def test_deterministic_of_observed_modified_interface(self):
rng = np.random.RandomState(4982)
meas_in_1 = pm.aesaraf.floatX(2 + 4 * rng.randn(100))
meas_in_2 = pm.aesaraf.floatX(5 + 4 * rng.randn(100))
with pm.Model(rng_seeder=rng) as model:
mu_in_1 = pm.Normal("mu_in_1", 0, 1, initval=0)
sigma_in_1 = pm.HalfNormal("sd_in_1", 1, initval=1)
mu_in_2 = pm.Normal("mu_in_2", 0, 1, initval=0)
sigma_in_2 = pm.HalfNormal("sd__in_2", 1, initval=1)
in_1 = pm.Normal("in_1", mu_in_1, sigma_in_1, observed=meas_in_1)
in_2 = pm.Normal("in_2", mu_in_2, sigma_in_2, observed=meas_in_2)
out_diff = in_1 + in_2
pm.Deterministic("out", out_diff)
trace = pm.sample(
100,
return_inferencedata=False,
compute_convergence_checks=False,
)
varnames = [v for v in trace.varnames if v != "out"]
ppc_trace = [
dict(zip(varnames, row)) for row in zip(*(trace.get_values(v) for v in varnames))
]
ppc = pm.sample_posterior_predictive(
return_inferencedata=False,
model=model,
trace=ppc_trace,
samples=len(ppc_trace),
var_names=[x.name for x in (model.deterministics + model.basic_RVs)],
)
rtol = 1e-5 if aesara.config.floatX == "float64" else 1e-3
npt.assert_allclose(ppc["in_1"] + ppc["in_2"], ppc["out"], rtol=rtol)
def setup_class(self):
super().setup_class()
self.data = np.random.normal(loc=0, scale=1, size=1000)
with pm.Model() as self.SMABC_test:
a = pm.Normal("a", mu=0, sigma=1)
b = pm.HalfNormal("b", sigma=1)
s = pm.Simulator("s", self.normal_sim, a, b, sum_stat="sort", observed=self.data)
self.s = s
with pm.Model() as self.SMABC_potential:
a = pm.Normal("a", mu=0, sigma=1, initval=0.5)
b = pm.HalfNormal("b", sigma=1)
c = pm.Potential("c", pm.math.switch(a > 0, 0, -np.inf))
s = pm.Simulator("s", self.normal_sim, a, b, observed=self.data)
def test_sample_deterministic():
with pm.Model() as model:
x = pm.HalfNormal("x", 1)
y = pm.Deterministic("y", x + 100)
idata = pm.sample(chains=1, draws=50, compute_convergence_checks=False)
np.testing.assert_allclose(idata.posterior["y"], idata.posterior["x"] + 100)
def build_constant_model(data, sigma_squared=10.0):
tau = 1.0 / sigma_squared
B_0 = pm.Normal('B_0', mu=0.0, tau=tau, doc='mean', rseed=0)
SI = pm.HalfNormal('SI', tau=tau, doc='sigma', rseed=0)
OUT = pm.Normal('accuracies', mu=B_0, tau=1.0/SI**2, value=data, \
observed=True, rseed=0)
return [B_0, SI, OUT]
def test_transform_samples():
aesara.config.on_opt_error = "raise"
np.random.seed(13244)
obs = np.random.normal(10, 2, size=100)
obs_at = aesara.shared(obs, borrow=True, name="obs")
with pm.Model() as model:
a = pm.Uniform("a", -20, 20)
sigma = pm.HalfNormal("sigma")
b = pm.Normal("b", a, sigma=sigma, observed=obs_at)
trace = sample_numpyro_nuts(chains=1, random_seed=1322, keep_untransformed=True)
log_vals = trace.posterior["sigma_log__"].values
trans_vals = trace.posterior["sigma"].values
assert np.allclose(np.exp(log_vals), trans_vals)
assert 8 < trace.posterior["a"].mean() < 11
assert 1.5 < trace.posterior["sigma"].mean() < 2.5
obs_at.set_value(-obs)
with model:
trace = sample_numpyro_nuts(chains=2, random_seed=1322, keep_untransformed=False)
assert -11 < trace.posterior["a"].mean() < -8
assert 1.5 < trace.posterior["sigma"].mean() < 2.5
def model_pymc(self, guess_value_for_pymc=None):
xdata1, ydata1, ydata_not_normalized, norm_const = self.fittingdata()
x = xdata1
f = ydata1
# if the selected model in PieceWise then we take the default values
# using the curve_fit as input, if
# if guess values are not provided then we calculate them using curve fit
if guess_value_for_pymc is None:
Fit_params_Piecewise, pcov = self.model_fitting_parameters(
function_to_fit="Piecewise", bounds=self.bounds)
# print("Test Successful")
else:
Fit_params_Piecewise = guess_value_for_pymc
# print("using stored values")
p0_center = Fit_params_Piecewise[0] # mean
p0_width = Fit_params_Piecewise[1] # sigma
p0_slope = Fit_params_Piecewise[2] # alpha
p0_TP = Fit_params_Piecewise[3] # Transition point
# if the curvy fit routines are not senstive to the changes
# then the intial conditions are imposed by hand
if Fit_params_Piecewise[3] >= np.max(
xdata1) or Fit_params_Piecewise[2] > 0:
p0_TP = x[np.where(f == max(f))][0] + np.std(x)
p0_slope = -3.
p0 = [p0_center, p0_width, p0_slope, p0_TP]
# A1 = pymc.Uniform("A1", 2.,6., value = p0[0])
x0 = pymc.Uniform("x0", p0[0] - .4, p0[0] + .4, value=p0[0])
sigma = pymc.Uniform("sigma", -0.01, 1., value=p0[1])
alpha = pymc.Uniform("alpha", -7., 0., value=p0[2])
TP_min = pymc.Uniform("TP_min", p0[3] - .4, p0[3] + .8, value=p0[3])
@pymc.deterministic(plot=False)
def function(x=x, x0=x0, sigma=sigma, alpha=alpha, TP_min=TP_min):
xG = np.array([xx for xx in x if xx <= TP_min])
def F1(xG):
p1 = np.log10(np.log(10) * 1 / (np.sqrt(2 * np.pi) * sigma))
p2 = np.log(10**xG)
p3 = p1 - (p2 - x0)**2 / (2 * np.log(10) * sigma**2)
return p3
xL = np.array([xx for xx in x if xx > TP_min])
A2 = F1(TP_min) - alpha * TP_min
def F2(xL):
return alpha * xL + A2
return np.concatenate((F1(xG), F2(xL)))
# self.lognormal_powerlaw_function(xdata=x, x0=x0, sigma=sigma, alpha=alpha, TP_min=TP_min)
s = pymc.HalfNormal('s', tau=1)
y = pymc.Normal("y", mu=function, tau=1 / s**2, value=f, observed=True)
return locals()
def model(x, f, p0):
# A1 = pymc.Uniform("A1", 2.,6., value = p0[0])
x0 = pymc.Uniform("x0", p0[0] - .4, p0[0] + .4, value=p0[0])
sigma = pymc.Uniform("sigma", -0.01, 1., value=p0[1])
alpha = pymc.Uniform("alpha", -7., 0., value=p0[2])
TP_min = pymc.Uniform("TP_min", p0[3] - .4, p0[3] + .8, value=p0[3])
@pymc.deterministic(plot=False)
def function(x=x, x0=x0, sigma=sigma, alpha=alpha, TP_min=TP_min):
xG = np.array([xx for xx in x if xx <= TP_min])
def F1(xG):
p1 = np.log10(np.log(10) * 1 / (np.sqrt(2 * np.pi) * sigma))
p2 = np.log(10**xG)
p3 = p1 - (p2 - x0)**2 / (2 * np.log(10) * sigma**2)
return p3
xL = np.array([xx for xx in x if xx > TP_min])
A2 = F1(TP_min) - alpha * TP_min
def F2(xL):
return alpha * xL + A2
return np.concatenate((F1(xG), F2(xL)))
s = pymc.HalfNormal('s', tau=1)
# return F1(xG)
# y = pymc.Normal("y", mu=function,tau = 1./f_err**2, value = f, observed = True)
y = pymc.Normal("y", mu=function, tau=1 / s**2, value=f, observed=True)
return locals()
def model_with_dims():
with pm.Model(
coords={"city": ["Aachen", "Maastricht", "London", "Bergheim"]
}) as pmodel:
economics = pm.Uniform("economics", lower=-1, upper=1, shape=(1, ))
population = pm.HalfNormal("population", sigma=5, dims=("city"))
time = pm.ConstantData("time", [2014, 2015, 2016], dims="year")
n = pm.Deterministic("tax revenue",
economics * population[None, :] * time[:, None],
dims=("year", "city"))
yobs = pm.MutableData("observed", np.ones((3, 4)))
L = pm.Normal("L", n, observed=yobs)
compute_graph = {
"economics": set(),
"population": set(),
"time": set(),
"tax revenue": {"economics", "population", "time"},
"L": {"tax revenue"},
"observed": {"L"},
}
plates = {
"1": {"economics"},
"city (4)": {"population"},
"year (3)": {"time"},
"year (3) x city (4)": {"tax revenue"},
"3 x 4": {"L", "observed"},
}
return pmodel, compute_graph, plates
def test_zeroinflatedpoisson(self):
with pm.Model():
theta = pm.Beta("theta", alpha=1, beta=1)
psi = pm.HalfNormal("psi", sd=1)
pm.ZeroInflatedPoisson("suppliers", psi=psi, theta=theta, size=20)
gen_data = pm.sample_prior_predictive(samples=5000)
assert gen_data.prior["theta"].shape == (1, 5000)
assert gen_data.prior["psi"].shape == (1, 5000)
assert gen_data.prior["suppliers"].shape == (1, 5000, 20)
def aevb_model():
with pm.Model() as model:
pm.HalfNormal("x", size=(2, ), total_size=5)
pm.Normal("y", size=(2, ))
x = model.x
y = model.y
xr = model.compute_initial_point(0)[model.rvs_to_values[x].name]
mu = aesara.shared(xr)
rho = aesara.shared(np.zeros_like(xr))
return {"model": model, "y": y, "x": x, "replace": dict(mu=mu, rho=rho)}
def test_missing_data():
X = np.random.normal(0, 1, size=(2, 50)).T
Y = np.random.normal(0, 1, size=50)
X[10:20, 0] = np.nan
with pm.Model() as model:
mu = pm.BART("mu", X, Y, m=10)
sigma = pm.HalfNormal("sigma", 1)
y = pm.Normal("y", mu, sigma, observed=Y)
idata = pm.sample(random_seed=3415)
def test_transformed_vars(self):
# Test that prior predictive returns transformation of RVs when these are
# passed explicitly in `var_names`
def ub_interval_forward(x, ub):
# Interval transform assuming lower bound is zero
return np.log(x - 0) - np.log(ub - x)
with pm.Model(rng_seeder=123) as model:
ub = pm.HalfNormal("ub", 10)
x = pm.Uniform("x", 0, ub)
prior = pm.sample_prior_predictive(
var_names=["ub", "ub_log__", "x", "x_interval__"],
samples=10,
)
# Check values are correct
assert np.allclose(prior.prior["ub_log__"].data, np.log(prior.prior["ub"].data))
assert np.allclose(
prior.prior["x_interval__"].data,
ub_interval_forward(prior.prior["x"].data, prior.prior["ub"].data),
)
# Check that it works when the original RVs are not mentioned in var_names
with pm.Model(rng_seeder=123) as model_transformed_only:
ub = pm.HalfNormal("ub", 10)
x = pm.Uniform("x", 0, ub)
prior_transformed_only = pm.sample_prior_predictive(
var_names=["ub_log__", "x_interval__"],
samples=10,
)
assert (
"ub" not in prior_transformed_only.prior.data_vars
and "x" not in prior_transformed_only.prior.data_vars
)
assert np.allclose(
prior.prior["ub_log__"].data, prior_transformed_only.prior["ub_log__"].data
)
assert np.allclose(
prior.prior["x_interval__"], prior_transformed_only.prior["x_interval__"].data
)
def test_start(self):
with pm.Model() as model:
a = pm.Poisson("a", 5)
b = pm.HalfNormal("b", 10)
y = pm.Normal("y", a, b, observed=[1, 2, 3, 4])
start = {
"a": np.random.poisson(5, size=500),
"b_log__": np.abs(np.random.normal(0, 10, size=500)),
}
trace = pm.sample_smc(500, chains=1, start=start)
def test_normal_model(self):
data = st.norm(10, 0.5).rvs(1000, random_state=self.get_random_state())
with pm.Model() as m:
mu = pm.Normal("mu", 0, 3)
sigma = pm.HalfNormal("sigma", 1)
y = pm.Normal("y", mu, sigma, observed=data)
idata = pm.sample_smc(draws=2000, kernel=pm.smc.MH)
post = idata.posterior.stack(sample=("chain", "draw"))
assert np.abs(post["mu"].mean() - 10) < 0.1
assert np.abs(post["sigma"].mean() - 0.5) < 0.05
def test_variable_type(self):
with pm.Model() as model:
mu = pm.HalfNormal("mu", 1)
a = pm.Normal("a", mu=mu, sigma=2, observed=np.array([1, 2]))
b = pm.Poisson("b", mu, observed=np.array([1, 2]))
trace = pm.sample(compute_convergence_checks=False, return_inferencedata=False)
with model:
ppc = pm.sample_posterior_predictive(trace, return_inferencedata=False, samples=1)
assert ppc["a"].dtype.kind == "f"
assert ppc["b"].dtype.kind == "i"
def test_nested_model_coords():
with pm.Model(name="m1", coords=dict(dim1=range(2))) as m1:
a = pm.Normal("a", dims="dim1")
with pm.Model(name="m2", coords=dict(dim2=range(4))) as m2:
b = pm.Normal("b", dims="dim1")
m1.add_coord("dim3", range(4))
c = pm.HalfNormal("c", dims="dim3")
d = pm.Normal("d", b, c, dims="dim2")
e = pm.Normal("e", a[None] + d[:, None], dims=("dim2", "dim1"))
assert m1.coords is m2.coords
assert m1.dim_lengths is m2.dim_lengths
assert set(m2.RV_dims) < set(m1.RV_dims)
def test_named_model(self):
# Named models used to fail with Simulator because the arguments to the
# random fn used to be passed by name. This is no longer true.
# https://github.com/pymc-devs/pymc/pull/4365#issuecomment-761221146
name = "NamedModel"
with pm.Model(name=name):
a = pm.Normal("a", mu=0, sigma=1)
b = pm.HalfNormal("b", sigma=1)
s = pm.Simulator("s", self.normal_sim, a, b, observed=self.data)
trace = pm.sample_smc(draws=10, chains=2, return_inferencedata=False)
assert f"{name}/a" in trace.varnames
assert f"{name}/b" in trace.varnames
assert f"{name}/b_log__" in trace.varnames
def fixture_model():
with pm.Model() as model:
n = 5
dim = 4
with pm.Model():
cov = pm.InverseGamma("cov", alpha=1, beta=1)
x = pm.Normal("x",
mu=np.ones((dim, )),
sigma=pm.math.sqrt(cov),
shape=(n, dim))
eps = pm.HalfNormal("eps", np.ones((n, 1)), shape=(n, dim))
mu = pm.Deterministic("mu", at.sum(x + eps, axis=-1))
y = pm.Normal("y", mu=mu, sigma=1, shape=(n, ))
return model, [cov, x, eps, y]
def test_iterator():
with pm.Model() as model:
a = pm.Normal("a", shape=1)
b = pm.HalfNormal("b")
step1 = pm.NUTS([model.rvs_to_values[a]])
step2 = pm.Metropolis([model.rvs_to_values[b]])
step = pm.CompoundStep([step1, step2])
start = {"a": floatX(np.array([1.0])), "b_log__": floatX(np.array(2.0))}
sampler = ps.ParallelSampler(10, 10, 3, 2, [2, 3, 4], [start] * 3, step, 0, False)
with sampler:
for draw in sampler:
pass
class TestUtils:
X = np.random.normal(0, 1, size=(2, 50)).T
Y = np.random.normal(0, 1, size=50)
with pm.Model() as model:
mu = pm.BART("mu", X, Y, m=10)
sigma = pm.HalfNormal("sigma", 1)
y = pm.Normal("y", mu, sigma, observed=Y)
idata = pm.sample(random_seed=3415)
def test_predict(self):
rng = RandomState(12345)
pred_all = pm.bart.utils.predict(self.idata, rng, size=2)
rng = RandomState(12345)
pred_first = pm.bart.utils.predict(self.idata, rng, X_new=self.X[:10])
assert_almost_equal(pred_first, pred_all[0, :10], decimal=4)
assert pred_all.shape == (2, 50)
assert pred_first.shape == (10, )
@pytest.mark.parametrize(
"kwargs",
[
{},
{
"kind": "pdp",
"samples": 2,
"xs_interval": "quantiles",
"xs_values": [0.25, 0.5, 0.75],
},
{
"kind": "ice",
"instances": 2
},
{
"var_idx": [0],
"rug": False,
"smooth": False,
"color": "k"
},
{
"grid": (1, 2),
"sharey": "none",
"alpha": 1
},
],
)
def test_pdp(self, kwargs):
pm.bart.utils.plot_dependence(self.idata, X=self.X, Y=self.Y, **kwargs)
def test_deterministic_of_observed(self):
rng = np.random.RandomState(8442)
meas_in_1 = pm.aesaraf.floatX(2 + 4 * rng.randn(10))
meas_in_2 = pm.aesaraf.floatX(5 + 4 * rng.randn(10))
nchains = 2
with pm.Model(rng_seeder=rng) as model:
mu_in_1 = pm.Normal("mu_in_1", 0, 2)
sigma_in_1 = pm.HalfNormal("sd_in_1", 1)
mu_in_2 = pm.Normal("mu_in_2", 0, 2)
sigma_in_2 = pm.HalfNormal("sd__in_2", 1)
in_1 = pm.Normal("in_1", mu_in_1, sigma_in_1, observed=meas_in_1)
in_2 = pm.Normal("in_2", mu_in_2, sigma_in_2, observed=meas_in_2)
out_diff = in_1 + in_2
pm.Deterministic("out", out_diff)
trace = pm.sample(
100,
chains=nchains,
return_inferencedata=False,
compute_convergence_checks=False,
)
rtol = 1e-5 if aesara.config.floatX == "float64" else 1e-4
ppc = pm.sample_posterior_predictive(
return_inferencedata=False,
model=model,
trace=trace,
samples=len(trace) * nchains,
random_seed=0,
var_names=[var.name for var in (model.deterministics + model.basic_RVs)],
)
npt.assert_allclose(ppc["in_1"] + ppc["in_2"], ppc["out"], rtol=rtol)
def test_bart_vi():
X = np.random.normal(0, 1, size=(3, 250)).T
Y = np.random.normal(0, 1, size=250)
X[:, 0] = np.random.normal(Y, 0.1)
with pm.Model() as model:
mu = pm.BART("mu", X, Y, m=10)
sigma = pm.HalfNormal("sigma", 1)
y = pm.Normal("y", mu, sigma, observed=Y)
idata = pm.sample(random_seed=3415)
var_imp = (idata.sample_stats["variable_inclusion"].stack(
samples=("chain", "draw")).mean("samples"))
var_imp /= var_imp.sum()
assert var_imp[0] > var_imp[1:].sum()
assert_almost_equal(var_imp.sum(), 1)
def test_density_dist(self):
obs = np.random.normal(-1, 0.1, size=10)
with pm.Model():
mu = pm.Normal("mu", 0, 1)
sd = pm.HalfNormal("sd", 1e-6)
a = pm.DensityDist(
"a",
mu,
sd,
random=lambda mu, sd, rng=None, size=None: rng.normal(loc=mu, scale=sd, size=size),
observed=obs,
)
prior = pm.sample_prior_predictive(return_inferencedata=False)
npt.assert_almost_equal((prior["a"] - prior["mu"][..., None]).mean(), 0, decimal=3)
def test_get_log_likelihood():
obs = np.random.normal(10, 2, size=100)
obs_at = aesara.shared(obs, borrow=True, name="obs")
with pm.Model() as model:
a = pm.Normal("a", 0, 2)
sigma = pm.HalfNormal("sigma")
b = pm.Normal("b", a, sigma=sigma, observed=obs_at)
trace = pm.sample(tune=10, draws=10, chains=2, random_seed=1322)
b_true = trace.log_likelihood.b.values
a = np.array(trace.posterior.a)
sigma_log_ = np.log(np.array(trace.posterior.sigma))
b_jax = _get_log_likelihood(model, [a, sigma_log_])["b"]
assert np.allclose(b_jax.reshape(-1), b_true.reshape(-1))
def test_init_jitter(initval, jitter_max_retries, expectation):
with pm.Model() as m:
pm.HalfNormal("x", transform=None, initval=initval)
with expectation:
# Starting value is negative (invalid) when np.random.rand returns 0 (jitter = -1)
# and positive (valid) when it returns 1 (jitter = 1)
with mock.patch("numpy.random.Generator.uniform", side_effect=[-1, -1, -1, 1, -1]):
start = pm.sampling._init_jitter(
model=m,
initvals=None,
seeds=[1],
jitter=True,
jitter_max_retries=jitter_max_retries,
)
m.check_start_vals(start)
def check_exec_nuts_init(method):
with pm.Model() as model:
pm.Normal("a", mu=0, sigma=1, size=2)
pm.HalfNormal("b", sigma=1)
with model:
start, _ = pm.init_nuts(init=method, n_init=10, seeds=[1])
assert isinstance(start, list)
assert len(start) == 1
assert isinstance(start[0], dict)
assert model.a.tag.value_var.name in start[0]
assert model.b.tag.value_var.name in start[0]
start, _ = pm.init_nuts(init=method, n_init=10, chains=2, seeds=[1, 2])
assert isinstance(start, list)
assert len(start) == 2
assert isinstance(start[0], dict)
assert model.a.tag.value_var.name in start[0]
assert model.b.tag.value_var.name in start[0]
def test_custom_dist_sum_stat(self):
with pm.Model() as m:
a = pm.Normal("a", mu=0, sigma=1)
b = pm.HalfNormal("b", sigma=1)
s = pm.Simulator(
"s",
self.normal_sim,
a,
b,
distance=self.abs_diff,
sum_stat=self.quantiles,
observed=self.data,
)
assert self.count_rvs(m.logpt) == 1
with m:
pm.sample_smc(draws=100)
def test_bart_random():
X = np.random.normal(0, 1, size=(2, 50)).T
Y = np.random.normal(0, 1, size=50)
with pm.Model() as model:
mu = pm.BART("mu", X, Y, m=10)
sigma = pm.HalfNormal("sigma", 1)
y = pm.Normal("y", mu, sigma, observed=Y)
idata = pm.sample(random_seed=3415, chains=1)
rng = RandomState(12345)
pred_all = mu.owner.op.rng_fn(rng, size=2)
rng = RandomState(12345)
pred_first = mu.owner.op.rng_fn(rng, X_new=X[:10])
assert_almost_equal(pred_first, pred_all[0, :10], decimal=4)
assert pred_all.shape == (2, 50)
assert pred_first.shape == (10, )
def build_linear_model(x_vals, data, sigma_squared=10.0):
tau = 1.0 / sigma_squared
B_0 = pm.Normal('B_0', mu=0.0, tau=tau, doc='line slope', rseed=0)
B_1 = pm.Normal('B_1', mu=0.0, tau=tau, doc='line intercept', rseed=0)
SI = pm.HalfNormal('SI', tau=tau, doc='line sigma', rseed=0)
MU = pm.Deterministic(
name='mus',
eval=lambda B_0, B_1: B_0 * x_vals + B_1,
parents={
'B_0': B_0,
'B_1': B_1
},
doc='mu for line',
plot=False,
# rseed=0 NOTE: PyMC version 2.3.6 throws an error here.
)
OUT = pm.Normal('accuracies', mu=MU, tau=1.0/SI**2, value=data, \
observed=True, rseed=0)
return [B_0, B_1, SI, MU, OUT]
def test_multiobservedrv_to_observed_data(self, multiobs):
# fake regression data, with weights (W)
np.random.seed(2019)
N = 100
X = np.random.uniform(size=N)
W = 1 + np.random.poisson(size=N)
a, b = 5, 17
Y = a + np.random.normal(b * X)
with pm.Model():
a = pm.Normal("a", 0, 10)
b = pm.Normal("b", 0, 10)
mu = a + b * X
sigma = pm.HalfNormal("sigma", 1)
w = W
def weighted_normal(value, mu, sigma, w):
return w * pm.Normal.logp(value, mu, sigma)
y_logp = pm.DensityDist( # pylint: disable=unused-variable
"y_logp",
mu,
sigma,
w,
logp=weighted_normal,
observed=Y,
size=N)
idata = pm.sample(20,
tune=20,
return_inferencedata=True,
idata_kwargs={"density_dist_obs": multiobs})
multiobs_str = "" if multiobs else "~"
test_dict = {
"posterior": ["a", "b", "sigma"],
"sample_stats": ["lp"],
"log_likelihood": ["y_logp"],
f"{multiobs_str}observed_data": ["y", "w"],
}
fails = check_multiple_attrs(test_dict, idata)
assert not fails
if multiobs:
assert idata.observed_data.y.dtype.kind == "f"