@blockify_third<EOL><INDENT>def d3logpdf_df3(self, f, y, Y_metadata=None):<DEDENT>
if isinstance(self.gp_link, link_functions.Identity):<EOL><INDENT>d3logpdf_df3 = self.d3logpdf_dlink3(f, y, Y_metadata=Y_metadata)<EOL><DEDENT>else:<EOL><INDENT>inv_link_f = self.gp_link.transf(f)<EOL>d3logpdf_dlink3 = self.d3logpdf_dlink3(inv_link_f, y, Y_metadata=Y_metadata)<EOL>dlink_df = self.gp_link.dtransf_df(f)<EOL>d2logpdf_dlink2 = self.d2logpdf_dlink2(inv_link_f, y, Y_metadata=Y_metadata)<EOL>d2link_df2 = self.gp_link.d2transf_df2(f)<EOL>dlogpdf_dlink = self.dlogpdf_dlink(inv_link_f, y, Y_metadata=Y_metadata)<EOL>d3link_df3 = self.gp_link.d3transf_df3(f)<EOL>d3logpdf_df3 = chain_3(d3logpdf_dlink3, dlink_df, d2logpdf_dlink2, d2link_df2, dlogpdf_dlink, d3link_df3)<EOL><DEDENT>return d3logpdf_df3<EOL>
Evaluates the link function link(f) then computes the third derivative of log likelihood using it
Uses the Faa di Bruno's formula for the chain rule

.. math::
    \\frac{d^{3}\\log p(y|\\lambda(f))}{df^{3}} = \\frac{d^{3}\\log p(y|\\lambda(f)}{d\\lambda(f)^{3}}\\left(\\frac{d\\lambda(f)}{df}\\right)^{3} + 3\\frac{d^{2}\\log p(y|\\lambda(f)}{d\\lambda(f)^{2}}\\frac{d\\lambda(f)}{df}\\frac{d^{2}\\lambda(f)}{df^{2}} + \\frac{d\\log p(y|\\lambda(f)}{d\\lambda(f)}\\frac{d^{3}\\lambda(f)}{df^{3}}

:param f: latent variables f
:type f: Nx1 array
:param y: data
:type y: Nx1 array
:param Y_metadata: Y_metadata which is not used in student t distribution - not used
:returns: third derivative of log likelihood evaluated for this point
:rtype: float