def pdf_link(self, inv_link_f, y, Y_metadata=None):
assert np.atleast_1d(inv_link_f).shape == np.atleast_1d(y).shape<EOL>e = y - inv_link_f<EOL>objective = ((np.exp(gammaln((self.v + <NUM_LIT:1>)*<NUM_LIT:0.5>) - gammaln(self.v * <NUM_LIT:0.5>))<EOL>/ (np.sqrt(self.v * np.pi * self.sigma2)))<EOL>* ((<NUM_LIT:1> + (<NUM_LIT:1.>/float(self.v))*((e**<NUM_LIT:2>)/float(self.sigma2)))**(-<NUM_LIT:0.5>*(self.v + <NUM_LIT:1>)))<EOL>)<EOL>return np.prod(objective)<EOL>
Likelihood function given link(f)

.. math::
    p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \\lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}}

:param inv_link_f: latent variables link(f)
:type inv_link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param Y_metadata: Y_metadata which is not used in student t distribution
:returns: likelihood evaluated for this point
:rtype: float