To write the multiple logistic regression model using PyMC3, we take advantages of its vectorization capabilities, allowing us to introduce only minor modifications to the previous simple logistic model (model_0):

with pm.Model() as model_1: 
    α = pm.Normal('α', mu=0, sd=10) 
    β = pm.Normal('β', mu=0, sd=2, shape=len(x_n)) 
     
    μ = α + pm.math.dot(x_1, β) 
    θ = pm.Deterministic('θ', 1 / (1 + pm.math.exp(-μ))) 
    bd = pm.Deterministic('bd', -α/β[1] - β[0]/β[1] * x_1[:,0])
     
    yl = pm.Bernoulli('yl', p=θ, observed=y_1) 
 
    trace_1 = pm.sample(2000)

As we did for a single predictor variable, we are going to plot the data and the decision boundary:

idx = np.argsort(x_1[:,0]) 
bd = trace_1['bd'].mean(0)[idx] 
plt.scatter(x_1[:,0], x_1[:,1], c=[f'C{x}' for x in y_0]) 
plt.plot(x_1[:,0][idx], bd, color='k'); 

az.plot_hpd(x_1[:,0], trace_1['bd'], color='k')
 
plt.xlabel(x_n[0]) 
plt.ylabel(x_n[1])

The boundary decision is a straight line, as we have already seen. Do not get confused by the curved aspect of the 94% HPD band. The apparent curvature is the result of having multiple lines pivoting around a central region (roughly around the mean of  and the mean of ).