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02b4163cb..6acc91819 100644 --- a/dev/_images/69539e2739458d7218e514133841304a4e4b0eb711fc8054497123f2e226d095.svg +++ b/dev/_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.svg @@ -9,22 +9,22 @@ %3 - - -hgf_loglike - -hgf_loglike -~ -Potential - - + tonic_volatility_3 tonic_volatility_3 ~ Normal + + +hgf_loglike + +hgf_loglike +~ +Potential + tonic_volatility_3->hgf_loglike @@ -32,7 +32,7 @@ - + tonic_volatility_2 tonic_volatility_2 diff --git a/dev/_images/e49ee6bf61f8ec5113be60ca12c8f9e3abce2e4c09875eb61e3a2d9c1dfc9925.svg b/dev/_images/e49ee6bf61f8ec5113be60ca12c8f9e3abce2e4c09875eb61e3a2d9c1dfc9925.svg new file mode 100644 index 000000000..230a1aa0a --- /dev/null +++ b/dev/_images/e49ee6bf61f8ec5113be60ca12c8f9e3abce2e4c09875eb61e3a2d9c1dfc9925.svg @@ -0,0 +1,135 @@ + + + + + + +%3 + + +cluster10 + +10 + + +cluster10 x 320 + +10 x 320 + + + +mu_volatility + +mu_volatility +~ +Normal + + + +volatility + +volatility +~ +Normal + + + +mu_volatility->volatility + + + + + +mu_temperature + +mu_temperature +~ +Normal + + + +inverse_temperature + +inverse_temperature +~ +LogNormal + + + +mu_temperature->inverse_temperature + + + + + +sigma_temperature + +sigma_temperature +~ +HalfNormal + + + +sigma_temperature->inverse_temperature + + + + + +sigma_volatility + +sigma_volatility +~ +HalfNormal + + + +sigma_volatility->volatility + + + + + +log_likelihood + +log_likelihood +~ +CustomDist_log_likelihood + + + +inverse_temperature->log_likelihood + + + + + +pointwise_loglikelihood + +pointwise_loglikelihood +~ +Deterministic + + + +inverse_temperature->pointwise_loglikelihood + + + + + +volatility->log_likelihood + + + + + +volatility->pointwise_loglikelihood + + + + + \ No newline at end of file diff --git a/dev/_images/e75f7696faddd35dad6478e201b2280d93b0ca0ce8375436e915cca683fea197.png b/dev/_images/e75f7696faddd35dad6478e201b2280d93b0ca0ce8375436e915cca683fea197.png deleted file mode 100644 index 8ff1d10dd..000000000 Binary files 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b/dev/_images/ff1c545bda0a03ff20d507d2860dadcb4863d4f57e4405425bd850653d54ebd6.png new file mode 100644 index 000000000..659c0908f Binary files /dev/null and b/dev/_images/ff1c545bda0a03ff20d507d2860dadcb4863d4f57e4405425bd850653d54ebd6.png differ diff --git a/dev/notebooks/0.1-Theory.html b/dev/notebooks/0.1-Theory.html index e8f848e7c..b06dce05e 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 39df70482..c6741e87d 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/402e6e226dd4ba4f0c98d72c4793cb487c6c5b292539457d4d75565159866ece.png +../_images/4ef45a14cef2cd824c9556b5027004b5d43b8c90c8e47f61fb1816952ad530c8.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 e2525477f..97411fa93 100644 --- a/dev/notebooks/0.3-Generalised_filtering.html +++ b/dev/notebooks/0.3-Generalised_filtering.html @@ -990,16 +990,16 @@

System configurationvar togglebuttonSelector = '.toggle, .admonition.dropdown'; - + @@ -803,7 +803,7 @@

Visualizing the model
-../_images/ecd192b619fcda3b40cdb5f737d2b936691486677eb7a4f82b5cbc7f55367e9e.svg +../_images/7d29572ae423fb4c8d4ea736f01dab651bf0ee09a3d53b5838bcf639ba2eaf01.svg
@@ -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/6a01f12344432ecd1787af24925f2d702d658cabfce294564107dda26f767a6a.png
+../_images/30515fecc95c03a43e02a323c41c298dc7a5c288e66ddd9823f0800a405a1320.png
 

 
 
@@ -883,7 +883,7 @@ 
Using the learned parameters
-../_images/5b0315ed98f1f3e8b2fde517529f59332e2426f7989313f156566ea2366d4ef2.png
+../_images/46ecb1a6dd3ce982621f3cb1db87c32a584469be54fb85f16e0dd15eb6f38948.png
 
 
 

@@ -893,7 +893,7 @@ 
Using the learned parameters
-
Array(202.5298, dtype=float32)
+
Array(202.52971, dtype=float32)
 

 

 

@@ -945,7 +945,7 @@ 
Visualizing the model
-../_images/69539e2739458d7218e514133841304a4e4b0eb711fc8054497123f2e226d095.svg
+../_images/e3093df40c606a365fce51328bb90c832e9b204e89fed0d0688e3e2fdb1677dd.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 9 seconds.
 

 

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

 
 

-../_images/a5f5a74e305aa411cd57e19dd0f0aab43ca8b10f0eae92c5d36fecf5dd090017.png
+../_images/b0395af2b43fca8410ef12bbe75377e5dc8803398a4756d3267a0c938e132074.png
 

 
 
@@ -1028,7 +1028,7 @@ 
Using the learned parameters
-../_images/428fb47dc3281ec0960bc4a68385e89a5aeea4e7f9ccad18f733bca2420d80a6.png
+../_images/070ccd28c438289844488e33724123736bfe70dd4e9458f00fbb2fce81cfc92b.png
 
 
 

@@ -1038,7 +1038,7 @@ 
Using the learned parameters
-
Array(203.0082, dtype=float32)
+
Array(203.01239, dtype=float32)
 

 

 

@@ -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 d0dc686ec..c19bba8d8 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/c6974a79783b5c79f7ac28b08dbc15c1bc074913b77316ad05a6aa44a30812b2.png
+../_images/ff1c545bda0a03ff20d507d2860dadcb4863d4f57e4405425bd850653d54ebd6.png
 

 
 

@@ -701,7 +701,7 @@ 
Fitting the model forwards
-../_images/070e2b22f4dbb8d08f1d0e86327b139527ca4dc80f7ebbe618a040bf580aa802.png
+../_images/b191a23473c273c8d47935dca3f903502835b1bb478b74835893468f5f643b92.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 9fc019593..5b53fada9 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_2711/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_2746/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/5772bcdb0d94258e89017578e3829b34c4c8b1a2154d3a0551d9ee698a63f8de.png
+../_images/d13548549880db216e4c6a06f5cd7bd7e73a27122a44c5acbdb3736c633be421.png
 

 

 
@@ -937,7 +937,7 @@ 
Using the learned parameters
-../_images/640f6a7370fcaa5aa31fa50b86fea4855db0c5c28b5e39656f40c356db1db2b4.png
+../_images/4b1f57d82d631c1e3c2cb3172970781f40b974f56e8436f54e42b89e174ac59b.png
 

 
 

@@ -947,7 +947,7 @@ 
Using the learned parameters
-
Array(-1106.1183, dtype=float32)
+
Array(-1106.127, 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/927a6cc2f688dd645b8de62834bba3285a2401f92adf1f38aa8fe5cdb334c81a.png
+../_images/fb2ee0f031c1bcb8a3a3f8e7d80296e72a4dae32495f5a5b04a7964bbbeda1fd.png
 

 

 
@@ -1074,7 +1074,7 @@ 
Using the learned parameters
-../_images/eafa0aedf6696d815f7dab7ec378082dd4c93307d17e9fa587a3e8ecadceee8b.png
+../_images/512879d2856cb4783036630f9967fab80870def7bb4d81966b9da990420d3e3c.png
 
 
 

@@ -1084,7 +1084,7 @@ 
Using the learned parameters
-
Array(-1117.9757, dtype=float32)
+
Array(-1118.0258, 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 d964a8b13..82231b19b 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
-      -3.958
-      0.492
-      -4.936
-      -3.126
-      0.018
-      0.013
-      786.0
-      1104.0
+      -3.954
+      0.497
+      -4.902
+      -3.037
+      0.017
+      0.012
+      918.0
+      1144.0
       1.0
     
   
 
-
../_images/cb7972c61d970bf4f097b420d604b321575ab34b5b044fe25d0f2cd355911f23.png
+../_images/18b53b9fbb70ca0153d4092a4f5dff8ecf79369bfb3033849810e8d20de1363f.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 c52850771..55563ac1c 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/4779ff3b5faaa0ea280d5666923fd77e5e110d01ecfb615e713b0c9bfdc3a5c1.svg
+../_images/e49ee6bf61f8ec5113be60ca12c8f9e3abce2e4c09875eb61e3a2d9c1dfc9925.svg
 
 
 
@@ -832,14 +832,23 @@ 
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 44 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 26 seconds.
+

+

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

 

 
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
+

+

+
The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details
+

+

 

 

 

@@ -866,7 +875,7 @@ 
Visualization of the posterior distributions
-../_images/e75f7696faddd35dad6478e201b2280d93b0ca0ce8375436e915cca683fea197.png
+../_images/82526e181e20b720f99653255ecd405c28274b7e85521b08f705c576b3dfc298.png
 

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

@@ -893,17 +902,17 @@ 
Model comparison
Computed from 2000 posterior samples and 3200 observations log-likelihood matrix.
 
          Estimate       SE
-elpd_loo -1684.09    25.66
-p_loo       17.90        -
+elpd_loo -2707.10    83.05
+p_loo      934.71        -
 
 There has been a warning during the calculation. Please check the results.
 ------
 
 Pareto k diagnostic values:
                          Count   Pct.
-(-Inf, 0.70]   (good)     3185   99.5%
-   (0.70, 1]   (bad)         1    0.0%
-   (1, Inf)   (very bad)   14    0.4%
+(-Inf, 0.70]   (good)     2196   68.6%
+   (0.70, 1]   (bad)         5    0.2%
+   (1, Inf)   (very bad)  999   31.2%
 

 
 
@@ -926,19 +935,19 @@ 
System configuration
diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index 02d4837e0..bf8a6938b 100644
--- a/dev/notebooks/4-Parameter_recovery.html
+++ b/dev/notebooks/4-Parameter_recovery.html
@@ -50,7 +50,7 @@
     
     
     
-    
+    
     
     
     
@@ -676,12 +676,12 @@ 
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 60 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 56 seconds.
 

 

-
There were 2000 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 1999 divergences after tuning. Increase `target_accept` or reparameterize.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -751,7 +751,7 @@ 
Visualizing parameters recovery
-../_images/912149e1e83e2c3714125ca7a668c6ec59d340bb5913e2838ed4a9f0cd6d6511.png
+../_images/9856672e27f939248514b092505b3c7c398c853c04933d546d73696f812b2a1e.png
 

 

 
@@ -772,18 +772,18 @@ 
System configurationSystem configuration

diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index f62a9afa8..f650fbbbd 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,  2.49it/s]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:00<00:00,  1.29it/s]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  2.49it/s]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  1.29it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:00<00:00,  2.35it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.04it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:00<00:00,  2.37it/s]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.07it/s]
 

 

 

@@ -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/249e0f27b2946032f2aeeb6f92aa2e42354857d2faf01e6e7597e1932d249453.png
+../_images/654580e251e268cd645533f265c8b3da9ff3a1406d91f939d2719261160daa6d.png
 

 

 

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

 

 

-../_images/fcaf294a75fafe9c0dabc7e2e2643f61e1c78b78bf8d7b7c74f489d637b37f5e.png
+../_images/6b073ff4da977796cd83cbde883fc57d2020aa49a030ad209caf50cf602d2ed0.png
 

 

 
@@ -750,18 +750,18 @@ 
System configuration

diff --git a/dev/notebooks/Example_2_Input_node_volatility_coupling.html b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
index 29cc860f9..c6fc1db16 100644
--- a/dev/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -700,16 +700,16 @@ 
System configuration

diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index 41a36795f..527d1dfac 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -1085,8 +1085,8 @@ 
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.
 

 

@@ -1108,7 +1108,7 @@ 
Bayesian inference
-../_images/0bba87b6564f6e1b89f69ac4008106745193c9ab38469327996d57ab691549af.png
+../_images/a77ae1bfd70fb40c608ea1fd03851f2e9bab02ee0c65d00b2c4657ea108a3ad3.png
 

 

 
@@ -1129,20 +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 ea656d53d..99ffb692a 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 232686e4e..9f84a03f2 100644
--- a/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
+++ b/dev/notebooks/Exercise_2_Bayesian_reinforcement_learning.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -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/991f82e9696cd7d3f0618e19ed129eec406af21ba5f7da9b1830c71a725bdcbb.png
+../_images/ee9dc392384b097f0725e665558746eda7bc4cb5a26c74e936a2f6571ca92a9f.png
 

 

 

@@ -785,14 +785,14 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.601
-      0.411
-      -3.451
-      -1.924
-      0.019
-      0.014
-      461.0
-      274.0
+      -2.635
+      0.424
+      -3.458
+      -1.963
+      0.022
+      0.016
+      366.0
+      357.0
       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/7aa075874fcdc60d20a74dc6c143db3a8778d60aafb03761ac29241d39cdbb46.png
+../_images/0125e6c24675587c8b7edcf6f0ae85f89ed272b8de9ac1c47d6633d0f4bf9dc3.png
 

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

@@ -925,7 +925,7 @@ 
Rescorla-Wagner{"version_major": 2, "version_minor": 0, "model_id": "303cb4d2facc4bb5a0848451139edf2c"}
/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()
 

 

@@ -945,7 +945,7 @@ 
Rescorla-Wagner
-../_images/ebaab3c7b7513465bdd12df482e37d906e122d25641f979da6146b8704bb3751.png
+../_images/4ff35c2f659d7121fcdddc93c7627afc1fbd58b23719c0a709cbcf52271258f7.png
 

 

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

 

@@ -1053,7 +1056,7 @@ 
Two-level HGF
-../_images/03caec3ab03f20294c3707833867f2cfcc2c1639c8fca63755c53aded3b75ae6.png
+../_images/039f964915013f97f932e89e63ab2bd81c1f9b6776452d2859b9500028c093fe.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 +1150,12 @@ 
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 59 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 62 divergences after tuning. Increase `target_accept` or reparameterize.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1167,7 +1170,7 @@ 
Three-level HGF
-../_images/cff5862e54ae3718509cae3aeee1750ba09ee6a1df969e8e5110ecee2c288e55.png
+../_images/72e042fb0474fb1af355d6d55333f206666e1511111ca20378de2227a2a360f2.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1240,11 +1243,11 @@ 
Model comparison
-../_images/9aa3f9497d9c23d0a39ec9860dc87b88a29e22b3a079756d74ba695ea5c9fed7.png
+../_images/70ee31cbcfdbe0cf420996ea0c7378a41deb35af77cb05422db1e8fb4d41d3b7.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 +1416,7 @@ 
Beliefs trajectories
 
 

-../_images/65ae9b8bebab8af2e4e4fed26ad7cd33c978cd405811eaf9b1bbbaf04b6b7d46.png
+../_images/7be18415119f0f3c70fbf54cd78a6021334671ac91bb9e71d48a8f0fc431b087.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 +1485,19 @@ 
System configuration
diff --git a/dev/searchindex.js b/dev/searchindex.js
index c79040e05..ced6bf91f 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, 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