"""Evidence accumulation: Markov versus quantum walk
=================================================

Perception and judgement over time: Markov versus quantum walks (Busemeyer, Kvam and Pleskac, 2019).

Confidence is judged at t1 and t2 or only at t2. The Markov walk predicts that the t2 distribution
does not depend on whether t1 was judged; the quantum walk predicts an interference effect.
Data are simulated from a quantum walk and both models are fitted.
"""
# sphinx_gallery_start_ignore
import sys, pathlib; sys.path.insert(0, str(pathlib.Path(sys.argv[0]).resolve().parents[1] / "src"))  # run without installing
# sphinx_gallery_end_ignore
# sphinx_gallery_thumbnail_path = '_static/thumbs/ex_04.png'
import numpy as np
from quantum_mind.core import compare
from quantum_mind.families.dynamics import MarkovWalk, QuantumWalk

# %%
# Design
# ------
# A single judgement at t = 1.5, and a pair of judgements at t = 0.5 and t = 1.5.
design = {'t2_only': ('single', 1.5), 'joint': ('joint', 0.5, 1.5)}
truth = QuantumWalk(mu=3.0, sigma=3.0)
p = truth.predict(design)
print('P(t2) alone      ', p['t2_only'].round(3))
print('P(t2) after t1   ', p['joint'].reshape(3, 3).sum(0).round(3), '(differs: interference of the first judgement)')

# %%
# Model comparison
# ----------------
# Judgements simulated from the quantum walk are fitted by both models.
data = truth.sample(design, 400, np.random.default_rng(2))
for fr in compare([QuantumWalk, MarkovWalk], data, design, restarts=6):
    print('  %-12s BIC %.1f params %s' % (type(fr.model).__name__, fr.bic, {k: round(v, 2) for k, v in fr.model.params.items()}))