def log_predictive_density(self, y_test, mu_star, var_star, Y_metadata=None):
        """
        assumes independence
        """
        v = var_star + self.variance
        return -0.5*np.log(2*np.pi) -0.5*np.log(v) - 0.5*np.square(y_test - mu_star)/v
assumes independence