Bayesian Inference¶

Fish Task¶

Participants observe a sequence of coloured fish and must infer which of three ponds the fish were drawn from. Each pond contains fish in a fixed 80–10–10 colour ratio. The single parameter lambda governs how quickly beliefs about the pondupdate as new fish are observed: lower values make observations less predictive, so more confirming evidence is required to gain confidence and reduce uncertainty.

In [1]:

import numpy as np
from pyem import EMModel
from pyem.models.bayes import bayes_model
from params import build_params

print(f"Model ID   : {bayes_model.id}")
print(f"Description: {bayes_model.desc}")
print(f"Spec       : {bayes_model.spec}")

import numpy as np from pyem import EMModel from pyem.models.bayes import bayes_model from params import build_params print(f"Model ID : {bayes_model.id}") print(f"Description: {bayes_model.desc}") print(f"Spec : {bayes_model.spec}")

Model ID   : bayes
Description: Bayesian belief-updating over which of three ponds a fish came
from, based on the fish's observed colour on each trial (no feedback given).
`lambda1` controls how strongly each observation updates the belief; smaller
values require more confirming evidence before confidence increases.
Free parameters: lambda1 (belief-update rate, in [0,1]).
Spec       : {'bu': {'belief_update': ['lambda1']}}

In [2]:

# simulate computer agents completing the fish task
nsubjects, nblocks, ntrials = 50, 6, 15

# generate "true" parameters using the shared parameter registry (examples/params.py)
param_names, param_xform, true_lambda = build_params(["lambda1"], nsubjects)

# simulate computer agents completing the fish task nsubjects, nblocks, ntrials = 50, 6, 15 # generate "true" parameters using the shared parameter registry (examples/params.py) param_names, param_xform, true_lambda = build_params(["lambda1"], nsubjects)

In [3]:

# fit and recover
model = EMModel(all_data=None, 
                fit_func=bayes_model.fit, 
                param_names=param_names, 
                param_xform=param_xform, 
                simulate_func=bayes_model.sim
                )

recovery = model.recover(true_lambda, 
                         pr_inputs=['choices','observations'], 
                         nblocks=nblocks, ntrials=ntrials
                         )

# scatter plot of recovered parameters
fig = model.plot_recovery(recovery)

# fit and recover model = EMModel(all_data=None, fit_func=bayes_model.fit, param_names=param_names, param_xform=param_xform, simulate_func=bayes_model.sim ) recovery = model.recover(true_lambda, pr_inputs=['choices','observations'], nblocks=nblocks, ntrials=ntrials ) # scatter plot of recovered parameters fig = model.plot_recovery(recovery)

recover(): this model's data and outfit now reflect the recovery fit; the recovered estimates are also in the returned dict['recovery_model'].

References

Fiore, V. G., & Gu, X. (2022). Similar network compositions, but distinct neural dynamics underlying belief updating in environments with and without explicit outcomes. NeuroImage, 247, 118821. https://doi.org/10.1016/j.neuroimage.2021.118821

Fiore, V., Kiely, A., Zhang, E., Simonetti, J., Phadnis, A., Yang, S., Berner, L., & Smith, A. (2026). Widely used bandit tasks elicit diverging belief updating phenotypes in healthy adults. Research Square Preprint. https://doi.org/10.21203/rs.3.rs-9439488/v1