Sampling semantics of multiple observed variables

[chartl]

Your model looks like a hierarchical linear model. The general way of doing this relies on a covariate data matrix that might look like

intercept  media_A  media_B  input_XOR
        1        1        0       0    
        1        1        0       1   
        1        0        1       0    
...

Here the XOR of the input bits is pre-computed. Then:

X = theano.shared(data_matrix)
y_obs = theano.shared(data_obs)
with pm.Model() as mod:
    beta_vals = pm.Normal('beta', 0., 2., shape=4)
    err_sd = pm.HalfNormal('err_sd', 1.)
    y_pred = pm.Deterministic('y_pred', tt.dot(X, beta_vals))
    lik = pm.Normal('y_obs', mu=y_pred, sd=err_sd, observed=y_obs)

In this way the (independent) observations map to the (dependent) observations through the unknown parameters; and X[i,:] corresponds to y_obs[i].

see

Hierarchical Linear Regression Model -- why is it not converging?

I created a toy example: 5 Regions with x and y Data; 30 data-items each; Region 5 contains just one pair: N = 30 beta_0 = [3, 3.2, 2.4, 4.1] beta_1 = [11, 10, 9.1, 14.1] idx = np.repeat(range(4),N) x = np.array([]) ; y = np.array([]) for b_0,b_1 in zip(beta_0,beta_1): x_new = st.uniform(0,20).rvs(N) x = np.append(x, x_new) eps = st.norm(0,10).rvs(N) y = np.append(y,b_0 + b_1*x_new + eps) x = np.append(x,10) ; y = np.append(y,3+11*10) idx = np.append(idx,4) A non-hierarchical …

Hierarchical linear model with two parent distributions

Hi, I would like to specify a hierarchical linear model where each coefficient is associated with one of two prior distributions. In particular, if you represent the N^2 coefficients as an NxN matrix, then the coefficients on the main diagonal should have as their prior some distribution D1 and the coefficients off the diagonal should have a different distribution D2. I’ve attempted to implement this myself, but running it even on data produced by this process results in a sampling failure (i.…

Problem with multivariate hierarchical linear model

I have a dataset with 2 covariates (i.e. X.shape = (600, 2)) and 1 dependent variable (y). As my data comes from two populations I want to use a mixed effects / hierarchical model. The non-hierarchical model looks like this (just treating all the data as equivalent): alpha = pm.Normal('alpha', mu=0, sd=1) beta = pm.Normal('beta', mu=0, sd=1, shape=2) # Expected value of outcome mu = alpha + T.dot(beta, minibatch_x.T) Y_obs = pm.Bernoulli('Y_obs', p=logistic(mu), observed=minibatch_y, tota…

for more examples