhgf     : 0.0.0.post1.dev0+388c79c
 IPython   : 8.29.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+seaborn   : 0.13.2
 jax       : 0.4.31
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 numpy     : 1.26.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+matplotlib: 3.9.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.1-Binary_HGF.html b/dev/notebooks/1.1-Binary_HGF.html
index d1ce69b4a..ebc326a14 100644
--- a/dev/notebooks/1.1-Binary_HGF.html
+++ b/dev/notebooks/1.1-Binary_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -803,7 +803,7 @@ 
Visualizing the model
 

 

-../_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg
+../_images/7d29572ae423fb4c8d4ea736f01dab651bf0ee09a3d53b5838bcf639ba2eaf01.svg
 

 

 
@@ -829,17 +829,14 @@ 
Sampling
 
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.
 

 

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

 

-
The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details
-

-

 

 

 

@@ -849,7 +846,7 @@ 
Sampling
 

 

 

-../_images/536e1b50b86d936e88003589f80485606a925aa5ff74b464a62f3d221648eaba.png
+../_images/e1fe190e0657ca858d27c49ba18dd490cbb71ae3d47767dfd05f14ed26689b5d.png
 

 

 
@@ -886,7 +883,7 @@ 
Using the learned parameters
-../_images/785c4e883d2d589f0109f5810c8cbae83ddc0fd6851a2ade38297b77cd977758.png
+../_images/b86cd998559c7def1f5df5fb9ebc7ebaac5192ccd7639d1a4f931fbb681ae7a6.png
 

 

 

@@ -896,7 +893,7 @@ 
Using the learned parameters
-
Array(202.5304, dtype=float32)
+
Array(202.5296, dtype=float32)
 

 

 

@@ -948,7 +945,7 @@ 
Visualizing the model
-../_images/906f003ac3c62510821da40b51513f921c716a616f423184ce543353e719929c.svg
+../_images/e23b939a310486df3afa5ada7aac1a37266da7c16855b27f94e2ecf820ea7441.svg
 

 

 
@@ -974,8 +971,8 @@ 
Sampling#
 
NUTS: [tonic_volatility_2, tonic_volatility_3]
 

 

-

-

+

+

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

 

@@ -993,7 +990,7 @@ 
Sampling#
 

 

 

-../_images/9516d89c9f0c1e3779538a26a2ff922b1aaf6864f3c79b8036d98022dda28f17.png
+../_images/5484c7a6143972525f8c006439155cfb13d71e0edf5b9f3e708c18f2f08b8cee.png
 

 

 
@@ -1031,7 +1028,7 @@ 
Using the learned parameters
-../_images/80b5037552fce7ba1519f75d844f096365f88a5a4fed9c435e1162142e6289ff.png
+../_images/b85d26e12a2129435e30c270530596c792e6d3d2df2f8cd3b19d001b4ce3b94f.png
 

 
 

@@ -1041,7 +1038,7 @@ 
Using the learned parameters
-
Array(203.0253, dtype=float32)
+
Array(203.00745, dtype=float32)
 

 

 

@@ -1059,23 +1056,23 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
+pymc      : 5.17.0
 arviz     : 0.20.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+matplotlib: 3.9.2
 jax       : 0.4.31
 IPython   : 8.29.0
-pymc      : 5.17.0
-matplotlib: 3.9.2
-pyhgf     : 0.0.0.post1.dev0+388c79c
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.2-Categorical_HGF.html b/dev/notebooks/1.2-Categorical_HGF.html
index 144ede16e..169531523 100644
--- a/dev/notebooks/1.2-Categorical_HGF.html
+++ b/dev/notebooks/1.2-Categorical_HGF.html
@@ -587,7 +587,7 @@ 
Simulating a dataset
 

 

-../_images/f343c3431b7c69c62a3e7bc181951ac90beafdfccc9d74b57a88a04f3520486f.png
+../_images/2df683e9c5dd47675cd8f977900000cfd78098a4eeae16ba51c3a490cf75a7ec.png
 

 

 

@@ -701,7 +701,7 @@ 
Fitting the model forwards
-../_images/3775fe2b1cd77b133efb2c111d2ada83090fea72c2c2c62c91b6d165ca6f0d7e.png
+../_images/52318f2960fdcf74f1e770cff800b8bc34b7014bc37a0e22d0f108614bedef8b.png
 

 

 
@@ -849,24 +849,24 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pytensor  : 2.25.5
-numpy     : 1.26.0
-seaborn   : 0.13.2
-pyhgf     : 0.0.0.post1.dev0+388c79c
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 jax       : 0.4.31
 IPython   : 8.29.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+numpy     : 1.26.0
+pytensor  : 2.25.5
 matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+seaborn   : 0.13.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.3-Continuous_HGF.html b/dev/notebooks/1.3-Continuous_HGF.html
index 99f0ebee3..37370dfbd 100644
--- a/dev/notebooks/1.3-Continuous_HGF.html
+++ b/dev/notebooks/1.3-Continuous_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -854,7 +854,7 @@ 
Visualizing the model
 

 

-../_images/276f245ebd9fd4bcae5e926f51a69ac0c4a8b7994776641b7ca80207aba0e073.svg
+../_images/0747ca4d2db1d73075db0036fa2d7adb40e86a06d3c587c73103c1d2a5698bb6.svg
 

 

 
@@ -880,8 +880,8 @@ 
Sampling
 
NUTS: [tonic_volatility_1]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 7 seconds.
 

 

@@ -898,11 +898,11 @@ 
Sampling
 

 

 

-
/tmp/ipykernel_2792/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_2672/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/b4ee11bd9cf047f0c0797525665fbdc4a79caf688343f74df9cb0a1db6b94055.png
+../_images/38e341e2b246b82ac0aaf0a83102cc806d9297cea1024cdc0dd9abd04ed255f3.png
 

 

 
@@ -937,7 +937,7 @@ 
Using the learned parameters
-../_images/4ab50732bcd05d082d0f892f89a63f5c6ae73cfdee140fe0cbb3e2c05c383d79.png
+../_images/0654015973a91d306adb272fbcc4682092de2e20d14e9438c2a0d62578a1f8bd.png
 

 

 

@@ -947,7 +947,7 @@ 
Using the learned parameters
-
Array(-1106.0854, dtype=float32)
+
Array(-1106.1259, dtype=float32)
 

 

 

@@ -997,7 +997,7 @@ 
Visualizing the model
-../_images/276f245ebd9fd4bcae5e926f51a69ac0c4a8b7994776641b7ca80207aba0e073.svg
+../_images/0747ca4d2db1d73075db0036fa2d7adb40e86a06d3c587c73103c1d2a5698bb6.svg
 

 

 
@@ -1023,8 +1023,8 @@ 
Sampling#
 
NUTS: [tonic_volatility_1]
 

 

-

-

+

+

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

 

@@ -1040,7 +1040,7 @@ 
Sampling#
 

 

 

-../_images/1a5f0d4050a93bd46b377379b4e0a6a5487e1fd7f67d226ed9f38273b0aafd13.png
+../_images/b42d163d3664ceea2d285c8746a05dcbaf0148e862ad7a1109e42b1ac8f1ef58.png
 

 
 
@@ -1074,7 +1074,7 @@ 
Using the learned parameters
-../_images/ffa7d51c2cee0d03faae07019dfe502e65a87e9b406b61881c17c703493a6c04.png
+../_images/1eae935e686318a9301a4de4fd0db93a9f5e531ae67db1c425897db03fdded0e.png
 
 
 

@@ -1084,7 +1084,7 @@ 
Using the learned parameters
-
Array(-1118.0106, dtype=float32)
+
Array(-1117.9713, dtype=float32)
 

 

 

@@ -1102,23 +1102,23 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 IPython   : 8.29.0
-matplotlib: 3.9.2
 pymc      : 5.17.0
-pyhgf     : 0.0.0.post1.dev0+388c79c
-arviz     : 0.20.0
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+matplotlib: 3.9.2
 jax       : 0.4.31
+arviz     : 0.20.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/2-Using_custom_response_functions.html b/dev/notebooks/2-Using_custom_response_functions.html
index 75cdee14e..5cb32ca12 100644
--- a/dev/notebooks/2-Using_custom_response_functions.html
+++ b/dev/notebooks/2-Using_custom_response_functions.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -890,8 +890,8 @@ 
Recovering HGF parameters from the observed behaviors
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.
 

 

@@ -940,19 +940,19 @@ 
Recovering HGF parameters from the observed behaviors
     
       tonic_volatility_2
-      -3.941
-      0.491
-      -4.884
-      -3.058
+      -3.955
+      0.497
+      -4.837
+      -2.989
       0.016
       0.012
-      917.0
-      1467.0
+      933.0
+      1068.0
       1.0
     
   
 
-
../_images/6c0afb4bb7d69218703e03ecd78554b9babed78800ccd121a2aff09b0c37cdf4.png
+
../_images/6c2bf7de3f7d18a57837c1922538813665b83c28181311dd5a673fb08b6d81a5.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.

@@ -980,24 +980,24 @@ 
System configuration
 
 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-arviz     : 0.20.0
-jax       : 0.4.31
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-matplotlib: 3.9.2
 IPython   : 8.29.0
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+matplotlib: 3.9.2
 numpy     : 1.26.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 pymc      : 5.17.0
-pyhgf     : 0.0.0.post1.dev0+388c79c
+arviz     : 0.20.0
+jax       : 0.4.31
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/3-Multilevel_HGF.html b/dev/notebooks/3-Multilevel_HGF.html
index 5ef2d5fac..dc6b3aa42 100644
--- a/dev/notebooks/3-Multilevel_HGF.html
+++ b/dev/notebooks/3-Multilevel_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -806,7 +806,7 @@ 
Plot the computational graph
-../_images/4e0668e9782a5934896508a7172b853db66596f0d46a9e048d24b9f15823d9ee.svg
+../_images/80eb33bae911dfeb334d2afc621d8f0cc12934a6af7a5dcf1d05fddd43719a4c.svg
 

 

 
@@ -832,11 +832,14 @@ 
Sampling
 
NUTS: [mu_volatility, sigma_volatility, volatility, mu_temperature, sigma_temperature, inverse_temperature]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 43 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
 

 

@@ -866,7 +869,7 @@ 
Visualization of the posterior distributions
-../_images/3a135af3dcff6c879f0659b361c5c0c0264db10faca31cbe4cb35b165e24af84.png
+../_images/e3167d393c55fb41be0e52818d3ef41370d0a22206ee5f3200044c3e96e06459.png
 

 

 
The reference values on both posterior distributions indicate the mean of the distribution used for simulation.

@@ -893,8 +896,8 @@ 
Model comparison
Computed from 2000 posterior samples and 3200 observations log-likelihood matrix.
 
          Estimate       SE
-elpd_loo -1684.32    25.64
-p_loo       18.06        -
+elpd_loo -1684.51    25.61
+p_loo       18.24        -
 
 There has been a warning during the calculation. Please check the results.
 ------
@@ -902,8 +905,8 @@ 
Model comparison
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-IPython   : 8.29.0
 seaborn   : 0.13.2
-arviz     : 0.20.0
 pytensor  : 2.25.5
-matplotlib: 3.9.2
 pymc      : 5.17.0
-pyhgf     : 0.0.0.post1.dev0+388c79c
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+arviz     : 0.20.0
 numpy     : 1.26.0
+IPython   : 8.29.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+matplotlib: 3.9.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index cc65de96a..0ae727cbb 100644
--- a/dev/notebooks/4-Parameter_recovery.html
+++ b/dev/notebooks/4-Parameter_recovery.html
@@ -50,7 +50,7 @@
     
     
     
-    
+    
     
     
     
@@ -676,9 +676,9 @@ 
Inference from the simulated behaviours
NUTS: [censored_volatility, inverse_temperature]
 

 

-

-

-
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 53 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 62 seconds.
 

 

 
There were 2000 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -751,7 +751,7 @@ 
Visualizing parameters recovery
-../_images/dcfb715e1b9875ee4fb1e188534363ddb0ab3215ffa149b8380c6b1214b46cc0.png
+../_images/0a1fb71846ff56a2d69b8c8660b0a202deea451c1d767b65eb4da5ee4b09e623.png
 

 

 
@@ -766,25 +766,25 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-IPython   : 8.29.0
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+arviz     : 0.20.0
+pymc      : 5.17.0
 seaborn   : 0.13.2
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+IPython   : 8.29.0
 matplotlib: 3.9.2
-pymc      : 5.17.0
-arviz     : 0.20.0
-numpy     : 1.26.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 jax       : 0.4.31
-pyhgf     : 0.0.0.post1.dev0+388c79c
+numpy     : 1.26.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/5-Non_linear_value_coupling.html b/dev/notebooks/5-Non_linear_value_coupling.html
index e5e4ac7f6..7da59a01f 100644
--- a/dev/notebooks/5-Non_linear_value_coupling.html
+++ b/dev/notebooks/5-Non_linear_value_coupling.html
@@ -978,23 +978,23 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pyhgf     : 0.0.0.post1.dev0+388c79c
-IPython   : 8.29.0
+seaborn   : 0.13.2
 numpy     : 1.26.0
+matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
+IPython   : 8.29.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 jax       : 0.4.31
-seaborn   : 0.13.2
-matplotlib: 3.9.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index 903327373..128726ac7 100644
--- a/dev/notebooks/Example_1_Heart_rate_variability.html
+++ b/dev/notebooks/Example_1_Heart_rate_variability.html
@@ -50,7 +50,7 @@
     
     
     
-    
+    
     
     
     
@@ -574,16 +574,16 @@ 
Loading and preprocessing physiological recording
Downloading ECG channel:   0%|          | 0/2 [00:00<?, ?it/s]
 

 

-
Downloading ECG channel:  50%|█████     | 1/2 [00:00<00:00,  1.35it/s]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:01<00:01,  1.46s/it]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  1.35it/s]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:01<00:01,  1.46s/it]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.23it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.18s/it]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.25it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.22s/it]
 

 

 

@@ -680,8 +680,8 @@ 
Model#<
 
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 11 seconds.
 

 

@@ -697,7 +697,7 @@ 
Model#<
 

 

 

-../_images/8984e47d50d9e601565862b53bae9b25aee55ff824cfb5a9ce4a0a223c87a3cc.png
+../_images/aa36a2480d89139474b84a2022ca8c230d467137bc8c969c07cade59b4ee36fb.png
 

 

 

@@ -729,7 +729,7 @@ 
Model#<
 

 

 

-../_images/7b0744c7e5b69a849d2431fb1af104b4e10e748028ff4716238396c0bf74a2da.png
+../_images/a1a0e916f2ce0120e93a63c17eef7a7370bbbd0cf48f1d624d5dc887827a45fc.png
 

 

 
@@ -744,24 +744,24 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
 pymc      : 5.17.0
+numpy     : 1.26.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+arviz     : 0.20.0
 matplotlib: 3.9.2
 IPython   : 8.29.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 systole   : 0.3.0
-pyhgf     : 0.0.0.post1.dev0+388c79c
-numpy     : 1.26.0
-arviz     : 0.20.0
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/Example_2_Input_node_volatility_coupling.html b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
index c1131f07c..48b85d924 100644
--- a/dev/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -694,22 +694,22 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-numpy     : 1.26.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-pyhgf     : 0.0.0.post1.dev0+388c79c
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 IPython   : 8.29.0
-matplotlib: 3.9.2
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 seaborn   : 0.13.2
+numpy     : 1.26.0
+matplotlib: 3.9.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index a31ed718d..2331c0599 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -1085,14 +1085,11 @@ 
Bayesian inference
NUTS: [omega]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 7 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
 

 

@@ -1108,7 +1105,7 @@ 
Bayesian inference
-../_images/96c70d75c9316ce896506c28e43db0960411e4eedb1e51b82873f27c453b0ccc.png
+../_images/df6b7cbc84dafbc0092dc0a013f4342f9b6876625305b25aabb6ee0d4a6a47fe.png
 

 

 
@@ -1123,25 +1120,25 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
 numpy     : 1.26.0
-jax       : 0.4.31
-seaborn   : 0.13.2
-pyhgf     : 0.0.0.post1.dev0+388c79c
 arviz     : 0.20.0
-pymc      : 5.17.0
-pytensor  : 2.25.5
 matplotlib: 3.9.2
+pytensor  : 2.25.5
+jax       : 0.4.31
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pymc      : 5.17.0
+seaborn   : 0.13.2
 IPython   : 8.29.0
 
 Watermark: 2.5.0
diff --git a/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html b/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
index efff74541..3163fc404 100644
--- a/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
+++ b/dev/notebooks/Exercise_1_Introduction_to_the_generalised_hierarchical_gaussian_filter.html
@@ -1034,23 +1034,23 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pyhgf     : 0.0.0.post1.dev0+388c79c
+pandas    : 2.2.3
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 IPython   : 8.29.0
 matplotlib: 3.9.2
-seaborn   : 0.13.2
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-pandas    : 2.2.3
 numpy     : 1.26.0
+seaborn   : 0.13.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
index 9fdd04579..758b0a779 100644
--- a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
+++ b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -703,7 +703,7 @@ 
Parameters optimization
 

 

-../_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg
+../_images/7d29572ae423fb4c8d4ea736f01dab651bf0ee09a3d53b5838bcf639ba2eaf01.svg
 

 

 

@@ -726,8 +726,8 @@ 
Parameters optimization
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.
 

 

@@ -743,7 +743,7 @@ 
Parameters optimization
 

 

-../_images/fa5c9ef313501f5221c5ef956cab0158eb941917cc2e7bc532ef953e4ad297de.png
+../_images/631c0c58966b536a9ed919fea3540fce7f0a3fcb7cc4dffcd03965b0763cba64.png
 

 

 

@@ -785,14 +785,14 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.598
-      0.401
-      -3.386
-      -1.887
-      0.019
-      0.014
-      410.0
-      251.0
+      -2.567
+      0.393
+      -3.299
+      -1.84
+      0.016
+      0.012
+      593.0
+      451.0
       1.0
     
   
@@ -836,8 +836,8 @@ 
Biased random
NUTS: [bias]
 

 

-

-

+

+

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

 

@@ -853,7 +853,7 @@ 
Biased random
-../_images/38fd2f6a2470f0f3da86dda245b6161ea20e3bd2e88bebdf127623d37fa6f802.png
+../_images/b6798699050a13f68aab11dbe4e0eb92d18170d7f346898a0de9f2063e96bf8c.png
 

 

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

@@ -925,12 +925,12 @@ 
Rescorla-Wagner{"version_major": 2, "version_minor": 0, "model_id": "e5378586906640f980f913fb7032e702"}
/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
+
/opt/hostedtoolcache/Python/3.12.7/x64/lib/python3.12/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
   self.pid = os.fork()
 

 

 

-
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 23 seconds.
+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 22 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -945,7 +945,7 @@ 
Rescorla-Wagner
-../_images/4923a87ee27e01e46361a45378d9a030c1fc8f00104456a336eda8eed7311f29.png
+../_images/272582ce5178828bdec6aea21d2ff8ecb23bfada59a9589e5efd762c7b38eea3.png
 

 

 
@@ -1036,8 +1036,8 @@ 
Two-level HGF
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.
 

 

@@ -1053,7 +1053,7 @@ 
Two-level HGF
-../_images/818fe4c65acb51ca1a988f8abf2abeb03d6c4059839a2cf91b514c132fe6561a.png
+../_images/414230378b6204c6024c01f9b0cab3f6da8cf2619ab2962cb5f60ee7f1c7f471.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.

@@ -1147,12 +1147,12 @@ 
Three-level HGF
NUTS: [tonic_volatility_2]
 

 

-

-

+

+

 
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 7 seconds.
 

 

-
There were 72 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 66 divergences after tuning. Increase `target_accept` or reparameterize.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1167,7 +1167,7 @@ 
Three-level HGF
-../_images/300716b311017ed59f7b96db199303d802131814888afd7eccb8f529df31153e.png
+../_images/b59e4c39c0affdd0425f1baef237f26596df3be32c4e68ed337d3c48a75a641f.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1240,11 +1240,11 @@ 
Model comparison
-../_images/ff19c1374f2eb28383b9ea44e3121b9d1b96fd03acd4086329620e2eb1fc1cbd.png
+../_images/cab5b47ef477b1050ece447e110fdd547961d1aa45550614e879cfaa13c92849.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.

@@ -1413,7 +1413,7 @@ 
Beliefs trajectories
 
 

-../_images/49053789a80ac1c23113d94699094f36e4eef6d139981b76163b3e90a2e0e4ed.png
+../_images/0f82fea3137470fabc42c7cdddaa3a39252881fee67615481ac9038267a40e54.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.

@@ -1476,25 +1476,25 @@ 
System configuration
 

 

-
Last updated: Tue Nov 26 2024
+
Last updated: Wed Nov 27 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+388c79c
+pyhgf : 0.0.0.post1.dev0+0d45e3e
 jax   : 0.4.31
 jaxlib: 0.4.31
 
 arviz     : 0.20.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-numpy     : 1.26.0
-matplotlib: 3.9.2
+seaborn   : 0.13.2
 IPython   : 8.29.0
-pymc      : 5.17.0
+pyhgf     : 0.0.0.post1.dev0+0d45e3e
 pytensor  : 2.25.5
-pyhgf     : 0.0.0.post1.dev0+388c79c
-seaborn   : 0.13.2
+matplotlib: 3.9.2
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pymc      : 5.17.0
+numpy     : 1.26.0
 
 Watermark: 2.5.0
 

diff --git a/dev/searchindex.js b/dev/searchindex.js
index 3e7af5ecf..4e806309b 100644
--- a/dev/searchindex.js
+++ b/dev/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"": [[80, "exercise1.1"], [80, "exercise1.2"], [80, "exercise1.3"], [80, "exercise1.4"], [80, "exercise1.5"], [80, "exercise1.6"], [81, "exercise2.1"], [81, "exercise2.2"]], "API": [[0, "api"]], "Acknowledgments": [[65, "acknowledgments"]], "Add data": [[70, "add-data"], [70, "id4"], [72, "add-data"], [72, "id3"]], "Adding a drift to the random walk": [[67, "adding-a-drift-to-the-random-walk"]], "Autoregressive processes": [[67, "autoregressive-processes"]], "Bayesian inference": [[79, "bayesian-inference"]], "Beliefs trajectories": [[81, "beliefs-trajectories"]], "Biased random": [[81, "biased-random"]], "Binary nodes": [[0, "binary-nodes"]], "Bivariate normal distribution": [[69, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id1"]], "Continuous value coupling": [[68, "continuous-value-coupling"]], "Continuous volatility coupling": [[68, 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"decision-rule"]], "Dirichlet processes": [[0, "dirichlet-processes"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[68, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[67, "dynamic-beliefs-updating"]], "Example 1: Bayesian filtering of cardiac volatility": [[77, null]], "Example 2: Estimating the mean and precision of a time-varying Gaussian distributions": [[78, null]], "Example 3: A multi-armed bandit task with independent rewards and punishments": [[79, null]], "Exercises": [[66, "exercises"]], "Filtering the Sufficient Statistics of a Non-Stationary Distribution": [[69, "filtering-the-sufficient-statistics-of-a-non-stationary-distribution"]], "Filtering the Sufficient Statistics of a Stationary Distribution": [[69, "filtering-the-sufficient-statistics-of-a-stationary-distribution"]], "Fitting behaviours to different RL models": [[81, "fitting-behaviours-to-different-rl-models"]], "Fitting the binary HGF with fixed parameters": [[70, "fitting-the-binary-hgf-with-fixed-parameters"]], "Fitting the continuous HGF with fixed parameters": [[72, "fitting-the-continuous-hgf-with-fixed-parameters"]], "Fitting the model forwards": [[71, "fitting-the-model-forwards"]], "Frequency tracking": [[76, "frequency-tracking"]], "From Reinforcement Learning to Generalised Bayesian Filtering": [[69, null]], "Gaussian Random Walks": [[67, "gaussian-random-walks"], [80, "gaussian-random-walks"]], "Getting started": [[65, "getting-started"]], "Glossary": [[67, "glossary"], [73, "glossary"]], "Group-level inference": [[74, "group-level-inference"]], "Hierarchical Bayesian modelling with probabilistic neural networks": [[74, null]], "How does it work?": [[65, "how-does-it-work"]], "How to cite?": [[1, null]], "Imports": [[70, "imports"]], "Inference from the simulated behaviours": [[75, "inference-from-the-simulated-behaviours"]], "Inference using MCMC sampling": [[71, "inference-using-mcmc-sampling"]], "Installation": [[65, "installation"]], "Introduction to the Generalised Hierarchical Gaussian Filter": [[67, null]], "Kown mean, unknown precision": [[78, "kown-mean-unknown-precision"]], "Learn": [[66, null]], "Learning parameters with MCMC sampling": [[70, "learning-parameters-with-mcmc-sampling"], [72, "learning-parameters-with-mcmc-sampling"]], "Loading and preprocessing physiological recording": [[77, "loading-and-preprocessing-physiological-recording"]], "Math": [[0, "math"]], "Model": [[0, "model"], [77, "model"]], "Model comparison": [[74, "model-comparison"], [81, "model-comparison"]], "Model fitting": [[65, "model-fitting"]], "Model inversion: the generalized Hierarchical Gaussian Filter": [[80, "model-inversion-the-generalized-hierarchical-gaussian-filter"]], "Modifying the attributes": [[68, "modifying-the-attributes"]], "Modifying the edges": [[68, "modifying-the-edges"]], "Multivariate coupling": [[68, "multivariate-coupling"]], "Non-linear predictions": [[76, "non-linear-predictions"]], "Non-linear value coupling between continuous state nodes": [[76, null]], "Parameter recovery": [[79, "parameter-recovery"]], "Parameters optimization": [[81, "parameters-optimization"]], "Plot correlation": [[72, "plot-correlation"]], "Plot the computational graph": [[74, "plot-the-computational-graph"]], "Plot the signal with instantaneous heart rate derivations": [[77, "plot-the-signal-with-instantaneous-heart-rate-derivations"]], "Plot trajectories": [[70, "plot-trajectories"], [70, "id5"], [72, "plot-trajectories"], [72, "id4"]], "Plots": [[0, "plots"]], "Posterior predictive sampling": [[81, "posterior-predictive-sampling"]], "Posterior updates": [[0, "posterior-updates"]], "Practice: Filtering the worlds weather": [[80, "practice-filtering-the-worlds-weather"]], "Prediction error steps": [[0, "prediction-error-steps"]], "Prediction steps": [[0, "prediction-steps"]], "Preprocessing": [[77, "preprocessing"]], "Probabilistic coupling between nodes": 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"the-categorical-state-node"]], "The categorical state-transition node": [[71, "the-categorical-state-transition-node"]], "The continuous Hierarchical Gaussian Filter": [[72, null]], "The generative model": [[67, "the-generative-model"], [80, "the-generative-model"]], "The propagation of prediction and prediction errors": [[67, "the-propagation-of-prediction-and-prediction-errors"]], "The three-level binary Hierarchical Gaussian Filter": [[70, "the-three-level-binary-hierarchical-gaussian-filter"]], "The three-level continuous Hierarchical Gaussian Filter": [[72, "the-three-level-continuous-hierarchical-gaussian-filter"]], "The two-level binary Hierarchical Gaussian Filter": [[70, "the-two-level-binary-hierarchical-gaussian-filter"]], "The two-level continuous Hierarchical Gaussian Filter": [[72, "the-two-level-continuous-hierarchical-gaussian-filter"]], "Theory": [[66, "theory"]], "Theory and implementation details": [[68, "theory-and-implementation-details"]], "Three-level HGF": [[81, "three-level-hgf"]], "Three-level model": [[70, "three-level-model"], [72, "three-level-model"]], "Time-varying update sequences": [[68, "time-varying-update-sequences"]], "Tutorials": [[66, "tutorials"]], "Two-level HGF": [[81, "two-level-hgf"]], "Two-level model": [[70, "two-level-model"], [72, "two-level-model"]], "Univariate normal distribution": [[69, "univariate-normal-distribution"]], "Unkown mean, known precision": [[78, "unkown-mean-known-precision"]], "Unkown mean, unknown precision": [[78, "unkown-mean-unknown-precision"]], "Update functions": [[68, "update-functions"]], "Updates functions": [[0, "updates-functions"]], "Use cases": [[66, "use-cases"]], "Using a dynamically adapted \\nu through a collection of Hierarchical Gaussian Filters": [[69, "using-a-dynamically-adapted-nu-through-a-collection-of-hierarchical-gaussian-filters"]], "Using a fixed \\nu": [[69, "using-a-fixed-nu"]], "Using custom response models": [[73, null]], "Using the learned parameters": [[70, 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