def test_gaussian_multiple_populations_crossval_kde(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 = ConstantPopulationSize(600)
parameter_given_model_prior_distribution = [
Distribution(x=st.norm(0, sigma_x))
]
parameter_perturbation_kernels = [
GridSearchCV(
MultivariateNormalTransition(),
{"scaling": np.logspace(-1, 1.5, 5)},
)
]
abc = ABCSMC(
models,
parameter_given_model_prior_distribution,
MinMaxDistance(measures_to_use=["y"]),
population_size,
transitions=parameter_perturbation_kernels,
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 < 0.052
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
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(FunctionModel, 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,
MinMaxDistance(measures_to_use=["y"]),
population_size,
eps=MedianEpsilon(0.1),
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"].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_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 = np.linspace(-8, 8)
max_distribution_difference = np.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) < 0.07
assert abs(std_emp - sigma_x_given_y) < 0.1
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))
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,
MinMaxDistanceFunction(measures_to_use=["y"]),
population_size,
eps=MedianEpsilon(.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"].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_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 = sp.linspace(-8, 8)
max_distribution_difference = sp.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) < .07
assert abs(std_emp - sigma_x_given_y) < .12
def test_two_competing_gaussians_single_population(db_path, sampler,
transition):
sigma_x = 0.5
sigma_y = 0.5
y_observed = 1
def model(args):
return {"y": st.norm(args['x'], sigma_y).rvs()}
models = [model, model]
models = list(map(FunctionModel, models))
population_size = ConstantPopulationSize(500)
mu_x_1, mu_x_2 = 0, 1
parameter_given_model_prior_distribution = [
Distribution(x=st.norm(mu_x_1, sigma_x)),
Distribution(x=st.norm(mu_x_2, sigma_x)),
]
abc = ABCSMC(
models,
parameter_given_model_prior_distribution,
MinMaxDistance(measures_to_use=["y"]),
population_size,
transitions=[transition(), transition()],
eps=MedianEpsilon(0.02),
sampler=sampler,
)
abc.new(db_path, {"y": y_observed})
minimum_epsilon = -1
nr_populations = 1
abc.do_not_stop_when_only_single_model_alive()
history = abc.run(minimum_epsilon, max_nr_populations=1)
mp = history.get_model_probabilities(history.max_t)
def p_y_given_model(mu_x_model):
return st.norm(mu_x_model,
np.sqrt(sigma_y**2 + sigma_x**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) < 0.07
def test_continuous_non_gaussian(db_path, sampler):
def model(args):
return {"result": sp.rand() * args['u']}
models = [model]
models = list(map(SimpleModel, models))
population_size = ConstantPopulationSize(250)
parameter_given_model_prior_distribution = [Distribution(u=RV("uniform", 0,
1))]
abc = ABCSMC(models, parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(.2),
sampler=sampler)
d_observed = .5
abc.new(db_path, {"result": d_observed})
abc.do_not_stop_when_only_single_model_alive()
minimum_epsilon = -1
history = abc.run(minimum_epsilon, max_nr_populations=2)
posterior_x, posterior_weight = history.get_distribution(0, None)
posterior_x = posterior_x["u"].values
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)))
@sp.vectorize
def f_expected(u):
return (sp.log(u)-sp.log(d_observed)) / (- sp.log(d_observed)) * \
(u > d_observed)
x = sp.linspace(0.1, 1)
max_distribution_difference = sp.absolute(f_empirical(x) -
f_expected(x)).max()
assert max_distribution_difference < 0.12
