Bistable perception and the quantum Zeno effect

Perception: the quantum Zeno model predicts that the mean dwell time in one interpretation of an ambiguous figure grows as the percept is checked more often. The example simulates dwell times at two check intervals and compares the Zeno model with Markov switching and gamma renewal by BIC.

import numpy as np
from quantum_mind.core import compare
from quantum_mind.families.perception import (QuantumZenoBistableModel, MarkovSwitchingModel, GammaRenewalModel,
                                              dwell_time_design, mean_dwell_time)

zeno = QuantumZenoBistableModel(g=1.5)
for dt in (0.035, 0.07, 0.14):
    print('check interval %.3f s -> mean dwell time %.2f s' % (dt, mean_dwell_time(zeno, dt)))

check interval 0.035 s -> mean dwell time 12.71 s
check interval 0.070 s -> mean dwell time 6.37 s
check interval 0.140 s -> mean dwell time 3.22 s

Two check intervals identify the model (simulated dwell times)

design = dwell_time_design({'fast': 0.035, 'slow': 0.14}, max_time=40, n_bins=25)
data = zeno.sample(design, 300, np.random.default_rng(0))
for r in compare([QuantumZenoBistableModel, MarkovSwitchingModel, GammaRenewalModel], data, design):
    print('  %-26s BIC %.1f' % (type(r.model).__name__, r.bic))

QuantumZenoBistableModel   BIC 2796.6
GammaRenewalModel          BIC 3031.8
MarkovSwitchingModel       BIC 3073.8