def test_gaussian_multiple_populations_crossval_kde(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 = ConstantPopulationSize(600)
parameter_given_model_prior_distribution = [
Distribution(x=st.norm(0, sigma_x))
]
parameter_perturbation_kernels = [
GridSearchCV(MultivariateNormalTransition(),
{"scaling": sp.logspace(-1, 1.5, 5)})
]
abc = ABCSMC(models,
parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["y"]),
population_size,
transitions=parameter_perturbation_kernels,
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 < 0.052
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) < .07
assert abs(std_emp - sigma_x_given_y) < .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_all_in_one_model(db_path, sampler):
models = [AllInOneModel() for _ in range(2)]
population_size = ConstantPopulationSize(800)
parameter_given_model_prior_distribution = [Distribution(theta=RV("beta",
1, 1))
for _ in range(2)]
abc = ABCSMC(models, parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(.1),
sampler=sampler)
abc.new(db_path, {"result": 2})
minimum_epsilon = .2
history = abc.run(minimum_epsilon, max_nr_populations=3)
mp = history.get_model_probabilities(history.max_t)
assert abs(mp.p[0] - .5) + abs(mp.p[1] - .5) < .08
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_beta_binomial_different_priors_initial_epsilon_from_sample(
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(FunctionModel, models))
population_size = ConstantPopulationSize(800)
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)),
]
abc = ABCSMC(
models,
parameter_given_model_prior_distribution,
MinMaxDistance(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(median_multiplier=0.9),
sampler=sampler,
)
n1 = 2
abc.new(db_path, {"result": n1})
minimum_epsilon = -1
history = abc.run(minimum_epsilon, max_nr_populations=5)
mp = history.get_model_probabilities(history.max_t)
def B(a, b):
return gamma(a) * gamma(b) / gamma(a + b)
def expected_p(a, b, n1):
return binom(binomial_n, n1) * B(a + n1, b + binomial_n - n1) / B(a, b)
p1_expected_unnormalized = expected_p(a1, b1, n1)
p2_expected_unnormalized = expected_p(a2, b2, n1)
p1_expected = p1_expected_unnormalized / (p1_expected_unnormalized +
p2_expected_unnormalized)
p2_expected = p2_expected_unnormalized / (p1_expected_unnormalized +
p2_expected_unnormalized)
assert abs(mp.p[0] - p1_expected) + abs(mp.p[1] - p2_expected) < 0.08
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
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))
population_size = ConstantPopulationSize(800)
parameter_given_model_prior_distribution = [Distribution(theta=st.beta(
1, 1))
for _ in range(2)]
abc = ABCSMC(models, parameter_given_model_prior_distribution,
MinMaxDistanceFunction(measures_to_use=["result"]),
population_size,
eps=MedianEpsilon(.1),
sampler=sampler)
abc.new(db_path, {"result": 2})
minimum_epsilon = .2
history = abc.run(minimum_epsilon, max_nr_populations=3)
mp = history.get_model_probabilities(history.max_t)
assert abs(mp.p[0] - .5) + abs(mp.p[1] - .5) < .08
def two_competing_gaussians_multiple_population(db_path, sampler, n_sim):
# 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))
# 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=RV("norm", mu_x_1, sigma)),
Distribution(x=RV("norm", mu_x_2, sigma)),
]
# We plug all the ABC setup together
nr_populations = 2
pop_size = ConstantPopulationSize(23, nr_samples_per_parameter=n_sim)
abc = ABCSMC(models, parameter_given_model_prior_distribution,
PercentileDistance(measures_to_use=["y"]),
pop_size,
eps=MedianEpsilon(),
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=nr_populations)
# Evaluate the model probabililties
mp = history.get_model_probabilities(history.max_t)
def p_y_given_model(mu_x_model):
res = st.norm(mu_x_model, np.sqrt(sigma**2 + sigma**2)).pdf(y_observed)
return res
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
# the next line only tests if we obtain correct numerical types
try:
mp0 = mp.p[0]
except KeyError:
mp0 = 0
try:
mp1 = mp.p[1]
except KeyError:
mp1 = 0
assert abs(mp0 - p1_expected) + abs(mp1 - p2_expected) < np.inf
# check that sampler only did nr_particles samples in first round
pops = history.get_all_populations()
# since we had calibration (of epsilon), check that was saved
pre_evals = pops[pops['t'] == History.PRE_TIME]['samples'].values
assert pre_evals >= pop_size.nr_particles
# our samplers should not have overhead in calibration, except batching
batch_size = sampler.batch_size if hasattr(sampler, 'batch_size') else 1
max_expected = pop_size.nr_particles + batch_size - 1
if pre_evals > max_expected:
# Violations have been observed occasionally for the redis server
# due to runtime conditions with the increase of the evaluations
# counter. This could be overcome, but as it usually only happens
# for low-runtime models, this should not be a problem. Thus, only
# print a warning here.
logger.warning(
f"Had {pre_evals} simulations in the calibration iteration, "
f"but a maximum of {max_expected} would have been sufficient for "
f"the population size of {pop_size.nr_particles}.")
def two_competing_gaussians_multiple_population(db_path, sampler, n_sim):
# 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))
# 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=RV("norm", mu_x_1, sigma)),
Distribution(x=RV("norm", mu_x_2, sigma))
]
# We plug all the ABC setup together
nr_populations = 2
pop_size = ConstantPopulationSize(40, nr_samples_per_parameter=n_sim)
abc = ABCSMC(models,
parameter_given_model_prior_distribution,
PercentileDistanceFunction(measures_to_use=["y"]),
pop_size,
eps=MedianEpsilon(),
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=nr_populations)
# Evaluate the model probabililties
mp = history.get_model_probabilities(history.max_t)
def p_y_given_model(mu_x_model):
res = st.norm(mu_x_model, sp.sqrt(sigma**2 + sigma**2)).pdf(y_observed)
return res
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
# the next line only tests if we obtain correct numerical types
try:
mp0 = mp.p[0]
except KeyError:
mp0 = 0
try:
mp1 = mp.p[1]
except KeyError:
mp1 = 0
assert abs(mp0 - p1_expected) + abs(mp1 - p2_expected) < sp.inf
