Source code for pyhgf.networks
+ Source code for pyhgf.utils
# Author: Nicolas Legrand <nicolas.legrand@cas.au.dk>
from functools import partial
@@ -477,7 +477,7 @@ Source code for pyhgf.networks
-[docs]
+[docs]
@partial(jit, static_argnames=("update_sequence", "structure"))
def beliefs_propagation(
attributes: Attributes,
@@ -551,7 +551,7 @@ Source code for pyhgf.networks
-[docs]
+[docs]
def trim_sequence(
exclude_node_idxs: List, update_sequence: UpdateSequence, edges: Tuple
) -> UpdateSequence:
@@ -587,7 +587,7 @@ Source code for pyhgf.networks
-[docs]
+[docs]
def list_branches(node_idxs: List, edges: Tuple, branch_list: List = []) -> List:
"""Return the branch of a network from a given set of root nodes.
@@ -647,7 +647,7 @@ Source code for pyhgf.networks
-[docs]
+[docs]
def fill_categorical_state_node(
network: "Network",
node_idx: int,
@@ -730,7 +730,7 @@ Source code for pyhgf.networks
-[docs]
+[docs]
def get_update_sequence(network: "Network", update_type: str) -> List:
"""Generate an update sequence from the network's structure.
diff --git a/_sources/api.rst.txt b/_sources/api.rst.txt
index c09fddf83..8802acd68 100644
--- a/_sources/api.rst.txt
+++ b/_sources/api.rst.txt
@@ -203,15 +203,15 @@ least the HGF instance as input after observation and returning surprise.
binary_softmax
binary_softmax_inverse_temperature
-Networks
-********
+Utils
+*****
-Utilities for manipulating networks of probabilistic nodes.
+Utilities for manipulating neural networks.
-.. currentmodule:: pyhgf.networks
+.. currentmodule:: pyhgf.utils
.. autosummary::
- :toctree: generated/pyhgf.networks
+ :toctree: generated/pyhgf.utils
beliefs_propagation
trim_sequence
diff --git a/_sources/generated/pyhgf.networks/pyhgf.networks.beliefs_propagation.rst.txt b/_sources/generated/pyhgf.networks/pyhgf.networks.beliefs_propagation.rst.txt
deleted file mode 100644
index cb2ecbd36..000000000
--- a/_sources/generated/pyhgf.networks/pyhgf.networks.beliefs_propagation.rst.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-pyhgf.networks.beliefs\_propagation
-===================================
-
-.. currentmodule:: pyhgf.networks
-
-.. autofunction:: beliefs_propagation
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.networks/pyhgf.networks.fill_categorical_state_node.rst.txt b/_sources/generated/pyhgf.networks/pyhgf.networks.fill_categorical_state_node.rst.txt
deleted file mode 100644
index c5147f3ca..000000000
--- a/_sources/generated/pyhgf.networks/pyhgf.networks.fill_categorical_state_node.rst.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-pyhgf.networks.fill\_categorical\_state\_node
-=============================================
-
-.. currentmodule:: pyhgf.networks
-
-.. autofunction:: fill_categorical_state_node
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.networks/pyhgf.networks.get_update_sequence.rst.txt b/_sources/generated/pyhgf.networks/pyhgf.networks.get_update_sequence.rst.txt
deleted file mode 100644
index 2f43b4ee2..000000000
--- a/_sources/generated/pyhgf.networks/pyhgf.networks.get_update_sequence.rst.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-pyhgf.networks.get\_update\_sequence
-====================================
-
-.. currentmodule:: pyhgf.networks
-
-.. autofunction:: get_update_sequence
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.networks/pyhgf.networks.list_branches.rst.txt b/_sources/generated/pyhgf.networks/pyhgf.networks.list_branches.rst.txt
deleted file mode 100644
index c25afbd3b..000000000
--- a/_sources/generated/pyhgf.networks/pyhgf.networks.list_branches.rst.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-pyhgf.networks.list\_branches
-=============================
-
-.. currentmodule:: pyhgf.networks
-
-.. autofunction:: list_branches
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.networks/pyhgf.networks.trim_sequence.rst.txt b/_sources/generated/pyhgf.networks/pyhgf.networks.trim_sequence.rst.txt
deleted file mode 100644
index 3bd08cd12..000000000
--- a/_sources/generated/pyhgf.networks/pyhgf.networks.trim_sequence.rst.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-pyhgf.networks.trim\_sequence
-=============================
-
-.. currentmodule:: pyhgf.networks
-
-.. autofunction:: trim_sequence
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.utils/pyhgf.utils.beliefs_propagation.rst.txt b/_sources/generated/pyhgf.utils/pyhgf.utils.beliefs_propagation.rst.txt
new file mode 100644
index 000000000..494978e3f
--- /dev/null
+++ b/_sources/generated/pyhgf.utils/pyhgf.utils.beliefs_propagation.rst.txt
@@ -0,0 +1,6 @@
+pyhgf.utils.beliefs\_propagation
+================================
+
+.. currentmodule:: pyhgf.utils
+
+.. autofunction:: beliefs_propagation
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.utils/pyhgf.utils.fill_categorical_state_node.rst.txt b/_sources/generated/pyhgf.utils/pyhgf.utils.fill_categorical_state_node.rst.txt
new file mode 100644
index 000000000..81450f4bf
--- /dev/null
+++ b/_sources/generated/pyhgf.utils/pyhgf.utils.fill_categorical_state_node.rst.txt
@@ -0,0 +1,6 @@
+pyhgf.utils.fill\_categorical\_state\_node
+==========================================
+
+.. currentmodule:: pyhgf.utils
+
+.. autofunction:: fill_categorical_state_node
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.utils/pyhgf.utils.get_update_sequence.rst.txt b/_sources/generated/pyhgf.utils/pyhgf.utils.get_update_sequence.rst.txt
new file mode 100644
index 000000000..bbe8607ae
--- /dev/null
+++ b/_sources/generated/pyhgf.utils/pyhgf.utils.get_update_sequence.rst.txt
@@ -0,0 +1,6 @@
+pyhgf.utils.get\_update\_sequence
+=================================
+
+.. currentmodule:: pyhgf.utils
+
+.. autofunction:: get_update_sequence
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.utils/pyhgf.utils.list_branches.rst.txt b/_sources/generated/pyhgf.utils/pyhgf.utils.list_branches.rst.txt
new file mode 100644
index 000000000..65a4d1c60
--- /dev/null
+++ b/_sources/generated/pyhgf.utils/pyhgf.utils.list_branches.rst.txt
@@ -0,0 +1,6 @@
+pyhgf.utils.list\_branches
+==========================
+
+.. currentmodule:: pyhgf.utils
+
+.. autofunction:: list_branches
\ No newline at end of file
diff --git a/_sources/generated/pyhgf.utils/pyhgf.utils.trim_sequence.rst.txt b/_sources/generated/pyhgf.utils/pyhgf.utils.trim_sequence.rst.txt
new file mode 100644
index 000000000..da88dd6e2
--- /dev/null
+++ b/_sources/generated/pyhgf.utils/pyhgf.utils.trim_sequence.rst.txt
@@ -0,0 +1,6 @@
+pyhgf.utils.trim\_sequence
+==========================
+
+.. currentmodule:: pyhgf.utils
+
+.. autofunction:: trim_sequence
\ No newline at end of file
diff --git a/_sources/notebooks/0.3-Generalised_filtering.ipynb.txt b/_sources/notebooks/0.3-Generalised_filtering.ipynb.txt
index 3ae750155..edc1a9f73 100644
--- a/_sources/notebooks/0.3-Generalised_filtering.ipynb.txt
+++ b/_sources/notebooks/0.3-Generalised_filtering.ipynb.txt
@@ -38,7 +38,7 @@
"from matplotlib.ticker import MultipleLocator\n",
"from pyhgf.math import MultivariateNormal, Normal, gaussian_predictive_distribution\n",
"from pyhgf.model import HGF\n",
- "from pyhgf.networks import beliefs_propagation\n",
+ "from pyhgf.utils import beliefs_propagation\n",
"from scipy.special import gammaln\n",
"from scipy.stats import norm, t\n",
"\n",
diff --git a/_sources/notebooks/Example_3_Multi_armed_bandit.ipynb.txt b/_sources/notebooks/Example_3_Multi_armed_bandit.ipynb.txt
index a63967026..1317b2413 100644
--- a/_sources/notebooks/Example_3_Multi_armed_bandit.ipynb.txt
+++ b/_sources/notebooks/Example_3_Multi_armed_bandit.ipynb.txt
@@ -942,7 +942,7 @@
"metadata": {},
"outputs": [],
"source": [
- "from pyhgf.networks import beliefs_propagation"
+ "from pyhgf.utils import beliefs_propagation"
]
},
{
diff --git a/api.html b/api.html
index 5ab3b0bc5..f3242540c 100644
--- a/api.html
+++ b/api.html
@@ -483,7 +483,7 @@
-
+
@@ -713,24 +713,24 @@ Response
-
-Networks#
-Utilities for manipulating networks of probabilistic nodes.
+
+Utils#
+Utilities for manipulating neural networks.
+
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.
@@ -977,7 +977,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -987,12 +987,12 @@ System configuration
diff --git a/notebooks/3-Multilevel_HGF.html b/notebooks/3-Multilevel_HGF.html
index 79f31f78e..88108fd81 100644
--- a/notebooks/3-Multilevel_HGF.html
+++ b/notebooks/3-Multilevel_HGF.html
@@ -51,7 +51,7 @@
-
+
@@ -707,7 +707,7 @@ Plot the computational graph
-
+
@@ -732,10 +732,10 @@ Sampling
NUTS: [mu_volatility, sigma_volatility, volatility, mu_temperature, sigma_temperature, inverse_temperature]
-
+
-
+
@@ -748,7 +748,7 @@ Visualization of the posterior distributions
-
+
The reference values on both posterior distributions indicate the mean of the distribution used for simulation.
@@ -764,7 +764,7 @@ System configuration
Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -774,10 +774,10 @@ System configurationvar togglebuttonSelector = '.toggle, .admonition.dropdown';
-
+
@@ -664,10 +664,10 @@ Inference from the simulated behavioursNUTS: [censored_volatility, inverse_temperature]
-
+
-
+
Visualizing parameters recovery - +
System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -748,13 +748,13 @@ System configuration
diff --git a/notebooks/Example_1_Heart_rate_variability.html b/notebooks/Example_1_Heart_rate_variability.html
index 1064b2bbc..c4f2b00a5 100644
--- a/notebooks/Example_1_Heart_rate_variability.html
+++ b/notebooks/Example_1_Heart_rate_variability.html
@@ -49,7 +49,7 @@
-
+
@@ -555,16 +555,16 @@ Loading and preprocessing physiological recordingDownloading ECG channel: 0%| | 0/2 [00:00<?, ?it/s]
-Downloading ECG channel: 50%|█████ | 1/2 [00:00<00:00, 1.45it/s]
+Downloading ECG channel: 50%|█████ | 1/2 [00:00<00:00, 1.72it/s]
-Downloading Respiration channel: 50%|█████ | 1/2 [00:00<00:00, 1.45it/s]
+Downloading Respiration channel: 50%|█████ | 1/2 [00:00<00:00, 1.72it/s]
-Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.60it/s]
+Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.78it/s]
-Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.57it/s]
+Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.77it/s]
@@ -638,7 +638,7 @@ Model#<
-
+
@@ -664,7 +664,7 @@ Model#<
self.pid = os.fork()
-/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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()
@@ -687,7 +687,7 @@ Model#<
-
+
@@ -719,7 +719,7 @@ Model#<
-
+
@@ -734,7 +734,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -744,12 +744,12 @@ System configuration
diff --git a/notebooks/Example_2_Input_node_volatility_coupling.html b/notebooks/Example_2_Input_node_volatility_coupling.html
index fff0d4550..9429da274 100644
--- a/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -681,7 +681,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -692,11 +692,11 @@ System configuration
diff --git a/notebooks/Example_3_Multi_armed_bandit.html b/notebooks/Example_3_Multi_armed_bandit.html
index e6aa3d1cd..3da28bb5e 100644
--- a/notebooks/Example_3_Multi_armed_bandit.html
+++ b/notebooks/Example_3_Multi_armed_bandit.html
@@ -51,7 +51,7 @@
-
+
@@ -821,10 +821,10 @@ Parameter recovery
Real-time decision and belief updating#
-We can implement this process using the pyhgf.networks.beliefs_propagation()
function. In other models, this step is called sequentially in a jax.lax.scan()
loop, but we can also use it for a single-step update.
+We can implement this process using the pyhgf.networks.beliefs_propagation()
function. In other models, this step is called sequentially in a jax.lax.scan()
loop, but we can also use it for a single-step update.
-from pyhgf.networks import beliefs_propagation
+from pyhgf.utils import beliefs_propagation
@@ -1081,16 +1081,16 @@ Bayesian inferenceNUTS: [omega]
-
+
-
+
-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 26 seconds.
-There were 2 divergences after tuning. Increase `target_accept` or reparameterize.
+There were 5 divergences after tuning. Increase `target_accept` or reparameterize.
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1108,7 +1108,7 @@ Bayesian inference
-
+
@@ -1123,7 +1123,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -1133,14 +1133,14 @@ System configuration
diff --git a/notebooks/Exercise_1_Using_the_HGF.html b/notebooks/Exercise_1_Using_the_HGF.html
index 4d3cb7189..0ffa953ab 100644
--- a/notebooks/Exercise_1_Using_the_HGF.html
+++ b/notebooks/Exercise_1_Using_the_HGF.html
@@ -51,7 +51,7 @@
-
+
@@ -758,7 +758,7 @@ Parameters optimization
-/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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()
@@ -771,7 +771,7 @@ Parameters optimization
-
+
@@ -813,15 +813,15 @@ Parameters optimization
tonic_volatility_1
- -5.988
- 0.919
- -7.608
- -4.236
- 0.027
- 0.019
- 1255.0
- 1111.0
- 1.0
+ -5.943
+ 0.946
+ -7.714
+ -4.169
+ 0.03
+ 0.022
+ 1079.0
+ 718.0
+ 1.01
@@ -1160,19 +1160,11 @@ Biased random{"version_major": 2, "version_minor": 0, "model_id": "6b990c3878b142398abc7fde6e6859b8"}/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 35 seconds.
-
-
-
-
@@ -1181,7 +1173,7 @@ Biased random
-
+
Assess model fitting, here using leave-one-out cross-validation from the Arviz library.
@@ -1196,8 +1188,8 @@ Biased randomComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -222.60 0.00
-p_loo 0.83 -
+elpd_loo -222.44 0.00
+p_loo 0.70 -
There has been a warning during the calculation. Please check the results.
------
@@ -1206,8 +1198,8 @@ Biased random{"version_major": 2, "version_minor": 0, "model_id": "f7fc458c340943bbb47a1a4f3f40cd97"}
-
-
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 102 seconds.
+/opt/hostedtoolcache/Python/3.12.3/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()
-
-
-
+
@@ -1323,7 +1311,7 @@ Rescorla-Wagner
-
+
@@ -1337,8 +1325,8 @@ Rescorla-WagnerComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -103.81 0.00
-p_loo 0.56 -
+elpd_loo -103.85 0.00
+p_loo 0.61 -
There has been a warning during the calculation. Please check the results.
------
@@ -1458,27 +1446,24 @@ Two-level HGFNUTS: [tonic_volatility_2]
-
+
-
+
-
+
-
+
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 35 seconds.
+
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 32 seconds.
-There were 1 divergences after tuning. Increase `target_accept` or reparameterize.
-
-
-
+
@@ -1487,7 +1472,7 @@ Two-level HGF
-
+
@@ -1501,7 +1486,7 @@ Two-level HGFComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -114.26 0.00
+elpd_loo -114.27 0.00
p_loo 0.95 -
There has been a warning during the calculation. Please check the results.
@@ -1581,24 +1566,24 @@ Three-level HGFNUTS: [tonic_volatility_2]
-
+
-
+
-
+
-
+
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 37 seconds.
+
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 38 seconds.
-There were 15 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 7 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -1611,7 +1596,7 @@ Three-level HGF
-
+
@@ -1625,8 +1610,8 @@ Three-level HGFComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -113.70 0.00
-p_loo 0.76 -
+elpd_loo -114.14 0.00
+p_loo 1.16 -
There has been a warning during the calculation. Please check the results.
------
@@ -1689,8 +1674,8 @@ Three-level HGF
-
+
@@ -1832,7 +1817,7 @@ System configuration
-Last updated: Thu May 23 2024
+
diff --git a/objects.inv b/objects.inv
index bc31aaee4..f88ae5525 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/searchindex.js b/searchindex.js
index bca6be893..5a459c7f0 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"A multilevel binary HGF": [[58, "a-multilevel-binary-hgf"]], "API": [[0, "api"]], "Acknowledgments": [[49, "acknowledgments"]], "Add data": [[54, "add-data"], [54, "id4"], [56, "add-data"], [56, "id3"]], "Adding a drift to the random walk": [[51, "adding-a-drift-to-the-random-walk"]], "An introduction to Hierarchical Gaussian Filters through practical exercises": [[63, "an-introduction-to-hierarchical-gaussian-filters-through-practical-exercises"]], "Autoregressive processes": [[51, "autoregressive-processes"]], "Bayesian inference": [[62, "bayesian-inference"]], "Bayesian reinforcement learning: the binary HGF": [[63, "bayesian-reinforcement-learning-the-binary-hgf"]], "Belief updating under uncertainty: the continuous Hierarchical Gaussian Filter": [[63, "belief-updating-under-uncertainty-the-continuous-hierarchical-gaussian-filter"]], "Biased random": [[63, "biased-random"]], "Binary inputs": [[0, "binary-inputs"]], "Binary nodes": [[0, "binary-nodes"], [0, "id1"]], "Binary state nodes": [[0, "binary-state-nodes"]], "Bivariate normal distribution": [[53, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous inputs": [[0, "continuous-inputs"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id2"]], "Continuous state nodes": [[0, "continuous-state-nodes"]], "Continuous value coupling": [[52, "continuous-value-coupling"]], "Continuous volatility coupling": [[52, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[52, "coupling-with-binary-nodes"]], "Create the model": [[54, "create-the-model"], [54, "id3"], [56, "create-the-model"], [56, "id2"]], "Creating a new response function": [[57, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[57, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[52, "creating-and-manipulating-networks-of-probabilistic-nodes"]], "Creating custom update functions": [[52, "creating-custom-update-functions"]], "Creating custom update sequences": [[52, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[52, "creating-probabilistic-nodes"]], "Creating the decision rule": [[57, "creating-the-decision-rule"]], "Creating the model": [[54, "creating-the-model"], [54, "id7"], [56, "creating-the-model"], [56, "id5"]], "Creating the probabilistic network": [[55, "creating-the-probabilistic-network"]], "Decision rule": [[62, "decision-rule"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[52, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[51, "dynamic-beliefs-updating"]], "Embeding Hierarchical Gaussian Filters in a multilevel Bayesian model": [[58, "embeding-hierarchical-gaussian-filters-in-a-multilevel-bayesian-model"]], "Example 1: Bayesian filtering of cardiac volatility": 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"fill_categorical_state_nod": 45, "filter": [49, 50, 51, 53, 54, 55, 56, 58, 60, 63], "first_level_binary_surpris": 21, "first_level_gaussian_surpris": 22, "fit": [49, 54, 55, 56], "fix": [53, 54, 56], "forward": 55, "from": [53, 57, 59, 62], "function": [0, 52, 57], "gaussian": [49, 50, 51, 53, 54, 55, 56, 58, 63], "gaussian_dens": 10, "gaussian_predictive_distribut": 11, "gaussian_surpris": 12, "gener": 51, "generalis": [51, 53], "get": 49, "get_update_sequ": 46, "glossari": [51, 57], "graph": 58, "heart": 60, "hgf": [14, 54, 56, 57, 58, 63], "hgf_logp": 4, "hgfdistribut": 2, "hgflogpgradop": 3, "hierarch": [49, 50, 51, 53, 54, 55, 56, 58, 63], "how": [1, 49], "implement": 52, "import": 54, "independ": 62, "infer": [55, 59, 62], "input": [0, 35, 36, 37, 38, 39, 52, 61], "instal": 49, "instantan": 60, "introduct": [51, 63], "known": 61, "kown": 61, "learn": [50, 53, 54, 56, 63], "level": [54, 56, 63], "librari": 49, "list_branch": 47, "load": 60, "manipul": 52, "math": [0, 5, 6, 7, 8, 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"pyhgf": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49], "random": [51, 63], "rate": 60, "real": 62, "record": 60, "recov": [57, 59], "recoveri": [59, 62], "refer": [49, 64], "reinforc": [53, 63], "rescorla": 63, "respons": [0, 19, 20, 21, 22, 23, 57, 62], "reward": 62, "rule": [57, 62], "sampl": [54, 55, 56, 58, 63], "sequenc": 52, "sigmoid": 13, "signal": 60, "simul": [55, 58, 59, 62], "start": 49, "state": [0, 55], "static": 52, "stationari": 53, "statist": 53, "step": 0, "structur": 62, "suffici": 53, "surpris": [54, 56, 57], "system": [51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63], "tabl": 0, "task": [59, 62], "theori": [50, 52], "three": [54, 56, 63], "through": [53, 63], "time": [52, 62], "total_gaussian_surpris": 23, "trajectori": [54, 56], "transit": 55, "trim_sequ": 48, "tutori": 50, "two": [54, 56, 63], "uncertainti": 63, "under": 63, "univari": 53, "unknown": 61, "unkown": 61, "unobserv": 52, "updat": [0, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 51, 52, 62, 63], "us": [50, 53, 54, 55, 56, 57], "util": [0, 44, 45, 46, 47, 48], "valu": [51, 52, 63], "vari": 52, "visual": [52, 54, 56, 58, 59], "volatil": [51, 52, 60, 63], "wagner": 63, "walk": [51, 63], "weather": 63, "work": [49, 52], "world": 63}})
\ No newline at end of file
Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -748,13 +748,13 @@ System configuration
diff --git a/notebooks/Example_1_Heart_rate_variability.html b/notebooks/Example_1_Heart_rate_variability.html
index 1064b2bbc..c4f2b00a5 100644
--- a/notebooks/Example_1_Heart_rate_variability.html
+++ b/notebooks/Example_1_Heart_rate_variability.html
@@ -49,7 +49,7 @@
-
+
@@ -555,16 +555,16 @@ Loading and preprocessing physiological recordingDownloading ECG channel: 0%| | 0/2 [00:00<?, ?it/s]
-Downloading ECG channel: 50%|█████ | 1/2 [00:00<00:00, 1.45it/s]
+Downloading ECG channel: 50%|█████ | 1/2 [00:00<00:00, 1.72it/s]
-Downloading Respiration channel: 50%|█████ | 1/2 [00:00<00:00, 1.45it/s]
+Downloading Respiration channel: 50%|█████ | 1/2 [00:00<00:00, 1.72it/s]
-Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.60it/s]
+Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.78it/s]
-Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.57it/s]
+Downloading Respiration channel: 100%|██████████| 2/2 [00:01<00:00, 1.77it/s]
@@ -638,7 +638,7 @@ Model#<
-
+
@@ -664,7 +664,7 @@ Model#<
self.pid = os.fork()
-/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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()
@@ -687,7 +687,7 @@ Model#<
-
+
@@ -719,7 +719,7 @@ Model#<
-
+
@@ -734,7 +734,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -744,12 +744,12 @@ System configuration
diff --git a/notebooks/Example_2_Input_node_volatility_coupling.html b/notebooks/Example_2_Input_node_volatility_coupling.html
index fff0d4550..9429da274 100644
--- a/notebooks/Example_2_Input_node_volatility_coupling.html
+++ b/notebooks/Example_2_Input_node_volatility_coupling.html
@@ -681,7 +681,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -692,11 +692,11 @@ System configuration
diff --git a/notebooks/Example_3_Multi_armed_bandit.html b/notebooks/Example_3_Multi_armed_bandit.html
index e6aa3d1cd..3da28bb5e 100644
--- a/notebooks/Example_3_Multi_armed_bandit.html
+++ b/notebooks/Example_3_Multi_armed_bandit.html
@@ -51,7 +51,7 @@
-
+
@@ -821,10 +821,10 @@ Parameter recovery
Real-time decision and belief updating#
-We can implement this process using the pyhgf.networks.beliefs_propagation()
function. In other models, this step is called sequentially in a jax.lax.scan()
loop, but we can also use it for a single-step update.
+We can implement this process using the pyhgf.networks.beliefs_propagation()
function. In other models, this step is called sequentially in a jax.lax.scan()
loop, but we can also use it for a single-step update.
-from pyhgf.networks import beliefs_propagation
+from pyhgf.utils import beliefs_propagation
@@ -1081,16 +1081,16 @@ Bayesian inferenceNUTS: [omega]
-
+
-
+
-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 26 seconds.
-There were 2 divergences after tuning. Increase `target_accept` or reparameterize.
+There were 5 divergences after tuning. Increase `target_accept` or reparameterize.
We recommend running at least 4 chains for robust computation of convergence diagnostics
@@ -1108,7 +1108,7 @@ Bayesian inference
-
+
@@ -1123,7 +1123,7 @@ System configuration
-Last updated: Thu May 23 2024
+Last updated: Fri May 24 2024
Python implementation: CPython
Python version : 3.12.3
@@ -1133,14 +1133,14 @@ System configuration
diff --git a/notebooks/Exercise_1_Using_the_HGF.html b/notebooks/Exercise_1_Using_the_HGF.html
index 4d3cb7189..0ffa953ab 100644
--- a/notebooks/Exercise_1_Using_the_HGF.html
+++ b/notebooks/Exercise_1_Using_the_HGF.html
@@ -51,7 +51,7 @@
-
+
@@ -758,7 +758,7 @@ Parameters optimization
-/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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()
@@ -771,7 +771,7 @@ Parameters optimization
-
+
@@ -813,15 +813,15 @@ Parameters optimization
tonic_volatility_1
- -5.988
- 0.919
- -7.608
- -4.236
- 0.027
- 0.019
- 1255.0
- 1111.0
- 1.0
+ -5.943
+ 0.946
+ -7.714
+ -4.169
+ 0.03
+ 0.022
+ 1079.0
+ 718.0
+ 1.01
@@ -1160,19 +1160,11 @@ Biased random{"version_major": 2, "version_minor": 0, "model_id": "6b990c3878b142398abc7fde6e6859b8"}/opt/hostedtoolcache/Python/3.12.3/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/3.12.3/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 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 35 seconds.
-
-
-
-
@@ -1181,7 +1173,7 @@ Biased random
-
+
Assess model fitting, here using leave-one-out cross-validation from the Arviz library.
@@ -1196,8 +1188,8 @@ Biased randomComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -222.60 0.00
-p_loo 0.83 -
+elpd_loo -222.44 0.00
+p_loo 0.70 -
There has been a warning during the calculation. Please check the results.
------
@@ -1206,8 +1198,8 @@ Biased random{"version_major": 2, "version_minor": 0, "model_id": "f7fc458c340943bbb47a1a4f3f40cd97"}
-
-
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 102 seconds.
+/opt/hostedtoolcache/Python/3.12.3/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()
-
-
-
+
@@ -1323,7 +1311,7 @@ Rescorla-Wagner
-
+
@@ -1337,8 +1325,8 @@ Rescorla-WagnerComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -103.81 0.00
-p_loo 0.56 -
+elpd_loo -103.85 0.00
+p_loo 0.61 -
There has been a warning during the calculation. Please check the results.
------
@@ -1458,27 +1446,24 @@ Two-level HGFNUTS: [tonic_volatility_2]
-
+
-
+
-
+
-
+
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 35 seconds.
+
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 32 seconds.
-There were 1 divergences after tuning. Increase `target_accept` or reparameterize.
-
-
-
+
@@ -1487,7 +1472,7 @@ Two-level HGF
-
+
@@ -1501,7 +1486,7 @@ Two-level HGFComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -114.26 0.00
+elpd_loo -114.27 0.00
p_loo 0.95 -
There has been a warning during the calculation. Please check the results.
@@ -1581,24 +1566,24 @@ Three-level HGFNUTS: [tonic_volatility_2]
-
+
-
+
-
+
-
+
-Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 37 seconds.
+
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 38 seconds.
-There were 15 divergences after tuning. Increase `target_accept` or reparameterize.
+
There were 7 divergences after tuning. Increase `target_accept` or reparameterize.
@@ -1611,7 +1596,7 @@ Three-level HGF
-
+
@@ -1625,8 +1610,8 @@ Three-level HGFComputed from 4000 posterior samples and 1.0 observations log-likelihood matrix.
Estimate SE
-elpd_loo -113.70 0.00
-p_loo 0.76 -
+elpd_loo -114.14 0.00
+p_loo 1.16 -
There has been a warning during the calculation. Please check the results.
------
@@ -1689,8 +1674,8 @@ Three-level HGF
-
+
@@ -1832,7 +1817,7 @@ System configuration
-Last updated: Thu May 23 2024
+
diff --git a/objects.inv b/objects.inv
index bc31aaee4..f88ae5525 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/searchindex.js b/searchindex.js
index bca6be893..5a459c7f0 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"A multilevel binary HGF": [[58, "a-multilevel-binary-hgf"]], "API": [[0, "api"]], "Acknowledgments": [[49, "acknowledgments"]], "Add data": [[54, "add-data"], [54, "id4"], [56, "add-data"], [56, "id3"]], "Adding a drift to the random walk": [[51, "adding-a-drift-to-the-random-walk"]], "An introduction to Hierarchical Gaussian Filters through practical exercises": [[63, "an-introduction-to-hierarchical-gaussian-filters-through-practical-exercises"]], "Autoregressive processes": [[51, "autoregressive-processes"]], "Bayesian inference": [[62, "bayesian-inference"]], "Bayesian reinforcement learning: the binary HGF": [[63, "bayesian-reinforcement-learning-the-binary-hgf"]], "Belief updating under uncertainty: the continuous Hierarchical Gaussian Filter": [[63, "belief-updating-under-uncertainty-the-continuous-hierarchical-gaussian-filter"]], "Biased random": [[63, "biased-random"]], "Binary inputs": [[0, "binary-inputs"]], "Binary nodes": [[0, "binary-nodes"], [0, "id1"]], "Binary state nodes": [[0, "binary-state-nodes"]], "Bivariate normal distribution": [[53, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous inputs": [[0, "continuous-inputs"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id2"]], "Continuous state nodes": [[0, "continuous-state-nodes"]], "Continuous value coupling": [[52, "continuous-value-coupling"]], "Continuous volatility coupling": [[52, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[52, "coupling-with-binary-nodes"]], "Create the model": [[54, "create-the-model"], [54, "id3"], [56, "create-the-model"], [56, "id2"]], "Creating a new response function": [[57, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[57, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[52, "creating-and-manipulating-networks-of-probabilistic-nodes"]], "Creating custom update functions": [[52, "creating-custom-update-functions"]], "Creating custom update sequences": [[52, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[52, "creating-probabilistic-nodes"]], "Creating the decision rule": [[57, "creating-the-decision-rule"]], "Creating the model": [[54, "creating-the-model"], [54, "id7"], [56, "creating-the-model"], [56, "id5"]], "Creating the probabilistic network": [[55, "creating-the-probabilistic-network"]], "Decision rule": [[62, "decision-rule"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[52, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[51, "dynamic-beliefs-updating"]], "Embeding Hierarchical Gaussian Filters in a multilevel Bayesian model": [[58, "embeding-hierarchical-gaussian-filters-in-a-multilevel-bayesian-model"]], "Example 1: Bayesian filtering of cardiac volatility": [[60, "example-1-bayesian-filtering-of-cardiac-volatility"]], "Example 2: Estimating the mean and precision of an input node": [[61, "example-2-estimating-the-mean-and-precision-of-an-input-node"]], "Example 3: A multi-armed bandit task with independent rewards and punishments": [[62, "example-3-a-multi-armed-bandit-task-with-independent-rewards-and-punishments"]], "Exercise 1": [[63, null]], "Exercise 2": [[63, null]], "Exercise 3": [[63, null]], "Exercises": [[50, "exercises"]], "Exercises 4": [[63, null]], "Exercises 5": [[63, null]], "Filtering the Sufficient Statistics of a Non-Stationary Distribution": [[53, "filtering-the-sufficient-statistics-of-a-non-stationary-distribution"]], "Filtering the Sufficient Statistics of a Stationary Distribution": [[53, "filtering-the-sufficient-statistics-of-a-stationary-distribution"]], "Fitting the binary HGF with fixed parameters": [[54, "fitting-the-binary-hgf-with-fixed-parameters"]], "Fitting the continuous HGF with fixed parameters": [[56, "fitting-the-continuous-hgf-with-fixed-parameters"]], "Fitting the model forwards": [[55, "fitting-the-model-forwards"]], "From Reinforcement Learning to Generalised Bayesian Filtering": [[53, "from-reinforcement-learning-to-generalised-bayesian-filtering"]], "Gaussian Random Walks": [[51, "gaussian-random-walks"]], "Gaussian random walks": [[63, "gaussian-random-walks"]], "Getting started": [[49, "getting-started"]], "Glossary": [[51, "glossary"], [57, "glossary"]], "How does it work?": [[49, "how-does-it-work"]], "How to cite?": [[1, "how-to-cite"]], "Imports": [[54, "imports"]], "Inference from the simulated behaviours": [[59, "inference-from-the-simulated-behaviours"]], "Inference using MCMC sampling": [[55, "inference-using-mcmc-sampling"]], "Inputs": [[0, "inputs"]], "Installation": [[49, "installation"]], "Introduction to the Generalised Hierarchical Gaussian Filter": [[51, "introduction-to-the-generalised-hierarchical-gaussian-filter"]], "Kown mean, unknown precision": 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\ No newline at end of file
+Search.setIndex({"alltitles": {"A multilevel binary HGF": [[58, "a-multilevel-binary-hgf"]], "API": [[0, "api"]], "Acknowledgments": [[49, "acknowledgments"]], "Add data": [[54, "add-data"], [54, "id4"], [56, "add-data"], [56, "id3"]], "Adding a drift to the random walk": [[51, "adding-a-drift-to-the-random-walk"]], "An introduction to Hierarchical Gaussian Filters through practical exercises": [[63, "an-introduction-to-hierarchical-gaussian-filters-through-practical-exercises"]], "Autoregressive processes": [[51, "autoregressive-processes"]], "Bayesian inference": [[62, "bayesian-inference"]], "Bayesian reinforcement learning: the binary HGF": [[63, "bayesian-reinforcement-learning-the-binary-hgf"]], "Belief updating under uncertainty: the continuous Hierarchical Gaussian Filter": [[63, "belief-updating-under-uncertainty-the-continuous-hierarchical-gaussian-filter"]], "Biased random": [[63, "biased-random"]], "Binary inputs": [[0, "binary-inputs"]], "Binary nodes": [[0, "binary-nodes"], [0, "id1"]], "Binary state nodes": [[0, "binary-state-nodes"]], "Bivariate normal distribution": [[53, "bivariate-normal-distribution"]], "Categorical nodes": [[0, "categorical-nodes"]], "Continuous inputs": [[0, "continuous-inputs"]], "Continuous nodes": [[0, "continuous-nodes"], [0, "id2"]], "Continuous state nodes": [[0, "continuous-state-nodes"]], "Continuous value coupling": [[52, "continuous-value-coupling"]], "Continuous volatility coupling": [[52, "continuous-volatility-coupling"]], "Coupling with binary nodes": [[52, "coupling-with-binary-nodes"]], "Create the model": [[54, "create-the-model"], [54, "id3"], [56, "create-the-model"], [56, "id2"]], "Creating a new response function": [[57, "creating-a-new-response-function"]], "Creating a new response function: the binary surprise": [[57, "creating-a-new-response-function-the-binary-surprise"]], "Creating and manipulating networks of probabilistic nodes": [[52, "creating-and-manipulating-networks-of-probabilistic-nodes"]], "Creating custom update functions": [[52, "creating-custom-update-functions"]], "Creating custom update sequences": [[52, "creating-custom-update-sequences"]], "Creating probabilistic nodes": [[52, "creating-probabilistic-nodes"]], "Creating the decision rule": [[57, "creating-the-decision-rule"]], "Creating the model": [[54, "creating-the-model"], [54, "id7"], [56, "creating-the-model"], [56, "id5"]], "Creating the probabilistic network": [[55, "creating-the-probabilistic-network"]], "Decision rule": [[62, "decision-rule"]], "Distribution": [[0, "distribution"]], "Dynamic assignation of update sequences": [[52, "dynamic-assignation-of-update-sequences"]], "Dynamic beliefs updating": [[51, "dynamic-beliefs-updating"]], "Embeding Hierarchical Gaussian Filters in a multilevel Bayesian model": [[58, "embeding-hierarchical-gaussian-filters-in-a-multilevel-bayesian-model"]], "Example 1: Bayesian filtering of cardiac volatility": [[60, "example-1-bayesian-filtering-of-cardiac-volatility"]], "Example 2: Estimating the mean and precision of an input node": [[61, "example-2-estimating-the-mean-and-precision-of-an-input-node"]], "Example 3: A multi-armed bandit task with independent rewards and punishments": [[62, "example-3-a-multi-armed-bandit-task-with-independent-rewards-and-punishments"]], "Exercise 1": [[63, null]], "Exercise 2": [[63, null]], "Exercise 3": [[63, null]], "Exercises": [[50, "exercises"]], "Exercises 4": [[63, null]], "Exercises 5": [[63, null]], "Filtering the Sufficient Statistics of a Non-Stationary Distribution": [[53, "filtering-the-sufficient-statistics-of-a-non-stationary-distribution"]], "Filtering the Sufficient Statistics of a Stationary Distribution": [[53, "filtering-the-sufficient-statistics-of-a-stationary-distribution"]], "Fitting the binary HGF with fixed parameters": [[54, "fitting-the-binary-hgf-with-fixed-parameters"]], "Fitting the continuous HGF with fixed parameters": 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