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a/dev/_images/2ec19856911096fbe9c3234ef83ab3600af54719c813af4a3f819412cb3c0342.svg b/dev/_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg similarity index 93% rename from dev/_images/2ec19856911096fbe9c3234ef83ab3600af54719c813af4a3f819412cb3c0342.svg rename to dev/_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg index 4e573a629..6acc91819 100644 --- a/dev/_images/2ec19856911096fbe9c3234ef83ab3600af54719c813af4a3f819412cb3c0342.svg +++ b/dev/_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg @@ -9,13 +9,13 @@ %3 - + -tonic_volatility_2 +tonic_volatility_3 -tonic_volatility_2 +tonic_volatility_3 ~ -Uniform +Normal @@ -25,23 +25,23 @@ ~ Potential - + -tonic_volatility_2->hgf_loglike +tonic_volatility_3->hgf_loglike - + -tonic_volatility_3 +tonic_volatility_2 -tonic_volatility_3 +tonic_volatility_2 ~ -Normal +Uniform - + -tonic_volatility_3->hgf_loglike +tonic_volatility_2->hgf_loglike diff --git a/dev/_images/e7c45b966db8853721d2a9a80952504f421a5bd34d4aaf97812b23a2f02b7577.png b/dev/_images/e7c45b966db8853721d2a9a80952504f421a5bd34d4aaf97812b23a2f02b7577.png new file mode 100644 index 000000000..4269dfd1e Binary files /dev/null and b/dev/_images/e7c45b966db8853721d2a9a80952504f421a5bd34d4aaf97812b23a2f02b7577.png 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/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png b/dev/_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png deleted file mode 100644 index e8393c60e..000000000 Binary files a/dev/_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png and /dev/null differ diff --git a/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png b/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png deleted file mode 100644 index b818df1a6..000000000 Binary files a/dev/_images/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png and /dev/null differ diff --git a/dev/notebooks/0.1-Theory.html b/dev/notebooks/0.1-Theory.html index b0a8fd0db..ac61922cd 100644 --- a/dev/notebooks/0.1-Theory.html +++ b/dev/notebooks/0.1-Theory.html @@ -927,15 +927,15 @@

System configuration diff --git a/dev/notebooks/0.2-Creating_networks.html b/dev/notebooks/0.2-Creating_networks.html index 4401b499e..96accea1f 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/2167ccc99323c237c9015c8b5c3e2c5ff0df0ea271d023c5adf6a809dfe368ab.png +../_images/325b1e8578798cd930ddf10fd5e57785d965b16804a582fe0b4298f835154a2c.png
@@ -1131,16 +1131,16 @@

System configuration

diff --git a/dev/notebooks/0.3-Generalised_filtering.html b/dev/notebooks/0.3-Generalised_filtering.html index 67d06c4c2..51240c717 100644 --- a/dev/notebooks/0.3-Generalised_filtering.html +++ b/dev/notebooks/0.3-Generalised_filtering.html @@ -990,17 +990,17 @@

System configuration diff --git a/dev/notebooks/1.1-Binary_HGF.html b/dev/notebooks/1.1-Binary_HGF.html index 6ea285990..a77150cb8 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/7ba29b6a14a4553c45c81e146c610f86085909429b44774236ab54f4f61b22ad.png
+../_images/9d96847a971c21e3830a12da0122da28f7edf25b29ec214da0294e1cdf680467.png
 

 
 
@@ -883,7 +883,7 @@ 
Using the learned parameters
-../_images/95d2c2154e403b320cf3713a1aa6a05386f7dd1da030689430b27a2437e3ec26.png
+../_images/7971b1be2d063b658af79b7ba2a17b8b8d41a5062ade93e6f55f3153f80479ce.png
 
 
 

@@ -893,7 +893,7 @@ 
Using the learned parameters
-
Array(202.52975, dtype=float32)
+
Array(202.5298, dtype=float32)
 

 

 

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

 

 
@@ -971,9 +971,9 @@ 
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.
+

+

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

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -990,7 +990,7 @@ 
Sampling#
 

 

 

-../_images/89417b1e62f0183ff40decddbec57294f2928d3246744538178ea748b3d124fa.png
+../_images/a6229fd578f5f0127e66f66d43c2ab10ba272ffac5afd739f6ea6f48694df8f4.png
 

 

 
@@ -1028,7 +1028,7 @@ 
Using the learned parameters
-../_images/4b377b4ee32d314e234bab8b9ad53cc7881d8c76640c3e0829b9a770044c1b29.png
+../_images/e7c45b966db8853721d2a9a80952504f421a5bd34d4aaf97812b23a2f02b7577.png
 

 
 

@@ -1062,17 +1062,17 @@ 
System configuration

diff --git a/dev/notebooks/1.2-Categorical_HGF.html b/dev/notebooks/1.2-Categorical_HGF.html
index 70fdcb04e..2e7715571 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/f312ce7c85b7ff261211a3a0a1791ef0a52b3ebe9b37e7f73953cb2fa1778b3d.png
+../_images/b64b9b585c6cc70259459b3bdff5bf6e3a004245d3d4db066cb37291b2a15838.png
 

 
 

@@ -701,7 +701,7 @@ 
Fitting the model forwards
-../_images/92b40a4aa78df0e756668b0af483fa9a0fd261dfdbb9e6fdc3988925bbfbabf2.png
+../_images/79f422989cb775a8dcf626c5734add6ecc111c34dc63bee7da66596e1899b673.png
 

 
 
@@ -855,18 +855,18 @@ 
System configuration
diff --git a/dev/notebooks/1.3-Continuous_HGF.html b/dev/notebooks/1.3-Continuous_HGF.html
index d8822c2b1..13cf192f5 100644
--- a/dev/notebooks/1.3-Continuous_HGF.html
+++ b/dev/notebooks/1.3-Continuous_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -880,9 +880,9 @@ 
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.
+

+

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

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -898,11 +898,11 @@ 
Sampling
 

 

 

-
/tmp/ipykernel_2782/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_2793/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/891136509878ef03a4f7d9bb946e77c1995ee5a9ed70b335571ce8943b28b11d.png
+../_images/a8eac0f07467d2a5a6cecc973149f0643e081ddd3b1d979ad94ed01c6e2f59b6.png
 

 

 
@@ -937,7 +937,7 @@ 
Using the learned parameters
-../_images/bc7fbfec19c0d3925f9c25f2babe6dad485a666a62a29f09e5476bb4344e9b02.png
+../_images/53e019177f7b423c33b31128cc97ba41fdcb1ffe96bd976914fe7164b9a62960.png
 

 

 

@@ -947,7 +947,7 @@ 
Using the learned parameters
-
Array(-1106.1078, dtype=float32)
+
Array(-1106.073, dtype=float32)
 

 

 

@@ -1023,9 +1023,9 @@ 
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.
+

+

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

 

 

-../_images/d4154620ab0010ad605eae092b608e72e20c8e5133d9a10a0c8804917fe11fb3.png
+../_images/2f58126e334ffa6b6a67163959058580f7315614ab552945e9d2914d38f7a29a.png
 

 

 
@@ -1074,7 +1074,7 @@ 
Using the learned parameters
-../_images/40601a81b8f83071e14dc3febf12b2d8e7a79e39b9e78fd142a152c743c88317.png
+../_images/67ef44ba6f3b52c67d07e743767a1b0a6f0b5912541da1ac27055996559ecb70.png
 

 

 

@@ -1084,7 +1084,7 @@ 
Using the learned parameters
-
Array(-1118.0359, dtype=float32)
+
Array(-1118.0452, dtype=float32)
 

 

 

@@ -1108,17 +1108,17 @@ 
System configuration

diff --git a/dev/notebooks/2-Using_custom_response_functions.html b/dev/notebooks/2-Using_custom_response_functions.html
index 1f09c06af..d0a62f46a 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 4 seconds.
+

+

+
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
@@ -941,18 +941,18 @@ 
Recovering HGF parameters from the observed behaviors
       tonic_volatility_2
       -3.958
-      0.485
-      -4.879
-      -3.063
-      0.015
-      0.01
-      1063.0
-      1476.0
+      0.494
+      -4.888
+      -3.075
+      0.018
+      0.013
+      750.0
+      1046.0
       1.0
     
   
 
-
../_images/efc05b204c793f66864d94895db78fd4d729478d6258d2ddf1bd1f1b44d39c72.png
+
../_images/6426bbbbf53684582cf3b0912f730e226ed962d5b77177015c6c041286469493.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.

@@ -986,18 +986,18 @@ 
System configuration
diff --git a/dev/notebooks/3-Multilevel_HGF.html b/dev/notebooks/3-Multilevel_HGF.html
index fcfc252ce..4c5308c32 100644
--- a/dev/notebooks/3-Multilevel_HGF.html
+++ b/dev/notebooks/3-Multilevel_HGF.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -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 25 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 29 seconds.
 

 

-
There were 1000 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 1001 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/773110e0a2a910e680a828febc0758d79bc87e954ce7b9c50c0ba4c597a10b77.png
+../_images/d1a8e91303a2c4dd313d0839aebe09a4805bcdf5418308fa704f704c2f8a8205.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 -2252.57    63.79
-p_loo      515.08        -
+elpd_loo -2407.43    68.09
+p_loo      648.04        -
 
 There has been a warning during the calculation. Please check the results.
 ------
 
 Pareto k diagnostic values:
                          Count   Pct.
-(-Inf, 0.70]   (good)     2285   71.4%
-   (0.70, 1]   (bad)         2    0.1%
-   (1, Inf)   (very bad)  913   28.5%
+(-Inf, 0.70]   (good)     2115   66.1%
+   (0.70, 1]   (bad)         1    0.0%
+   (1, Inf)   (very bad) 1084   33.9%
 

 

 

@@ -935,19 +935,19 @@ 
System configuration

diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index 5ed28862b..29ce5972f 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 48 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 65 seconds.
 

 

 
There were 2000 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -751,7 +751,7 @@ 
Visualizing parameters recovery
-../_images/6e9373eb760ec3c6bb2bee2065daad85a4614370a199c98a3e764a65bf20ee11.png
+../_images/93cc4a88b588c555509d90650a215a02da8f0bb99f5cc57e9c03b593d863d647.png
 

 

 
@@ -772,19 +772,19 @@ 
System configuration

diff --git a/dev/notebooks/5-Non_linear_value_coupling.html b/dev/notebooks/5-Non_linear_value_coupling.html
index 6f2c7507c..84cf891b8 100644
--- a/dev/notebooks/5-Non_linear_value_coupling.html
+++ b/dev/notebooks/5-Non_linear_value_coupling.html
@@ -984,17 +984,17 @@ 
System configuration

diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index 65a761998..965c0b0ae 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 [00:01<00:01,  1.11s/it]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:00<00:00,  1.76it/s]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:01<00:01,  1.11s/it]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  1.76it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.03s/it]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.91it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.04s/it]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.88it/s]
 

 

 

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

 

 

-../_images/8fc9c210ab62f5dd9a3be3ce533d3c8c7ee05351b66a0f94da4f8a26be10ae39.svg
+../_images/8f02834ccc45a1fbb4bd4aabfac2d75a89a86b3ef90438ded772ac7bf43de688.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 10 seconds.
+

+

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

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -697,7 +697,7 @@ 
Model#<
 

 

 

-../_images/cf3f3a9d66a5d762ac19fe1cbef6e223dce12d568239d9e5a180457795462c1f.png
+../_images/4d2b5629253a7aad67ce6b981fe58be0196907bda11e061c106bd592766cb54f.png
 

 

 

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

 

 

-../_images/543db542df16a7681d3b72a722653b6598b2d1e06fc5c4d3cf7a9b8da13ebbcc.png
+../_images/7f13c4bf803eed6fc5cda11bb80b1f738d3028dcd3ddbd4bc851152ea3fcac74.png
 

 

 
@@ -750,17 +750,17 @@ 
System configurationSystem configuration

diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index 0bc31c436..d63bf9b7b 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -1085,9 +1085,12 @@ 
Bayesian inference
NUTS: [omega]
 

 

-

-

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

+

+
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
@@ -1105,7 +1108,7 @@ 
Bayesian inference
-../_images/3e9200da479f43d2a0f6ae9f9b90c5362a3b5f451d827f5107fb54f93d0a7799.png
+../_images/4baf7a7c97af70c81b93f901c5a469e60c58889a6de3661065d08320f52f7bba.png
 

 

 
@@ -1126,20 +1129,20 @@ 
System configuration

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 347ced8ea..86ab052cc 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
@@ -1040,17 +1040,17 @@ 
System configuration

diff --git a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
index 4a83afde7..3a9a17f11 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/7d29572ae423fb4c8d4ea736f01dab651bf0ee09a3d53b5838bcf639ba2eaf01.svg
+../_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.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/8caf92f5ae0ba940256e664ef5b7334b9747081112bbc44e3616eb436eb84484.png
+../_images/9cea41b5ca942fd324b9b6486eeda15404c4e9cee28e3f9e217a95d21712a521.png
 

 

 

@@ -785,15 +785,15 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.588
-      0.4
-      -3.345
-      -1.874
+      -2.58
+      0.41
+      -3.419
+      -1.887
       0.017
       0.013
-      506.0
-      358.0
-      1.0
+      576.0
+      424.0
+      1.01
     
   
 
@@ -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/b47434316fdf9c08705bfd62ac0f47dee0d4b6365566c6f64c72e661fdbb1feb.png
+../_images/8332655480dbf9601a101d407d2c397b5ca8dafd0f6d3612f475699c673fe5d1.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": "2d8c098e9b964d17b842f241b93f9a13"}
/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 22 seconds.
+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 24 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -945,7 +945,7 @@ 
Rescorla-Wagner
-../_images/bdfbd94522ae64e37e17f9f59bd8f7f681b46c3940ba84e06320d1f9ecb043a5.png
+../_images/aa86bce64f720a064bd6ba0b34383472abef9875fa30064d5b63e8d80ab84729.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/2059426ad2f3319e839d0aff485e0e14675f57355a9b58472e3bdf75ffaedff5.png
+../_images/7f634b9f5f2960f3020274e8d569a5e4729ec7c0ccee553847f85b3a45aa9b52.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 66 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 52 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/7c9c5cd89da3f16d7542a1619530ad2049147c775e6341faacce721ca4eaf61c.png
+../_images/895420c415c8a953d268308c77dc757a917a312576ef872542cb54763c156f5d.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1240,11 +1240,11 @@ 
Model comparison
-../_images/335cddb217afd62029b02f6b6afec50173f76a1865157e1fe4212ed9fa7b99f5.png
+../_images/a2ccb842031d9c7d0cfd0c098b02160db435e4c070b039ffbbd786b30367dedb.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/472d09d46198daebd1172c7e9fe8dfbc43852041c32839ca967a6e2a98fac92d.png
+../_images/aff44d4776c37663d3045fd279ed36bd27a78f9dcb486951fbe404895eb200ea.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.

@@ -1482,19 +1482,19 @@ 
System configuration

diff --git a/dev/searchindex.js b/dev/searchindex.js
index 5d23b3377..2f52aecf0 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, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[68, "coupling-with-binary-nodes"]], "Create the model": [[70, "create-the-model"], [70, "id3"], [72, "create-the-model"], [72, "id2"]], "Creating a new response function": [[73, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[73, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[68, null]], "Creating custom update functions": [[68, "creating-custom-update-functions"]], "Creating custom update sequences": [[68, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[68, "creating-probabilistic-nodes"]], "Creating the decision rule": [[73, "creating-the-decision-rule"]], "Creating the model": [[70, "creating-the-model"], [70, "id7"], [72, "creating-the-model"], [72, "id5"]], "Creating the probabilistic network": [[71, "creating-the-probabilistic-network"]], "Decision rule": [[79, "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": [[80, "probabilistic-coupling-between-nodes"]], "PyHGF: A Neural Network Library for Predictive Coding": [[65, null]], "ReLU (rectified linear unit) activation function": [[76, "relu-rectified-linear-unit-activation-function"]], "Real-time decision and belief updating": [[79, "real-time-decision-and-belief-updating"]], "Recovering HGF parameters from the observed behaviors": [[73, "recovering-hgf-parameters-from-the-observed-behaviors"]], "Recovering computational parameters from observed behaviours": [[75, null]], "References": [[65, "references"], [82, null]], "Rescorla-Wagner": [[81, "rescorla-wagner"]], "Response": [[0, "response"]], "Sampling": [[70, "sampling"], [70, "id9"], [72, "sampling"], [72, "id7"], [74, "sampling"]], "Simulate a dataset": [[74, "simulate-a-dataset"], [79, "simulate-a-dataset"]], "Simulate behaviours from a one-armed bandit task": [[75, "simulate-behaviours-from-a-one-armed-bandit-task"]], "Simulate responses from a participant": [[79, "simulate-responses-from-a-participant"]], "Simulating a dataset": [[71, "simulating-a-dataset"]], "Solution to Exercise 1": [[80, "solution-exercise1.1"]], "Solution to Exercise 2": [[80, "solution-exercise1.2"]], "Solution to Exercise 3": [[80, "solution-exercise1.3"]], "Solution to Exercise 4": [[80, "solution-exercise1.4"]], "Solution to Exercise 5": [[80, "solution-exercise1.5"]], "Solution to Exercise 7": [[81, "solution-exercise2.1"]], "Solution to Exercise 8": [[81, "solution-exercise2.2"]], "Solutions": [[80, "solutions"], [81, "solutions"]], "Static assignation of update sequences": [[68, "static-assignation-of-update-sequences"]], "Surprise": [[70, "surprise"], [70, "id6"], [72, "surprise"]], "System configuration": [[67, "system-configuration"], [68, "system-configuration"], [69, "system-configuration"], [70, "system-configuration"], [71, "system-configuration"], [72, "system-configuration"], [73, "system-configuration"], [74, "system-configuration"], [75, "system-configuration"], [76, "system-configuration"], [77, "system-configuration"], [78, "system-configuration"], [79, "system-configuration"], [80, "system-configuration"], [81, "system-configuration"]], "Table of Contents": [[0, null]], "Task structure": [[79, "task-structure"]], "The Generalized Hierarchical Gaussian Filter": [[65, "the-generalized-hierarchical-gaussian-filter"]], "The Hierarchical Gaussian Filter": [[66, "the-hierarchical-gaussian-filter"]], "The Hierarchical Gaussian Filter in a network of predictive nodes": [[67, "the-hierarchical-gaussian-filter-in-a-network-of-predictive-nodes"]], "The binary HGF": [[81, "the-binary-hgf"]], "The binary Hierarchical Gaussian Filter": [[70, null]], "The case of multivariate ascendency": [[68, "the-case-of-multivariate-ascendency"]], "The case of multivariate descendency": [[68, "the-case-of-multivariate-descendency"]], "The categorical Hierarchical Gaussian Filter": [[71, null]], "The categorical state node": [[71, "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": 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"pyhgf.utils.beliefs_propagation", "pyhgf.utils.fill_categorical_state_node", "pyhgf.utils.get_input_idxs", "pyhgf.utils.get_update_sequence", "pyhgf.utils.list_branches", "pyhgf.utils.to_pandas", "PyHGF: A Neural Network Library for Predictive Coding", "Learn", "Introduction to the Generalised Hierarchical Gaussian Filter", "Creating and manipulating networks of probabilistic nodes", "From Reinforcement Learning to Generalised Bayesian Filtering", "The binary Hierarchical Gaussian Filter", "The categorical Hierarchical Gaussian Filter", "The continuous Hierarchical Gaussian Filter", "Using custom response models", "Hierarchical Bayesian modelling with probabilistic neural networks", "Recovering computational parameters from observed behaviours", "Non-linear value coupling between continuous state nodes", "Example 1: Bayesian filtering of cardiac volatility", "Example 2: Estimating the mean and precision of a time-varying Gaussian distributions", "Example 3: A multi-armed bandit task 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\ No newline at end of file