def evidence(self, D):
"""Return Pr(D) = \int Pr(D | theta) Pr(theta)"""
shape = D.shape
if len(shape) == 2:
n, d = shape
elif len(shape) == 1:
n, d = 1, shape[0]
assert d == self.d
# Eq (266)
mu_n, kappa_n, Lam_n, nu_n = self._post_params(D)
detLam0 = np.linalg.det(self.Lam_0)
detLamn = np.linalg.det(Lam_n)
num = gammad(d, nu_n/2.0) * detLam0**(self.nu_0/2.0)
den = np.pi**(n*d/2.0) * gammad(d, self.nu_0/2.0) * detLamn**(nu_n/2.0)
return num/den * (self.kappa_0/kappa_n)**(d/2.0)
def __call__(self, *args):
"""Returns Pr(mu, Sig), i.e., the prior."""
if len(args) == 1:
mu = args[0]['mu']
Sig = args[0]['Sig']
elif len(args) == 2:
mu, Sig = args
nu_0, d = self.nu_0, self.d
# Eq (249)
Z = (2.0**(nu_0*d/2.0) * gammad(d, nu_0/2.0) *
(2.0*np.pi/self.kappa_0)**(d/2.0) / np.linalg.det(self.Lam_0)**(nu_0/2.0))
detSig = np.linalg.det(Sig)
invSig = np.linalg.inv(Sig)
einsum = np.einsum("...i,...ij,...j", mu-self.mu_0, invSig, mu-self.mu_0)
# Eq (248)
return 1./Z * detSig**(-((nu_0+d)/2.0+1.0)) * np.exp(
-0.5*np.trace(np.einsum("...ij,...jk->...ik", self.Lam_0, invSig), axis1=-2, axis2=-1) -
self.kappa_0/2.0*einsum)
