def test_frozen(self):
# Test that the frozen and non-frozen Wishart gives the same answers
# Construct an arbitrary positive definite scale matrix
dim = 4
scale = np.diag(np.arange(dim)+1)
scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
scale = np.dot(scale.T, scale)
# Construct a collection of positive definite matrices to test the PDF
X = []
for i in range(5):
x = np.diag(np.arange(dim)+(i+1)**2)
x[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim-1) // 2)
x = np.dot(x.T, x)
X.append(x)
X = np.array(X).T
# Construct a 1D and 2D set of parameters
parameters = [
(10, 1, np.linspace(0.1, 10, 5)), # 1D case
(10, scale, X)
]
for (df, scale, x) in parameters:
w = wishart(df, scale)
assert_equal(w.var(), wishart.var(df, scale))
assert_equal(w.mean(), wishart.mean(df, scale))
assert_equal(w.mode(), wishart.mode(df, scale))
assert_equal(w.entropy(), wishart.entropy(df, scale))
assert_equal(w.pdf(x), wishart.pdf(x, df, scale))
def test_frozen(self):
# Test that the frozen and non-frozen Wishart gives the same answers
# Construct an arbitrary positive definite scale matrix
dim = 4
scale = np.diag(np.arange(dim) + 1)
scale[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim - 1) // 2)
scale = np.dot(scale.T, scale)
# Construct a collection of positive definite matrices to test the PDF
X = []
for i in range(5):
x = np.diag(np.arange(dim) + (i + 1)**2)
x[np.tril_indices(dim, k=-1)] = np.arange(dim * (dim - 1) // 2)
x = np.dot(x.T, x)
X.append(x)
X = np.array(X).T
# Construct a 1D and 2D set of parameters
parameters = [
(10, 1, np.linspace(0.1, 10, 5)), # 1D case
(10, scale, X)
]
for (df, scale, x) in parameters:
w = wishart(df, scale)
assert_equal(w.var(), wishart.var(df, scale))
assert_equal(w.mean(), wishart.mean(df, scale))
assert_equal(w.mode(), wishart.mode(df, scale))
assert_equal(w.entropy(), wishart.entropy(df, scale))
assert_equal(w.pdf(x), wishart.pdf(x, df, scale))
def wishart(covariance,mean,df):
if isinstance(covariance, int) or isinstance(covariance, float):
return chi2.pdf(covariance, scale=mean/df, df=df)
return scip_wishart.pdf(covariance, scale=mean/df, df=df)
std_sigma2_hat = np.sqrt(wishart.var(t_ - 1, sigma2_hat / t_))
exp_sigma2_pri = invwishart.mean(v_pri, v_pri * sigma2_pri)
std_sigma2_pri = np.sqrt(invwishart.var(v_pri, v_pri * sigma2_pri))
exp_sigma2_pos = invwishart.mean(v_pos, v_pos * sigma2_pos)
std_sigma2_pos = np.sqrt(invwishart.var(v_pos, v_pos * sigma2_pos))
# ## [Step 4](https://www.arpm.co/lab/redirect.php?permalink=s_bayes_posterior_niw-implementation-step04): Compute marginal pdfs of the sample, prior and posterior distributions of Sigma2
# +
s_max = np.max([
exp_sigma2_hat + 3. * std_sigma2_hat, exp_sigma2_pri + 3. * std_sigma2_pri,
exp_sigma2_pos + 3. * std_sigma2_pos
])
s = np.linspace(0.01, s_max, k_) # grid
f_sigma2_hat = wishart.pdf(s, t_ - 1, sigma2_hat / t_) # sample pdf
f_sigma2_pri = invwishart.pdf(s, v_pri, v_pri * sigma2_pri) # prior pdf
f_sigma2_pos = invwishart.pdf(s, v_pos, v_pos * sigma2_pos) # posterior pdf
# -
# ## [Step 5](https://www.arpm.co/lab/redirect.php?permalink=s_bayes_posterior_niw-implementation-step05): Compute the pdf of the sample, prior and posterior distributions of M
# +
m_min = np.min([
mu_hat - 3. * np.sqrt(sigma2_hat / t_),
mu_pri - 3. * np.sqrt(sigma2_pri / t_pri),
mu_pos - 3. * np.sqrt(sigma2_pos / t_pos)
])
m_max = np.max([
mu_hat + 3. * np.sqrt(sigma2_hat / t_),
mu_pri + 3. * np.sqrt(sigma2_pri / t_pri),
import matplotlib.pyplot as plt from scipy.stats import wishart, chi2 x = np.linspace(1e-5, 8, 100) w = wishart.pdf(x, df=3, scale=1) w[:5] # array([ 0.00126156, 0.10892176, 0.14793434, 0.17400548, 0.1929669 ]) c = chi2.pdf(x, 3) c[:5] # array([ 0.00126156, 0.10892176, 0.14793434, 0.17400548, 0.1929669 ]) plt.plot(x, w) # The input quantiles can be any shape of array, as long as the last # axis labels the components.
def g0(theta, mu0, beta, nu, S):
"""(12.32) の式"""
mu, Lambda = theta
return multivariate_normal.pdf(mu, mu0, inv(beta * Lambda)) * wishart.pdf(
Lambda, nu, S)