How to use the pyabc.MultivariateNormalTransition function in pyabc

def test_grid_search_multivariate_normal():
    m = MultivariateNormalTransition()
    m_grid = GridSearchCV(m, {"scaling": np.logspace(-5, 1.5, 5)}, n_jobs=1)
    df, w = data(20)
    m_grid.fit(df, w)

def test_gaussian_multiple_populations_adpative_population_size(db_path, sampler):
    sigma_x = 1
    sigma_y = .5
    y_observed = 2

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

    models = [model]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 1)
    nr_populations = 4
    population_size = AdaptivePopulationStrategy(600, nr_populations)
    parameter_given_model_prior_distribution = [Distribution(x=RV("norm", 0, sigma_x))]
    parameter_perturbation_kernels = [MultivariateNormalTransition()]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(1, probability_to_stay=1),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 PercentileDistanceFunction(measures_to_use=["y"]), MedianEpsilon(.2),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    abc.set_data({"y": y_observed}, 0, {}, options)

    minimum_epsilon = -1

    abc.do_not_stop_when_only_single_model_alive()
    history = abc.run(minimum_epsilon)
    posterior_x, posterior_weight = history.get_results_distribution(0, "x")
    sort_indices = sp.argsort(posterior_x)
    f_empirical = sp.interpolate.interp1d(sp.hstack((-200, posterior_x[sort_indices], 200)),

def test_beta_binomial_two_identical_models(db_path, sampler):
    binomial_n = 5

    def model_fun(args):
        return {"result": st.binom(binomial_n, args.theta).rvs()}

    models = [model_fun for _ in range(2)]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 2)
    population_size = ConstantPopulationStrategy(800, 3)
    parameter_given_model_prior_distribution = [Distribution(theta=RV("beta", 1, 1))
                                                for _ in range(2)]
    parameter_perturbation_kernels = [MultivariateNormalTransition() for _ in range(2)]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(2, probability_to_stay=.8),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 MinMaxDistanceFunction(measures_to_use=["result"]), MedianEpsilon(.1),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    abc.set_data({"result": 2}, 0, {}, options)

    minimum_epsilon = .2
    history = abc.run( minimum_epsilon)
    mp = history.get_model_probabilities(history.max_t)
    assert abs(mp.p[0] - .5) + abs(mp.p[1] - .5) < .08

@pytest.fixture(params=[LocalTransition, MultivariateNormalTransition])
def transition(request):
    return request.param

def test_gaussian_multiple_populations(db_path, sampler):
    sigma_x = 1
    sigma_y = .5
    y_observed = 2

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

    models = [model]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 1)
    nr_populations = 4
    population_size = ConstantPopulationStrategy(600, nr_populations)
    parameter_given_model_prior_distribution = [Distribution(x=RV("norm", 0, sigma_x))]
    parameter_perturbation_kernels = [MultivariateNormalTransition()]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(1, probability_to_stay=1),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 PercentileDistanceFunction(measures_to_use=["y"]), MedianEpsilon(.2),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    abc.set_data({"y": y_observed}, 0, {}, options)

    minimum_epsilon = -1

    abc.do_not_stop_when_only_single_model_alive()
    history = abc.run(minimum_epsilon)
    posterior_x, posterior_weight = history.get_results_distribution(0, "x")
    sort_indices = sp.argsort(posterior_x)
    f_empirical = sp.interpolate.interp1d(sp.hstack((-200, posterior_x[sort_indices], 200)),

def test_beta_binomial_different_priors(db_path, sampler):
    binomial_n = 5

    def model(args):
        return {"result": st.binom(binomial_n, args['theta']).rvs()}

    models = [model for _ in range(2)]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 2)
    population_size = ConstantPopulationStrategy(800, 3)
    a1, b1 = 1, 1
    a2, b2 = 10, 1
    parameter_given_model_prior_distribution = [Distribution(theta=RV("beta", a1, b1)),
                                                Distribution(theta=RV("beta", a2, b2))]
    parameter_perturbation_kernels = [MultivariateNormalTransition() for _ in range(2)]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(2, probability_to_stay=.8),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 MinMaxDistanceFunction(measures_to_use=["result"]), MedianEpsilon(.1),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    n1 = 2
    abc.set_data({"result": n1}, 0, {}, options)

    minimum_epsilon = .2
    history = abc.run(minimum_epsilon)
    mp = history.get_model_probabilities(history.max_t)

    def B(a, b):
        return gamma(a) * gamma(b) / gamma(a + b)

def test_continuous_non_gaussian(db_path, sampler):
    def model(args):
        return {"result": sp.rand() * args['u']}

    models = [model]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 1)
    population_size = ConstantPopulationStrategy(250, 2)
    parameter_given_model_prior_distribution = [Distribution(u=RV("uniform", 0, 1))]
    parameter_perturbation_kernels = [MultivariateNormalTransition()]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(1, probability_to_stay=1),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 PercentileDistanceFunction(measures_to_use=["result"]), MedianEpsilon(.2),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    d_observed = .5
    abc.set_data({"result": d_observed}, 0, {}, options)
    abc.do_not_stop_when_only_single_model_alive()

    minimum_epsilon = -1
    history = abc.run(minimum_epsilon)
    posterior_x, posterior_weight = history.get_results_distribution(0, "u")
    sort_indices = sp.argsort(posterior_x)
    f_empirical = sp.interpolate.interp1d(sp.hstack((-200, posterior_x[sort_indices], 200)),

def test_beta_binomial_two_identical_models_adaptive(db_path, sampler):
    binomial_n = 5

    def model_fun(args):
        return {"result": st.binom(binomial_n, args.theta).rvs()}

    models = [model_fun for _ in range(2)]
    models = list(map(SimpleModel, models))
    model_prior = RV("randint", 0, 2)
    population_size = AdaptivePopulationStrategy(800, 3)
    parameter_given_model_prior_distribution = [Distribution(theta=RV("beta", 1, 1)) for _ in range(2)]
    parameter_perturbation_kernels = [MultivariateNormalTransition() for _ in range(2)]
    abc = ABCSMC(models, model_prior, ModelPerturbationKernel(2, probability_to_stay=.8),
                 parameter_given_model_prior_distribution, parameter_perturbation_kernels,
                 MinMaxDistanceFunction(measures_to_use=["result"]), MedianEpsilon(.1),
                 population_size,
                 sampler=sampler)

    options = {'db_path': db_path}
    abc.set_data({"result": 2}, 0, {}, options)

    minimum_epsilon = .2
    history = abc.run( minimum_epsilon)
    mp = history.get_model_probabilities(history.max_t)
    assert abs(mp.p[0] - .5) + abs(mp.p[1] - .5) < .08

@pytest.fixture(params=[LocalTransition, MultivariateNormalTransition])
def transition(request):
    return request.param()

rate = pars.rate
    arr = sp.rand(4)
    return arr


def distance(x, y):
        return ((x - y)**2).sum()
    

mapper = parallel.SGE().map if parallel.sge_available() else map
abc = pyabc.ABCSMC([pyabc.SimpleModel(model_1),
                    pyabc.SimpleModel(model_2)],
                    model_prior,
                    pyabc.ModelPerturbationKernel(2, probability_to_stay=.8),
                    [rate_prior, rate_prior],
                    [pyabc.MultivariateNormalTransition(),
                     pyabc.MultivariateNormalTransition()],
                    distance,
                    pyabc.MedianEpsilon(),
                    population_strategy,
                    sampler=parallel.sampler.MappingSampler(map=mapper))
abc.stop_if_only_single_model_alive = False


options = {'db_path': "sqlite:///" + sm.output[0]}
abc.set_data(sp.rand(4), 0, {}, options)
history = abc.run(.01)