def test_empty_population_adaptive(db_path, sampler):
def make_model(theta):
def model(args):
return {"result": 1 if random.random() > theta else 0}
return model
theta1 = .2
theta2 = .6
model1 = make_model(theta1)
model2 = make_model(theta2)
models = [model1, model2]
models = list(map(SimpleModel, models))
population_size = AdaptivePopulationSize(1500)
parameter_given_model_prior_distribution = [Distribution(), Distribution()]
abc = ABCSMC(models, parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(0),
sampler=sampler)
abc.new(db_path, {"result": 0})
minimum_epsilon = -1
history = abc.run(minimum_epsilon, max_nr_populations=3)
mp = history.get_model_probabilities(history.max_t)
expected_p1, expected_p2 = theta1 / (theta1 + theta2), theta2 / (theta1 + theta2)
assert abs(mp.p[0] - expected_p1) + abs(mp.p[1] - expected_p2) < .1
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(FunctionModel, models))
population_size = AdaptivePopulationSize(800)
parameter_given_model_prior_distribution = [
Distribution(theta=st.beta(1, 1)) for _ in range(2)
]
abc = ABCSMC(
models,
parameter_given_model_prior_distribution,
MinMaxDistance(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(0.1),
sampler=sampler,
)
abc.new(db_path, {"result": 2})
minimum_epsilon = 0.2
history = abc.run(minimum_epsilon, max_nr_populations=3)
mp = history.get_model_probabilities(history.max_t)
assert abs(mp.p[0] - 0.5) + abs(mp.p[1] - 0.5) < 0.08
def test_two_competing_gaussians_multiple_population_adaptive_populatin_size(db_path, sampler):
# Define a gaussian model
sigma = .5
def model(args):
return {"y": st.norm(args['x'], sigma).rvs()}
# We define two models, but they are identical so far
models = [model, model]
models = list(map(SimpleModel, models))
# The prior over the model classes is uniform
model_prior = RV("randint", 0, 2)
# However, our models' priors are not the same. Their mean differs.
mu_x_1, mu_x_2 = 0, 1
parameter_given_model_prior_distribution = [Distribution(x=st.norm(mu_x_1, sigma)),
Distribution(x=st.norm(mu_x_2, sigma))]
# Particles are perturbed in a Gaussian fashion
parameter_perturbation_kernels = [MultivariateNormalTransition() for _ in range(2)]
# We plug all the ABC setup together
nr_populations = 3
population_size = AdaptivePopulationSize(400, mean_cv=0.05,
max_population_size=1000)
abc = ABCSMC(models, parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["y"]),
population_size,
model_prior=model_prior,
eps=MedianEpsilon(.2),
sampler=sampler)
# Finally we add meta data such as model names and define where to store the results
# y_observed is the important piece here: our actual observation.
y_observed = 1
abc.new(db_path, {"y": y_observed})
# We run the ABC with 3 populations max
minimum_epsilon = .05
history = abc.run(minimum_epsilon, max_nr_populations=3)
# Evaluate the model probabililties
mp = history.get_model_probabilities(history.max_t)
def p_y_given_model(mu_x_model):
return st.norm(mu_x_model, sp.sqrt(sigma ** 2 + sigma ** 2)).pdf(y_observed)
p1_expected_unnormalized = p_y_given_model(mu_x_1)
p2_expected_unnormalized = p_y_given_model(mu_x_2)
p1_expected = p1_expected_unnormalized / (p1_expected_unnormalized + p2_expected_unnormalized)
p2_expected = p2_expected_unnormalized / (p1_expected_unnormalized + p2_expected_unnormalized)
assert history.max_t == nr_populations-1
assert abs(mp.p[0] - p1_expected) + abs(mp.p[1] - p2_expected) < .07
def test_gaussian_multiple_populations_adpative_population_size(
db_path, sampler):
sigma_x = 1
sigma_y = 0.5
y_observed = 2
def model(args):
return {"y": st.norm(args['x'], sigma_y).rvs()}
models = [model]
models = list(map(FunctionModel, models))
nr_populations = 4
population_size = AdaptivePopulationSize(600)
parameter_given_model_prior_distribution = [
Distribution(x=st.norm(0, sigma_x))
]
abc = ABCSMC(
models,
parameter_given_model_prior_distribution,
MinMaxDistance(measures_to_use=["y"]),
population_size,
eps=MedianEpsilon(0.2),
sampler=sampler,
)
abc.new(db_path, {"y": y_observed})
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"].values
sort_indices = np.argsort(posterior_x)
f_empirical = sp.interpolate.interp1d(
np.hstack((-200, posterior_x[sort_indices], 200)),
np.hstack((0, np.cumsum(posterior_weight[sort_indices]), 1)),
)
sigma_x_given_y = 1 / np.sqrt(1 / sigma_x**2 + 1 / sigma_y**2)
mu_x_given_y = sigma_x_given_y**2 * y_observed / sigma_y**2
expected_posterior_x = st.norm(mu_x_given_y, sigma_x_given_y)
x = np.linspace(-8, 8)
max_distribution_difference = np.absolute(
f_empirical(x) - expected_posterior_x.cdf(x)).max()
assert max_distribution_difference < 0.15
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) < 0.07
assert abs(std_emp - sigma_x_given_y) < 0.12