def infer_newX(model, Y_new, optimize=True, init='L2'):
    """
    Infer the distribution of X for the new observed data *Y_new*.

    :param model: the GPy model used in inference
    :type model: GPy.core.Model
    :param Y_new: the new observed data for inference
    :type Y_new: numpy.ndarray
    :param optimize: whether to optimize the location of new X (True by default)
    :type optimize: boolean
    :return: a tuple containing the estimated posterior distribution of X and the model that optimize X
    :rtype: (GPy.core.parameterization.variational.VariationalPosterior, GPy.core.Model)
    """
    infr_m = InferenceX(model, Y_new, init=init)

    if optimize:
        infr_m.optimize()

    return infr_m.X, infr_m