PrincetonUniversity / PsyNeuLink / 36515852469

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Hierarchical PEC Fitting #1: KDE+LaplaceEM (#3619)

Fits a group of participants jointly rather than one at a time, so each
participant's estimate is informed by the population. Estimation is by
empirical-Bayes Laplace EM, with participants drawn from `z_s ~ N(beta,
diag(sigma))` in an unconstrained space derived from the search ranges.

```
pec = ParameterEstimationComposition(
    ..., data=stacked, fit_method="hierarchical",
    hierarchical_options={"subject_id": "subject"},
    distributed_options={"pec_factory": build_participant_pec},
)
results = pec.run()
results.group_parameters
```

`hierarchical_options["subject_id"]` in the data identifies
participants. PEC requires every column of data to be an outcome
variable, so the column is removed both from the group composition's own
data and from each participant's slice before it reaches the factory.
pec_factory builds one participant's model from their slice, and is
required because a Composition cannot be copied.

Setting distributed=True fits participants across a Dask cluster, one
per task, resolved through the same helpers as distributed
maximum-likelihood fitting. Results are collected by participant index
rather than completion order, so distributed and in-process fits agree
exactly.

Documented in `HierarchicalFitting.rst`, with a runnable example that
fits a simulated group and reports recovery.

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