test_abc_smc_algorithm.py 文件源码

def test_gaussian_single_population(db_path, sampler):
    sigma_prior = 1
    sigma_ground_truth = 1
    observed_data = 1

    def model(args):
        return {"y": st.norm(args['x'], sigma_ground_truth).rvs()}

    models = [model]
    models = list(map(SimpleModel, models))
    nr_populations = 1
    population_size = ConstantPopulationSize(600)
    parameter_given_model_prior_distribution = [Distribution(x=RV("norm", 0,
                                                                  sigma_prior))
                                                ]
    abc = ABCSMC(models, parameter_given_model_prior_distribution,
                 MinMaxDistanceFunction(measures_to_use=["y"]),
                 population_size,
                 eps=MedianEpsilon(.1),
                 sampler=sampler)
    abc.new(db_path, {"y": observed_data})

    minimum_epsilon = -1


    abc.do_not_stop_when_only_single_model_alive()
    history = abc.run(minimum_epsilon, max_nr_populations=nr_populations)
    posterior_x, posterior_weight = history.get_distribution(0, None)
    posterior_x = posterior_x["x"].as_matrix()
    sort_indices = sp.argsort(posterior_x)
    f_empirical = sp.interpolate.interp1d(sp.hstack((-200, posterior_x[sort_indices], 200)),
                                          sp.hstack((0, sp.cumsum(posterior_weight[sort_indices]), 1)))

    sigma_x_given_y = 1 / sp.sqrt(1 / sigma_prior**2 + 1 / sigma_ground_truth**2)
    mu_x_given_y = sigma_x_given_y**2 * observed_data / sigma_ground_truth**2
    expected_posterior_x = st.norm(mu_x_given_y, sigma_x_given_y)
    x = sp.linspace(-8, 8)
    max_distribution_difference = sp.absolute(f_empirical(x) - expected_posterior_x.cdf(x)).max()
    assert max_distribution_difference < 0.12
    assert history.max_t == nr_populations-1
    mean_emp, std_emp = mean_and_std(posterior_x, posterior_weight)
    assert abs(mean_emp - mu_x_given_y) < .07
    assert abs(std_emp - sigma_x_given_y) < .1