def simple_categorical(): p = floatX_array([0.1, 0.2, 0.3, 0.4]) v = floatX_array([0.0, 1.0, 2.0, 3.0]) with Model() as model: Categorical("x", p, size=3, initval=[1, 2, 3]) mu = np.dot(p, v) var = np.dot(p, (v - mu)**2) return model.initial_point, model, (mu, var)
def mv_simple(): mu = floatX_array([-0.1, 0.5, 1.1]) p = floatX_array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]]) tau = np.dot(p, p.T) with pm.Model() as model: pm.MvNormal( "x", at.constant(mu), tau=at.constant(tau), initval=floatX_array([0.1, 1.0, 0.8]), ) H = tau C = np.linalg.inv(H) return model.initial_point, model, (mu, C)
def mv_simple_very_coarse(): mu = floatX_array([-0.3, 0.7, 1.3]) p = floatX_array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]]) tau = np.dot(p, p.T) with pm.Model() as model: pm.MvNormal( "x", at.constant(mu), tau=at.constant(tau), shape=3, testval=floatX_array([0.1, 1.0, 0.8]), ) H = tau C = np.linalg.inv(H) return model.test_point, model, (mu, C)
def simple_model(): mu = -2.1 tau = 1.3 with Model() as model: Normal("x", mu, tau=tau, size=2, initval=floatX_array([0.1, 0.1])) return model.initial_point, model, (mu, tau**-0.5)
def mv_prior_simple(): n = 3 noise = 0.1 X = np.linspace(0, 1, n)[:, None] K = pm.gp.cov.ExpQuad(1, 1)(X).eval() L = np.linalg.cholesky(K) K_noise = K + noise * np.eye(n) obs = floatX_array([-0.1, 0.5, 1.1]) # Posterior mean L_noise = np.linalg.cholesky(K_noise) alpha = np.linalg.solve(L_noise.T, np.linalg.solve(L_noise, obs)) mu_post = np.dot(K.T, alpha) # Posterior standard deviation v = np.linalg.solve(L_noise, K) std_post = (K - np.dot(v.T, v)).diagonal()**0.5 with pm.Model() as model: x = pm.Flat("x", shape=n) x_obs = pm.MvNormal("x_obs", observed=obs, mu=x, cov=noise * np.eye(n), shape=n) return model.test_point, model, (K, L, mu_post, std_post, noise)
def simple_arbitrary_det(): scalar_type = at.dscalar if aesara.config.floatX == "float64" else at.fscalar @as_op(itypes=[scalar_type], otypes=[scalar_type]) def arbitrary_det(value): return value with Model() as model: a = Normal("a") b = arbitrary_det(a) Normal("obs", mu=b.astype("float64"), observed=floatX_array([1, 3, 5])) return model.initial_point, model
def mv_simple_discrete(): d = 2 n = 5 p = floatX_array([0.15, 0.85]) with pm.Model() as model: pm.Multinomial("x", n, at.constant(p), initval=np.array([1, 4])) mu = n * p # covariance matrix C = np.zeros((d, d)) for (i, j) in product(range(d), range(d)): if i == j: C[i, i] = n * p[i] * (1 - p[i]) else: C[i, j] = -n * p[i] * p[j] return model.initial_point, model, (mu, C)