def sample_individual_estimates(model,
parameters=None,
samples_per_id=100,
seed=None):
"""Sample individual estimates given their covariance.
Parameters
----------
parameters
A list of a subset of parameters to sample. Default is None, which means all.
Returns
-------
Pool of samples in a DataFrame
"""
if seed is None or isinstance(seed, int):
seed = np.random.default_rng(seed)
ests = model.modelfit_results.individual_estimates
covs = model.modelfit_results.individual_estimates_covariance
if parameters is None:
parameters = ests.columns
ests = ests[parameters]
samples = pd.DataFrame()
for (idx, mu), sigma in zip(ests.iterrows(), covs):
sigma = sigma[parameters].loc[parameters]
sigma = nearest_posdef(sigma)
id_samples = seed.multivariate_normal(mu.values,
sigma.values,
size=samples_per_id)
id_df = pd.DataFrame(id_samples, columns=ests.columns)
id_df.index = [idx] * len(id_df) # ID as index
samples = pd.concat((samples, id_df))
return samples
def sample_from_covariance_matrix(
model,
modelfit_results=None,
parameters=None,
force_posdef_samples=None,
force_posdef_covmatrix=False,
n=1,
seed=None,
):
"""Sample parameter vectors using the covariance matrix
If modelfit_results is not provided the results from the model will be used
Parameters
----------
parameters
Use to only sample a subset of the parameters. None means all
force_posdef_samples
Set to how many iterations to do before forcing all samples to be positive definite. None is
default and means never and 0 means always
Returns
-------
A dataframe with one sample per row
"""
if modelfit_results is None:
modelfit_results = model.modelfit_results
if parameters is None:
parameters = list(modelfit_results.parameter_estimates.index)
if seed is None or isinstance(seed, int):
seed = np.random.default_rng(seed)
pe = modelfit_results.parameter_estimates[parameters]
index = pe.index
mu = pe.to_numpy()
sigma = modelfit_results.covariance_matrix[parameters].loc[
parameters].to_numpy()
if not is_posdef(sigma):
if force_posdef_covmatrix:
old_sigma = sigma
sigma = nearest_posdef(sigma)
delta_frobenius = np.linalg.norm(old_sigma) - np.linalg.norm(sigma)
delta_max = np.abs(old_sigma).max() - np.abs(sigma).max()
warnings.warn(
f'Covariance matrix was forced to become positive definite.\n'
f' Difference in the frobenius norm: {delta_frobenius:.3e}\n'
f' Difference in the max norm: {delta_max:.3e}\n')
else:
raise ValueError(
"Uncertainty covariance matrix not positive-definite")
fn = partial(sample_truncated_joint_normal, mu, sigma, seed=seed)
samples = sample_from_function(model,
fn,
parameters=index,
force_posdef_samples=force_posdef_samples,
n=n)
return samples
def _choose_param_init(model, rvs, params):
res = model.modelfit_results
rvs_names = [rv.name for rv in rvs]
etas = []
for i in range(len(rvs)):
elem = rvs.covariance_matrix.row(i).col(i)[0]
if str(elem) in [p.name for p in params]:
etas.append(rvs_names[i])
sd = np.array([np.sqrt(params[0].init), np.sqrt(params[1].init)])
init_default = round(0.1 * sd[0] * sd[1], 7)
if res is not None:
try:
ie = res.individual_estimates
if not all(eta in ie.columns for eta in etas):
return init_default
except KeyError:
return init_default
eta_corr = ie[etas].corr()
cov = math.corr2cov(eta_corr.to_numpy(), sd)
cov[cov == 0] = 0.0001
cov = math.nearest_posdef(cov)
return round(cov[1][0], 7)
else:
return init_default
def sample_from_covariance_matrix(model,
modelfit_results=None,
parameters=None,
force_posdef_samples=None,
force_posdef_covmatrix=False,
n=1):
"""Sample parameter vectors using the covariance matrix
if modelfit_results is not provided the results from the model will be used
:param parameters: use to only sample a subset of the parameters. None means all
:param force_posdef_samples: Set to how many iterations to do before forcing all
samples to be positive definite. None is default and means
never and 0 means always
:return: a dataframe with one sample per row
"""
if modelfit_results is None:
modelfit_results = model.modelfit_results
if parameters is None:
parameters = list(modelfit_results.parameter_estimates.index)
pe = modelfit_results.parameter_estimates[parameters]
index = pe.index
mu = pe.to_numpy()
sigma = modelfit_results.covariance_matrix[parameters].loc[
parameters].to_numpy()
if not is_posdef(sigma):
if force_posdef_covmatrix:
sigma = nearest_posdef(sigma)
else:
raise ValueError(
"Uncertainty covariance matrix not positive-definite")
parameter_summary = model.parameters.summary().loc[parameters]
parameter_summary = parameter_summary[~parameter_summary['fix']]
a = parameter_summary.lower.astype('float64').to_numpy()
b = parameter_summary.upper.astype('float64').to_numpy()
# reject non-posdef
kept_samples = pd.DataFrame()
remaining = n
if force_posdef_samples == 0:
force_posdef = True
else:
force_posdef = False
i = 0
while remaining > 0:
samples = sample_truncated_joint_normal(mu, sigma, a, b, n=remaining)
df = pd.DataFrame(samples, columns=index)
if not force_posdef:
selected = df[df.apply(model.random_variables.validate_parameters,
axis=1,
use_cache=True)]
else:
selected = df.transform(
model.random_variables.nearest_valid_parameters, axis=1)
kept_samples = pd.concat((kept_samples, selected))
remaining = n - len(kept_samples)
i += 1
if not force_posdef and force_posdef_samples is not None and i >= force_posdef_samples:
force_posdef = True
return kept_samples.reset_index(drop=True)