This experiment creates a Bayesian cognitive model from experimental data to predict amyloid positivity, which is a marker of Alzheimer's disease.
Signal Detection Theory (SDT) literally studies how to separate signal from noise. More formally, how to separate information-bearing patterns from random noise. It is used to analyze decision making under uncertainty.
Ideal for forced choice experiments with two alternatives. Every choice the subject makes is either a "hit", "false alarm", "miss", or a "correct rejection." Specifically, we are interested in what criteria the decision-maker uses.
All trials are generated from a Gaussian mixture of "signal" and "noise" The subject can respond to a "signal" trial with either a "hit" or a "miss" The subject can respond to a "noise" trial with either a "false alarm" or a "correct rejection"
with pm.Model() as model1:
discriminability = pm.Normal('Discriminability', mu=0, tau=.5, shape=k)
bias = pm.Normal('Bias', mu=0, tau=2, shape=k)
theta_h = pm.Deterministic('Hit Rate', Phi((.5 * discriminability) - bias))
theta_f = pm.Deterministic('False Alarm Rate', Phi(-(.5 * discriminability) - bias))
N = np.ones_like(D.drec_hits) * 15
hit_rate = pm.Binomial('hit_rate', p=theta_h, n=[15]*k, observed=D.hit_rate[:k])
fa_rate = pm.Binomial('fa_rate', p=theta_f, n=[15]*k, observed=D.fa_rate[k])
trace1=pm.sample(init='adapt_diag')From the MCMC sampler:
LASSO results show features in order of importance for prediction:
