Hi Junpeng,
Thank you for your thoughts!
I chose better priors for beta, and fixed the ranges for alpha and forget, like you suggested. I was not sure how to use the softmax instead of T.repeat for the weights though, because my matrix is 4d and won’t be accepted by T.nnet.sofmax - or were you thinking about a different softmax function? As for the scan, I don’t think there is a way to get rid of it unfortunately, because each row of Q_sub depends on the previous row, so I need to pass the previous results to new each iteration.
For the priors, I am now using:
beta_mu = pm.Gamma('beta_mu', mu=1, sd=2, testval=1.25)
beta_sd = pm.HalfNormal('beta_sd', sd=0.5, testval=0.1)
alpha_mu = pm.Uniform('alpha_mu', lower=0, upper=1, testval=0.15)
alpha_sd = pm.HalfNormal('alpha_sd', sd=0.1, testval=0.05)
forget_mu = pm.Uniform('forget_mu', lower=0, upper=1, testval=0.06)
forget_sd = pm.HalfNormal('forget_sd', sd=0.1, testval=0.03)
I fixed the ranges of all parameters using pm.Bound on the individual non-central parameters:
beta_matt = pm.Bound(pm.Normal, lower=-beta_mu / beta_sd)(
'beta_matt', mu=0, sd=1, shape=n_subj, testval=np.random.choice([-1, 0, 1], n_subj))
beta = pm.Deterministic('beta', beta_mu + beta_sd * beta_matt)
alpha_matt = pm.Bound(pm.Normal, lower=-alpha_mu / alpha_sd, upper=(1 - alpha_mu) / alpha_sd)(
'alpha_matt', mu=0, sd=1, shape=n_subj, testval=np.random.choice([-1, 0, 1], n_subj))
alpha = pm.Deterministic('alpha', alpha_mu + alpha_sd * alpha_matt)
forget_matt = pm.Bound(pm.Normal, lower=-forget_mu / forget_sd, upper=(1 - forget_mu) / forget_sd)(
'forget_matt', mu=0, sd=1, shape=n_subj, testval=np.random.choice([-1, 0, 1], n_subj))
forget = pm.Deterministic('forget', forget_mu + forget_sd * forget_matt)
After these fixes, the results still look the same (excuse the small number of samples).
First, flat model:
Second, hierarchical model:
I am nor sure what to try next. Do you have any ideas?
I also found a great PyMC3 tutorial by Chris Fonnesbeck with a notebook about model checking and will go through it next, to see what else I could check or fix. Do you know of any other resources that could be helpful?
Thanks!