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/dev/null +++ b/dev/_images/0ba20fbb366350193d13c30d326774e36b8529d96dbc0b304f8fa0174a2a7502.svg @@ -0,0 +1,135 @@ + + + + + + +%3 + + +cluster10 + +10 + + +cluster10 x 320 + +10 x 320 + + + +sigma_temperature + +sigma_temperature +~ +HalfNormal + + + +inverse_temperature + +inverse_temperature +~ +LogNormal + + + +sigma_temperature->inverse_temperature + + + + + +mu_temperature + +mu_temperature +~ +Normal + + + +mu_temperature->inverse_temperature + + + + + +mu_volatility + +mu_volatility +~ +Normal + + + +volatility + +volatility +~ +Normal + + + +mu_volatility->volatility + + + + + +sigma_volatility + +sigma_volatility +~ +HalfNormal + + + +sigma_volatility->volatility + + + + + +pointwise_loglikelihood + +pointwise_loglikelihood +~ +Deterministic + + + +volatility->pointwise_loglikelihood + + + + + +log_likelihood + +log_likelihood +~ +CustomDist_log_likelihood + + + +volatility->log_likelihood + + + + + +inverse_temperature->pointwise_loglikelihood + + + + + 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b/dev/_images/fdd6d877846c97d412099272c3cda0b105e770024d9b6e23f6b5263597b4fc60.png deleted file mode 100644 index f3ff43a4e..000000000 Binary files a/dev/_images/fdd6d877846c97d412099272c3cda0b105e770024d9b6e23f6b5263597b4fc60.png and /dev/null differ diff --git a/dev/_images/ff6ae2c0ae1851f198ac15a979cfa4ebb5d5bfc268b50bc68ad883e32a14a80f.svg b/dev/_images/ff6ae2c0ae1851f198ac15a979cfa4ebb5d5bfc268b50bc68ad883e32a14a80f.svg deleted file mode 100644 index b34093df5..000000000 --- a/dev/_images/ff6ae2c0ae1851f198ac15a979cfa4ebb5d5bfc268b50bc68ad883e32a14a80f.svg +++ /dev/null @@ -1,135 +0,0 @@ - - - - - - -%3 - - -cluster10 - -10 - - -cluster10 x 320 - -10 x 320 - - - -mu_temperature - -mu_temperature -~ -Normal - - - -inverse_temperature - -inverse_temperature -~ -LogNormal - - - -mu_temperature->inverse_temperature - - - - - -mu_volatility - -mu_volatility -~ -Normal - - - -volatility - -volatility -~ -Normal - - - -mu_volatility->volatility - - - - - -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/trajectories.png b/dev/_images/trajectories.png index 516bdb54d..6ddb75ac4 100644 Binary files a/dev/_images/trajectories.png and b/dev/_images/trajectories.png differ diff --git a/dev/notebooks/0.1-Theory.html b/dev/notebooks/0.1-Theory.html index 35a6ed428..cabba75b7 100644 --- a/dev/notebooks/0.1-Theory.html +++ b/dev/notebooks/0.1-Theory.html @@ -931,11 +931,11 @@

System configuration diff --git a/dev/notebooks/0.2-Creating_networks.html b/dev/notebooks/0.2-Creating_networks.html index 34479d2dd..de2a5544d 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/af4d4741e5bc71839707ead7a8738ea417a80edb7eb6eeb7458d70423dd9d49b.png +../_images/36e465fb8605174b008e3d5a72d3c6f83da6bdfba2981e44944201a7e3298d83.png
@@ -1135,12 +1135,12 @@

System configuration

diff --git a/dev/notebooks/0.3-Generalised_filtering.html b/dev/notebooks/0.3-Generalised_filtering.html index ffc470056..37cb80549 100644 --- a/dev/notebooks/0.3-Generalised_filtering.html +++ b/dev/notebooks/0.3-Generalised_filtering.html @@ -1000,13 +1000,13 @@

System configuration diff --git a/dev/notebooks/1.1-Binary_HGF.html b/dev/notebooks/1.1-Binary_HGF.html index 5de22db6d..b8a6f5d44 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/685fda99af028c72672e3206ea8ee16c1a52789d27948be8eaf87fa8d7d98181.png
+../_images/c2cf3897d7a4070491b2a526f6461af4509dc2827162e699e1a294cfdea4cfb5.png
 

 
 
@@ -883,7 +883,7 @@ 
Using the learned parameters
-../_images/15dc40f4e6e445ad3c9d895fa3a76748cacf076c24ee80be754b237051cdc03c.png
+../_images/ced23699c810d7a2480c199c0919d48ccd3ff10c48f3dc1437724fc5ac2ace92.png
 
 
 

@@ -893,7 +893,7 @@ 
Using the learned parameters
-
Array(202.52992, dtype=float32)
+
Array(202.53122, dtype=float32)
 

 

 

@@ -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/621bd4bc41eb3bb1c3ba37af682abf523053170fe477709fab35f9e596212895.png
+../_images/932ecb6a0e5ec59c3732c1f51e60cc875f3e17d28d655bee42f984b34376573d.png
 

 

 
@@ -1028,7 +1028,7 @@ 
Using the learned parameters
-../_images/3f9c9d096d1b45be79de680296b186aa4ef181d7e4390ab20a6046f038f7a98c.png
+../_images/30bd96556d8fc100293737420d8e30cb63bedffcb9cbabe04860e93054d5e632.png
 

 

 

@@ -1038,7 +1038,7 @@ 
Using the learned parameters
-
Array(203.00859, dtype=float32)
+
Array(203.0094, dtype=float32)
 

 

 

@@ -1066,13 +1066,13 @@ 
System configuration

diff --git a/dev/notebooks/1.2-Categorical_HGF.html b/dev/notebooks/1.2-Categorical_HGF.html
index 8135a8d2f..def3cf0e3 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/4535da753e514502a56155b3635236909cb08ff6c3118a75b2b5c95c8c290167.png
+../_images/a80ebe6b1ccad68df46f36a0528d4d87f6ce986899833e43f58eb7712d2b561c.png
 

 

 

@@ -701,7 +701,7 @@ 
Fitting the model forwards
-../_images/8b6be87835fa80f2997c25a27b88d7803528429bdf38de7af260c18a3c7aec03.png
+../_images/b2d813276b4b0dbd76aa9185852eddfdc3f39d064a64f2b3270b387c698fa53b.png
 

 
 
@@ -859,14 +859,14 @@ 
System configuration
diff --git a/dev/notebooks/1.3-Continuous_HGF.html b/dev/notebooks/1.3-Continuous_HGF.html
index 053a25f9c..e561914e7 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_3070/2516081684.py:2: UserWarning: The figure layout has changed to tight
+
/tmp/ipykernel_3083/2516081684.py:2: UserWarning: The figure layout has changed to tight
   plt.tight_layout()
 

 

-../_images/346c7d30a296bd356a4761f846cd627fa166eed929d24c1963d7e4fa286b9638.png
+../_images/2ac5867a267acde37b6c94879e0e94d75c938b2829d2d37fb61be7f161e91560.png
 

 

 
@@ -937,7 +937,7 @@ 
Using the learned parameters
-../_images/c33edbdb345ad850c93c219b866a261642054de85b00a5c8ce9f5886f0db4526.png
+../_images/c06aa9c543950b9451a72f407f8609e33c323cd8e7394ebeefe20feb5f0e0319.png
 

 
 

@@ -947,7 +947,7 @@ 
Using the learned parameters
-
Array(-1106.1111, dtype=float32)
+
Array(-1106.1184, 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 10 seconds.
 

 

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

 

 

-../_images/fdd6d877846c97d412099272c3cda0b105e770024d9b6e23f6b5263597b4fc60.png
+../_images/45af09e6c0b93d7873ac0b696788c8ec8676af1d5c65bfbc5762c08fd92d4800.png
 

 

 
@@ -1074,7 +1074,7 @@ 
Using the learned parameters
-../_images/fb695e13af21b24d9a38ac92d4775b743612ac26e9b6366320449a27e8706e8a.png
+../_images/dfee39395ca83be65ed14d8c727befd0d88e3b40fec47a6c77d8172320319348.png
 
 
 

@@ -1084,7 +1084,7 @@ 
Using the learned parameters
-
Array(-1118.0354, dtype=float32)
+
Array(-1118.0209, dtype=float32)
 

 

 

@@ -1113,11 +1113,11 @@ 
System configurationvar togglebuttonSelector = '.toggle, .admonition.dropdown';
     
     
-    
+    
     
     
     
@@ -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
-      -3.98
-      0.487
-      -4.858
-      -3.059
-      0.016
+      -3.949
+      0.483
+      -4.846
+      -3.057
+      0.017
       0.012
-      906.0
-      1453.0
+      845.0
+      1191.0
       1.0
     
   
 
-
../_images/df92baea67d169287416455df87f373ce1d18462d4cca6db3be6d2ff9d46f2e6.png
+../_images/9ede295df2d6a861f1b4d38fcccdd431d4b454af14f961e9227d9654f0407c48.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.

@@ -990,14 +990,14 @@ 
System configuration
diff --git a/dev/notebooks/3-Multilevel_HGF.html b/dev/notebooks/3-Multilevel_HGF.html
index d3d46f280..6baeb19d9 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/ff6ae2c0ae1851f198ac15a979cfa4ebb5d5bfc268b50bc68ad883e32a14a80f.svg
+../_images/0ba20fbb366350193d13c30d326774e36b8529d96dbc0b304f8fa0174a2a7502.svg
 
 
 
@@ -832,23 +832,17 @@ 
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 27 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 46 seconds.
 

 

-
There were 1000 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 1 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
-

-

 

 

 

@@ -875,7 +869,7 @@ 
Visualization of the posterior distributions
-../_images/ed02c4af08d89f5d7ab0b508f60c80b173f5b42ea7caa307bb171a51dd6ca7a9.png
+../_images/efb6e5302e23e8f405e403663102c1763cdc0d44db7d1f221863b65b447fc2e0.png
 

 

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

@@ -902,17 +896,17 @@ 
Model comparison
Computed from 2000 posterior samples and 3200 observations log-likelihood matrix.
 
          Estimate       SE
-elpd_loo -2554.73    78.30
-p_loo      794.16        -
+elpd_loo -1684.22    25.63
+p_loo       17.90        -
 
 There has been a warning during the calculation. Please check the results.
 ------
 
 Pareto k diagnostic values:
                          Count   Pct.
-(-Inf, 0.70]   (good)     2281   71.3%
-   (0.70, 1]   (bad)         1    0.0%
-   (1, Inf)   (very bad)  918   28.7%
+(-Inf, 0.70]   (good)     3184   99.5%
+   (0.70, 1]   (bad)         3    0.1%
+   (1, Inf)   (very bad)   13    0.4%
 

 

 
@@ -939,15 +933,15 @@ 
System configuration
diff --git a/dev/notebooks/4-Parameter_recovery.html b/dev/notebooks/4-Parameter_recovery.html
index 3369cec97..671a30c97 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 63 seconds.
+

+

+
Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 67 seconds.
 

 

-
There were 1997 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 2000 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/777aa544ac4dcbf5f106862e13b673416c3e48aed23b0ed7616079e97a3e5e32.png
+../_images/e6c46af75bd253363d1ec14112c61c8aa36ffaec1fc953620f1074188dd23223.png
 

 

 
@@ -776,15 +776,15 @@ 
System configuration

diff --git a/dev/notebooks/5-Non_linear_value_coupling.html b/dev/notebooks/5-Non_linear_value_coupling.html
index 89d9de3d1..57d4ca324 100644
--- a/dev/notebooks/5-Non_linear_value_coupling.html
+++ b/dev/notebooks/5-Non_linear_value_coupling.html
@@ -988,13 +988,13 @@ 
System configuration

diff --git a/dev/notebooks/Example_1_Heart_rate_variability.html b/dev/notebooks/Example_1_Heart_rate_variability.html
index 3ccf70aa7..40c63c19c 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,  1.14s/it]
+
Downloading ECG channel:  50%|█████     | 1/2 [00:00<00:00,  2.46it/s]
 

 

-
Downloading Respiration channel:  50%|█████     | 1/2 [00:01<00:01,  1.14s/it]
+
Downloading Respiration channel:  50%|█████     | 1/2 [00:00<00:00,  2.46it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.09s/it]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.92it/s]
 

 

-
Downloading Respiration channel: 100%|██████████| 2/2 [00:02<00:00,  1.10s/it]
+
Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00,  1.99it/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/1b2cd3602e88f0369f1e7f6ddc2996c4ff2d4d8f6adad0df74624b86e44acae7.png
+../_images/eab636586c81918384f64a1ef77a5ddda1e64fb4c611acbfc726ce9c8cc8d14e.png
 

 

 

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

 

 

-../_images/42ece0c760ca3462d1a64a909fdbb445dec3a2a13903bb304382033cc9c81657.png
+../_images/bcc592c2fe5c76053ebf8dec58aa730efc69eba303d8cf4ec9b4a8393a019bcd.png
 

 

 
@@ -754,14 +754,14 @@ 
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 8fbb38e1f..4fbfc5ec2 100644
--- a/dev/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/dev/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -704,12 +704,12 @@ 
System configuration

diff --git a/dev/notebooks/Example_3_Multi_armed_bandit.html b/dev/notebooks/Example_3_Multi_armed_bandit.html
index ddb261107..fb25993f5 100644
--- a/dev/notebooks/Example_3_Multi_armed_bandit.html
+++ b/dev/notebooks/Example_3_Multi_armed_bandit.html
@@ -52,7 +52,7 @@
     
     
     
-    
+    
     
     
     
@@ -1085,14 +1085,11 @@ 
Bayesian inference
NUTS: [omega]
 

 

-

-

+

+

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

 

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

-

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

 

@@ -1108,7 +1105,7 @@ 
Bayesian inference
-../_images/d5c5a97398656d0686b9767717490d1e07025f0da2e68fbe4d7a5a702cfc5da9.png
+../_images/2b35f0d9c22535e9e06d45a238d0dcf81cd4f23e61d378c608e7726c99a6864b.png
 

 

 
@@ -1133,16 +1130,16 @@ 
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 0b1f34205..bdac28fa4 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
@@ -1044,11 +1044,11 @@ 
System configurationvar togglebuttonSelector = '.toggle, .admonition.dropdown';
     
     
-    
+    
     
     
     
@@ -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/d26c403c9e83b0b3dff7c5485a76b7732915a7254507dcead6ade3245ca07266.png
+../_images/68f847f3566113cdd57d337150751098e051c403a40a9022b9f5c96137a3c871.png
 

 
 

@@ -785,15 +785,15 @@ 
Parameters optimization
     
       tonic_volatility_2
-      -2.583
-      0.379
-      -3.286
-      -1.916
-      0.015
-      0.011
-      610.0
-      590.0
-      1.01
+      -2.591
+      0.41
+      -3.358
+      -1.87
+      0.019
+      0.014
+      481.0
+      772.0
+      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/0471bfc7f5b457136d95ba644a9bfe011b2f621280ffbb07488b7d5a793e6a04.png
+../_images/18fda00659913f2d6c6328e86805a52a7ee3e15cde9d53d3c135e0d2821e8eaf.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": "d2909941bbf543408537e457029c0c8f"}
/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 23 seconds.
 

 

 
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -945,7 +945,7 @@ 
Rescorla-Wagner
-../_images/27c79f989dc37a089cf770c31b5b78ec48ceb2afa29bf7edf7045201c97ee7e8.png
+../_images/702737f2196865d58fb741b4552727fcfc2f4116e156d4063376af74b6f48fd9.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/552486a3c2daff615e891fe08898274f80724ae60307d06194a91ea136381d07.png
+../_images/28e2845ab02f424a08a9a2b1f4dca0afbc2aad29a72c95311865cc999b365676.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 52 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 55 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/5cd5e876923055f6e9a080fad3af8d7656f54bdf27cfed81f3dd2225946b8e1f.png
+../_images/0266e1b56849deff151b4a1b0999eb0915e320b7c60f891bfbf4d2d8ca461dbf.png
 

 

 
Move pointwise estimate into the likelihood field.

@@ -1240,11 +1240,11 @@ 
Model comparison
-../_images/368f7131ff797a25bddc793b46fefba095de3636305043a4322297ba6f4b8b45.png
+../_images/ee3019523e7abcf16a1c79102a6a253aecbec5758ba38d23b9da02a3ba419d39.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/beb370f4030370a25b65ecc7562478b3edc6cf905fd72a41d5096c626c408c88.png
+../_images/d8cb827f38937c1873e6c640c4130560cf2f8c8dd845a6b78374d34709239142.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.

@@ -1486,14 +1486,14 @@ 
System configuration