:param link_f: latent variables link(f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: Nx1 array

def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
        """
        :param link_f: latent variables link(f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: Nx1 array
        """
        c = np.zeros_like(y)
        if Y_metadata is not None and 'censored' in Y_metadata.keys():
            c = Y_metadata['censored']

        val = np.log(y) - link_f
        val_scaled = val/np.sqrt(self.variance)
        val_scaled2 = val/self.variance
        a = (1 - stats.norm.cdf(val_scaled))
        uncensored = (1-c)*(-val/(self.variance**2))
        censored = c * (-val*np.exp(-val**2/self.variance)/( 4*np.pi*(self.variance**2)*(a**2)) +
                         (-1 + (val**2)/self.variance)*np.exp(-val**2/(2*self.variance) ) /
                        ( a*(np.sqrt(2.*np.pi)*2*self.variance**1.5)) )
        dlik_grad_dsigma = uncensored + censored
        # dlik_grad_dsigma = dlik_grad_dsigma*self.variance
        return dlik_grad_dsigma