def METHOD_NAME(self, variational_dist_f, target, *args, **kwargs):
    shifted_gamma = self.gamma - 1
    muf, varf = variational_dist_f.mean, variational_dist_f.variance
    # Get noise from likelihood
    noise = self.likelihood._shaped_noise_covar(muf.shape, *args, **kwargs).diagonal(dim1=-1, dim2=-2)
    # Potentially reshape the noise to deal with the multitask case
    noise = noise.view(*noise.shape[:-1], *variational_dist_f.event_shape)
    # adapted from https://github.com/JeremiasKnoblauch/GVIPublic/
    mut = shifted_gamma * target / noise + muf / varf
    sigmat = 1.0 / (shifted_gamma / noise + 1.0 / varf)
    log_integral = -0.5 * shifted_gamma * torch.log(2.0 * math.pi * noise) - 0.5 * np.log1p(shifted_gamma)
    log_tempered = (
        -math.log(shifted_gamma)
        - 0.5 * shifted_gamma * torch.log(2.0 * math.pi * noise)
        - 0.5 * torch.log1p(shifted_gamma * varf / noise)
        - 0.5 * (shifted_gamma * target.pow(2.0) / noise)
        - 0.5 * muf.pow(2.0) / varf
        + 0.5 * mut.pow(2.0) * sigmat
    )
    factor = log_tempered + shifted_gamma / self.gamma * log_integral
    factor = self.gamma * factor.exp()
    # Do appropriate summation for multitask Gaussian likelihoods
    num_event_dim = len(variational_dist_f.event_shape)
    if num_event_dim > 1:
        factor = factor.sum(list(range(-1, -num_event_dim, -1)))
    return factor.sum(-1)