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b/dev/_images/8fc9c210ab62f5dd9a3be3ce533d3c8c7ee05351b66a0f94da4f8a26be10ae39.svg similarity index 100% rename from dev/_images/8f02834ccc45a1fbb4bd4aabfac2d75a89a86b3ef90438ded772ac7bf43de688.svg rename to dev/_images/8fc9c210ab62f5dd9a3be3ce533d3c8c7ee05351b66a0f94da4f8a26be10ae39.svg index 0255e9b57..a85f1c417 100644 --- a/dev/_images/8f02834ccc45a1fbb4bd4aabfac2d75a89a86b3ef90438ded772ac7bf43de688.svg +++ b/dev/_images/8fc9c210ab62f5dd9a3be3ce533d3c8c7ee05351b66a0f94da4f8a26be10ae39.svg @@ -9,22 +9,22 @@ %3 - - -hgf_loglike - -hgf_loglike -~ -Potential - - + tonic_volatility_2 tonic_volatility_2 ~ Normal + + +hgf_loglike + +hgf_loglike +~ +Potential + tonic_volatility_2->hgf_loglike diff --git a/dev/_images/92274084c43343457cfbe933888bb1dd2716bf25083d3e45ea9d19e3ddb37e73.png b/dev/_images/92274084c43343457cfbe933888bb1dd2716bf25083d3e45ea9d19e3ddb37e73.png deleted file mode 100644 index e4588727f..000000000 Binary files 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0a0877fe9..000000000 --- a/dev/_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg +++ /dev/null @@ -1,35 +0,0 @@ - - - - - - -%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/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png b/dev/_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png new file mode 100644 index 000000000..e8393c60e Binary files /dev/null and b/dev/_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png differ diff --git a/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png b/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png new file mode 100644 index 000000000..b818df1a6 Binary files /dev/null and b/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png differ diff --git a/dev/_images/fb30ad50512fa98d7a3ccb9ce3bbeaa964e8971e08bdf749547c02cfcebfaaac.png b/dev/_images/fb30ad50512fa98d7a3ccb9ce3bbeaa964e8971e08bdf749547c02cfcebfaaac.png deleted file mode 100644 index ee2461402..000000000 Binary files a/dev/_images/fb30ad50512fa98d7a3ccb9ce3bbeaa964e8971e08bdf749547c02cfcebfaaac.png and /dev/null differ diff --git a/dev/notebooks/0.1-Theory.html b/dev/notebooks/0.1-Theory.html index 7f3bcd0ff..b0a8fd0db 100644 --- a/dev/notebooks/0.1-Theory.html +++ b/dev/notebooks/0.1-Theory.html @@ -921,21 +921,21 @@

System configuration
-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
 IPython   : 8.29.0
-numpy     : 1.26.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-matplotlib: 3.9.2
+numpy     : 1.26.0
 seaborn   : 0.13.2
+matplotlib: 3.9.2
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/0.2-Creating_networks.html b/dev/notebooks/0.2-Creating_networks.html
index 15428a5dd..4401b499e 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/9a1bacc5a7efe588e6e951b4a45f3b5cb1c4b8985b1fc3506d07ed6cf4b79189.png
+../_images/2167ccc99323c237c9015c8b5c3e2c5ff0df0ea271d023c5adf6a809dfe368ab.png
@@ -1125,22 +1125,22 @@

System configuration

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-pyhgf     : 0.0.0.post1.dev0+d064162
-numpy     : 1.26.0
-seaborn   : 0.13.2
 IPython   : 8.29.0
+pyhgf     : 0.0.0.post1.dev0+304ea45
+seaborn   : 0.13.2
 matplotlib: 3.9.2
+numpy     : 1.26.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/0.3-Generalised_filtering.html b/dev/notebooks/0.3-Generalised_filtering.html
index 404a13c4e..67d06c4c2 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 Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-IPython   : 8.29.0
+numpy     : 1.26.0
 jax       : 0.4.31
-pyhgf     : 0.0.0.post1.dev0+d064162
 seaborn   : 0.13.2
-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+304ea45
 matplotlib: 3.9.2
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+IPython   : 8.29.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.1-Binary_HGF.html b/dev/notebooks/1.1-Binary_HGF.html
index 3ff419c9b..6ea285990 100644
--- a/dev/notebooks/1.1-Binary_HGF.html
+++ b/dev/notebooks/1.1-Binary_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -829,8 +829,8 @@ 
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.
 

 

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

 

 

-../_images/92274084c43343457cfbe933888bb1dd2716bf25083d3e45ea9d19e3ddb37e73.png
+../_images/7ba29b6a14a4553c45c81e146c610f86085909429b44774236ab54f4f61b22ad.png
 

 

 
@@ -883,7 +883,7 @@ 
Using the learned parameters
-../_images/239e94793fde85a8a7b5fa37525fe62f2106aa7bb41aeb50bdad09751ace89ef.png
+../_images/95d2c2154e403b320cf3713a1aa6a05386f7dd1da030689430b27a2437e3ec26.png
 

 

 

@@ -893,7 +893,7 @@ 
Using the learned parameters
-
Array(202.5297, dtype=float32)
+
Array(202.52975, dtype=float32)
 

 

 

@@ -945,7 +945,7 @@ 
Visualizing the model
-../_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg
+../_images/2ec19856911096fbe9c3234ef83ab3600af54719c813af4a3f819412cb3c0342.svg
 

 

 
@@ -971,8 +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 8 seconds.
 

 

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

 

 

-../_images/8c687424d28c53a14096bfa3bc810e1bf1a53fb5d072a06832843dcadb9a8aed.png
+../_images/89417b1e62f0183ff40decddbec57294f2928d3246744538178ea748b3d124fa.png
 

 

 
@@ -1028,7 +1028,7 @@ 
Using the learned parameters
-../_images/6bbb0356a7d2e791451021478051210bca9e8a126f077782093e97fb0f9fecaf.png
+../_images/4b377b4ee32d314e234bab8b9ad53cc7881d8c76640c3e0829b9a770044c1b29.png
 

 

 

@@ -1038,7 +1038,7 @@ 
Using the learned parameters
-
Array(203.01866, dtype=float32)
+
Array(203.0046, dtype=float32)
 

 

 

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

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 pymc      : 5.17.0
 jax       : 0.4.31
+pyhgf     : 0.0.0.post1.dev0+304ea45
+IPython   : 8.29.0
 matplotlib: 3.9.2
 arviz     : 0.20.0
-pyhgf     : 0.0.0.post1.dev0+d064162
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-IPython   : 8.29.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.2-Categorical_HGF.html b/dev/notebooks/1.2-Categorical_HGF.html
index 0b3445481..70fdcb04e 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/1131a3fca5e90e926c1cc411081758c951984ba25ec23f26ee25bdc2ac0ef5a3.png
+../_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png
 

 

 

@@ -701,7 +701,7 @@ 
Fitting the model forwards
-../_images/496d4dbfbdd619abcfe152a1723b8a871f7bc93e03e3922b9cf6110337888440.png
+../_images/92b40a4aa78df0e756668b0af483fa9a0fd261dfdbb9e6fdc3988925bbfbabf2.png
 

 

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

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
+pytensor  : 2.25.5
+matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+304ea45
+IPython   : 8.29.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+numpy     : 1.26.0
 jax       : 0.4.31
-matplotlib: 3.9.2
 seaborn   : 0.13.2
-numpy     : 1.26.0
-pyhgf     : 0.0.0.post1.dev0+d064162
-pytensor  : 2.25.5
-IPython   : 8.29.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/1.3-Continuous_HGF.html b/dev/notebooks/1.3-Continuous_HGF.html
index 59e02b8ca..d8822c2b1 100644
--- a/dev/notebooks/1.3-Continuous_HGF.html
+++ b/dev/notebooks/1.3-Continuous_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -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_2716/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_2782/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/0be1fc85be22b2b446cc5a2e5d78a8e444248ee1f0a7a72d8fbe9b4baa452940.png
+../_images/891136509878ef03a4f7d9bb946e77c1995ee5a9ed70b335571ce8943b28b11d.png
 

 

 
@@ -937,7 +937,7 @@ 
Using the learned parameters
-../_images/de779af140e9c8170604b81a129ccec3af9e9517410441493b2ff64776ad917d.png
+../_images/bc7fbfec19c0d3925f9c25f2babe6dad485a666a62a29f09e5476bb4344e9b02.png
 

 

 

@@ -947,7 +947,7 @@ 
Using the learned parameters
-
Array(-1106.1298, dtype=float32)
+
Array(-1106.1078, dtype=float32)
 

 

 

@@ -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/5c151dc5ff581ecf21238d061d1c7af058ffdb8cd86e183349a9eb3cef93eb73.png
+../_images/d4154620ab0010ad605eae092b608e72e20c8e5133d9a10a0c8804917fe11fb3.png
 

 

 
@@ -1074,7 +1074,7 @@ 
Using the learned parameters
-../_images/b9a9de1907f3220c9552221fdfdb27555353584d767cfc1d838f3553532291d3.png
+../_images/40601a81b8f83071e14dc3febf12b2d8e7a79e39b9e78fd142a152c743c88317.png
 

 

 

@@ -1084,7 +1084,7 @@ 
Using the learned parameters
-
Array(-1118.013, dtype=float32)
+
Array(-1118.0359, dtype=float32)
 

 

 

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

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-matplotlib: 3.9.2
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-jax       : 0.4.31
 IPython   : 8.29.0
 arviz     : 0.20.0
+matplotlib: 3.9.2
+jax       : 0.4.31
+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+d064162
+pyhgf     : 0.0.0.post1.dev0+304ea45
 
 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 0ee11a4e9..1f09c06af 100644
--- a/dev/notebooks/2-Using_custom_response_functions.html
+++ b/dev/notebooks/2-Using_custom_response_functions.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -890,9 +890,9 @@ 
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.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 4 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -940,19 +940,19 @@ 
Recovering HGF parameters from the observed behaviors
     
       tonic_volatility_2
-      -3.935
-      0.471
-      -4.737
-      -2.969
+      -3.958
+      0.485
+      -4.879
+      -3.063
       0.015
-      0.011
-      974.0
-      1318.0
+      0.01
+      1063.0
+      1476.0
       1.0
     
   
 
-
../_images/b4a68fe9c3b9611968bd5c2e49721bf92da0e9a5e7d37efd792044215c9096b4.png
+
../_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.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 Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-numpy     : 1.26.0
-pyhgf     : 0.0.0.post1.dev0+d064162
-jax       : 0.4.31
+pyhgf     : 0.0.0.post1.dev0+304ea45
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+IPython   : 8.29.0
+jax       : 0.4.31
+arviz     : 0.20.0
+numpy     : 1.26.0
 matplotlib: 3.9.2
 pymc      : 5.17.0
-arviz     : 0.20.0
-IPython   : 8.29.0
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/3-Multilevel_HGF.html b/dev/notebooks/3-Multilevel_HGF.html
index e16ed22f6..fcfc252ce 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/5adbb6e59a7b4be9d4fe6e6dbb81b6a04f44eb22c14261ce8afc8abb6251da7c.svg
+../_images/4050fe0347ded05a53df568aec1b49d7910606a6343c0c108276244496910f8b.svg
 

 

 
@@ -832,12 +832,12 @@ 
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 26 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 25 seconds.
 

 

-
There were 1001 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 1000 divergences after tuning. Increase `target_accept` or reparameterize.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -875,7 +875,7 @@ 
Visualization of the posterior distributions
-../_images/b51ae87a99338380519629d52d9146a05ba297f831a2d2dda60c7925019181fd.png
+../_images/773110e0a2a910e680a828febc0758d79bc87e954ce7b9c50c0ba4c597a10b77.png
 

 

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

@@ -902,17 +902,17 @@ 
Model comparison
Computed from 2000 posterior samples and 3200 observations log-likelihood matrix.
 
          Estimate       SE
-elpd_loo -2996.16    99.70
-p_loo     1220.25        -
+elpd_loo -2252.57    63.79
+p_loo      515.08        -
 
 There has been a warning during the calculation. Please check the results.
 ------
 
 Pareto k diagnostic values:
                          Count   Pct.
-(-Inf, 0.70]   (good)     2256   70.5%
-   (0.70, 1]   (bad)         0    0.0%
-   (1, Inf)   (very bad)  944   29.5%
+(-Inf, 0.70]   (good)     2285   71.4%
+   (0.70, 1]   (bad)         2    0.1%
+   (1, Inf)   (very bad)  913   28.5%
 

 

 

@@ -929,25 +929,25 @@ 
System configuration
 

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pyhgf     : 0.0.0.post1.dev0+304ea45
+numpy     : 1.26.0
+IPython   : 8.29.0
 pymc      : 5.17.0
-pytensor  : 2.25.5
 arviz     : 0.20.0
-numpy     : 1.26.0
 matplotlib: 3.9.2
 seaborn   : 0.13.2
-pyhgf     : 0.0.0.post1.dev0+d064162
-IPython   : 8.29.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+pytensor  : 2.25.5
 
 Watermark: 2.5.0
 

diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index ad4078110..5ed28862b 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 52 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 48 seconds.
 

 

 
There were 2000 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -751,7 +751,7 @@ 
Visualizing parameters recovery
-../_images/22ec1fe2b65fd02c0149da478b434f72aac818456e6b8116506bd870ca97dcbf.png
+../_images/6e9373eb760ec3c6bb2bee2065daad85a4614370a199c98a3e764a65bf20ee11.png
 

 

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

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pyhgf     : 0.0.0.post1.dev0+d064162
-IPython   : 8.29.0
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 jax       : 0.4.31
-numpy     : 1.26.0
-arviz     : 0.20.0
 matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+304ea45
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+arviz     : 0.20.0
+IPython   : 8.29.0
 seaborn   : 0.13.2
 pymc      : 5.17.0
+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 7512e43a7..6f2c7507c 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 Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-jax       : 0.4.31
-IPython   : 8.29.0
-pyhgf     : 0.0.0.post1.dev0+d064162
-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
+jax       : 0.4.31
+pyhgf     : 0.0.0.post1.dev0+304ea45
+IPython   : 8.29.0
+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 f56252b63..65a761998 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,  1.05it/s]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:01<00:01,  1.11s/it]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  1.05it/s]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:01<00:01,  1.11s/it]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.01it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.03s/it]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.02it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.04s/it]
 

 

 

@@ -657,7 +657,7 @@ 
Model#<
 

 

 

-../_images/8f02834ccc45a1fbb4bd4aabfac2d75a89a86b3ef90438ded772ac7bf43de688.svg
+../_images/8fc9c210ab62f5dd9a3be3ce533d3c8c7ee05351b66a0f94da4f8a26be10ae39.svg
 

 

 

@@ -680,9 +680,9 @@ 
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.
+

+

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

 

 

-../_images/5aa278b211b6a409bf8958da879a5249962c00cd3cff9ffe61c1ac7fc8780fb3.png
+../_images/cf3f3a9d66a5d762ac19fe1cbef6e223dce12d568239d9e5a180457795462c1f.png
 

 

 

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

 

 

-../_images/8da2eae63f79146baec13996b7f83f3f12f7c09283b70bd98903dd078f7ac15d.png
+../_images/543db542df16a7681d3b72a722653b6598b2d1e06fc5c4d3cf7a9b8da13ebbcc.png
 

 

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

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-numpy     : 1.26.0
-matplotlib: 3.9.2
-pyhgf     : 0.0.0.post1.dev0+d064162
-systole   : 0.3.0
 pymc      : 5.17.0
 arviz     : 0.20.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+systole   : 0.3.0
+numpy     : 1.26.0
+pyhgf     : 0.0.0.post1.dev0+304ea45
 IPython   : 8.29.0
+matplotlib: 3.9.2
 
 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 dd1f0f067..25892259a 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 Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pyhgf     : 0.0.0.post1.dev0+d064162
-sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-IPython   : 8.29.0
+pyhgf     : 0.0.0.post1.dev0+304ea45
 matplotlib: 3.9.2
-numpy     : 1.26.0
+sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
 seaborn   : 0.13.2
+numpy     : 1.26.0
+IPython   : 8.29.0
 
 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 0d519ceab..0bc31c436 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -1085,12 +1085,9 @@ 
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 3 divergences after tuning. Increase `target_accept` or reparameterize.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 6 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1108,7 +1105,7 @@ 
Bayesian inference
-../_images/42a00d49502a9df956747c2ded1a31ed98388ae5ae7979036ad01d0e7232ae71.png
+../_images/3e9200da479f43d2a0f6ae9f9b90c5362a3b5f451d827f5107fb54f93d0a7799.png
 

 

 
@@ -1123,26 +1120,26 @@ 
System configuration
 

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-pymc      : 5.17.0
 numpy     : 1.26.0
-jax       : 0.4.31
-pyhgf     : 0.0.0.post1.dev0+d064162
-pytensor  : 2.25.5
-IPython   : 8.29.0
 arviz     : 0.20.0
-matplotlib: 3.9.2
+pyhgf     : 0.0.0.post1.dev0+304ea45
 seaborn   : 0.13.2
+pymc      : 5.17.0
+jax       : 0.4.31
+pytensor  : 2.25.5
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
+matplotlib: 3.9.2
+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 c67b240f8..347ced8ea 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 Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-IPython   : 8.29.0
-matplotlib: 3.9.2
 numpy     : 1.26.0
-seaborn   : 0.13.2
+pyhgf     : 0.0.0.post1.dev0+304ea45
 pandas    : 2.2.3
+IPython   : 8.29.0
 sys       : 3.12.7 (main, Oct  1 2024, 15:17:55) [GCC 11.4.0]
-pyhgf     : 0.0.0.post1.dev0+d064162
+seaborn   : 0.13.2
+matplotlib: 3.9.2
 
 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 e14433a00..4a83afde7 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/fb30ad50512fa98d7a3ccb9ce3bbeaa964e8971e08bdf749547c02cfcebfaaac.png
+../_images/8caf92f5ae0ba940256e664ef5b7334b9747081112bbc44e3616eb436eb84484.png
 

 

 

@@ -785,14 +785,14 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.578
-      0.401
-      -3.318
-      -1.838
-      0.014
-      0.011
-      738.0
-      600.0
+      -2.588
+      0.4
+      -3.345
+      -1.874
+      0.017
+      0.013
+      506.0
+      358.0
       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/1cb865b4870a04f288adde0555c636bbd6db7a5d43331b70ebbc54e64c336108.png
+../_images/b47434316fdf9c08705bfd62ac0f47dee0d4b6365566c6f64c72e661fdbb1feb.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": "5ad1605315cc4ddfbd83fb20533a7f21"}
/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 24 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/025c6ad68f3b001693ab50fc2ce308dd35dd28546cfa83d91ba655a814893f5f.png
+../_images/bdfbd94522ae64e37e17f9f59bd8f7f681b46c3940ba84e06320d1f9ecb043a5.png
 

 

 
@@ -1036,14 +1036,11 @@ 
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.
 

 

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

-

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

 

@@ -1056,7 +1053,7 @@ 
Two-level HGF
-../_images/482aae5bf99898ae3540fd296dda1db83ddbbdf3d25d7e588dccd997fe0c90d0.png
+../_images/2059426ad2f3319e839d0aff485e0e14675f57355a9b58472e3bdf75ffaedff5.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.

@@ -1150,12 +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
@@ -1170,7 +1167,7 @@ 
Three-level HGF
-../_images/a76761bc41cbe345a0018b344b165c554dcab9b1476ed2096cae1010bc43a3c2.png
+../_images/7c9c5cd89da3f16d7542a1619530ad2049147c775e6341faacce721ca4eaf61c.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1243,11 +1240,11 @@ 
Model comparison
-../_images/800b38e1870212139dc19c838b5f6f772a0589c7f0093457677241c62940fb77.png
+../_images/335cddb217afd62029b02f6b6afec50173f76a1865157e1fe4212ed9fa7b99f5.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.

@@ -1416,7 +1413,7 @@ 
Beliefs trajectories
 
 

-../_images/84a2c4a9be6742369a78abbadbbcbce3e11b6798e80017dad90de03e875ca35e.png
+../_images/472d09d46198daebd1172c7e9fe8dfbc43852041c32839ca967a6e2a98fac92d.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.

@@ -1479,25 +1476,25 @@ 
System configuration
 

 

-
Last updated: Tue Dec 10 2024
+
Last updated: Wed Dec 11 2024
 
 Python implementation: CPython
 Python version       : 3.12.7
 IPython version      : 8.29.0
 
-pyhgf : 0.0.0.post1.dev0+d064162
+pyhgf : 0.0.0.post1.dev0+304ea45
 jax   : 0.4.31
 jaxlib: 0.4.31
 
-matplotlib: 3.9.2
-pyhgf     : 0.0.0.post1.dev0+d064162
-pymc      : 5.17.0
+pyhgf     : 0.0.0.post1.dev0+304ea45
 arviz     : 0.20.0
-IPython   : 8.29.0
-seaborn   : 0.13.2
+pytensor  : 2.25.5
+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
-pytensor  : 2.25.5
+pymc      : 5.17.0
+IPython   : 8.29.0
 
 Watermark: 2.5.0
 

diff --git a/dev/searchindex.js b/dev/searchindex.js
index 383d5aef9..5d23b3377 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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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, "using-the-learned-parameters"], [70, "id10"], [72, "using-the-learned-parameters"], [72, "id8"]], "Utils": [[0, "utils"]], "Value coupling": [[67, "value-coupling"], [68, "value-coupling"], [80, "value-coupling"]], "Visualization of the posterior distributions": [[74, "visualization-of-the-posterior-distributions"]], "Visualizing parameters recovery": [[75, "visualizing-parameters-recovery"]], "Visualizing probabilistic networks": [[68, "visualizing-probabilistic-networks"]], "Visualizing the model": [[70, "visualizing-the-model"], [70, "id8"], [72, "visualizing-the-model"], [72, "id6"]], "Volatility coupling": [[67, "volatility-coupling"], [68, "volatility-coupling"], [80, "volatility-coupling"]], "Where to go next?": [[81, "where-to-go-next"]], "Working with missing or unobserved input sequences": [[68, "working-with-missing-or-unobserved-input-sequences"]], "Zurich CPC I: Introduction to the Generalised Hierarchical Gaussian Filter": [[80, null]], "Zurich CPC II: Application to 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