def logpdf_link(self, inv_link_f, y, Y_metadata=None):
e = y - inv_link_f<EOL>objective = (+ gammaln((self.v + <NUM_LIT:1>) * <NUM_LIT:0.5>)<EOL>- gammaln(self.v * <NUM_LIT:0.5>)<EOL>- <NUM_LIT:0.5>*np.log(self.sigma2 * self.v * np.pi)<EOL>- <NUM_LIT:0.5>*(self.v + <NUM_LIT:1>)*np.log(<NUM_LIT:1> + (<NUM_LIT:1>/np.float(self.v))*((e**<NUM_LIT:2>)/self.sigma2))<EOL>)<EOL>return objective<EOL>
Log Likelihood Function given link(f)

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

: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