def get_errors(self, quiet=False):
"""
Compute the errors on the parameters using the profile likelihood method.
:return: a dictionary containing the asymmetric errors for each parameter.
"""
# Check that the user performed a fit first
assert (self._current_minimum is not None
), "You have to run the .fit method before calling errors."
errors = self._minimizer.get_errors()
# Set the parameters back to the best fit value
self.restore_best_fit()
# Print a table with the errors
parameter_names = list(self._free_parameters.keys())
best_fit_values = [
x.value for x in list(self._free_parameters.values())
]
negative_errors = [errors[k][0] for k in parameter_names]
positive_errors = [errors[k][1] for k in parameter_names]
units = [par.unit for par in list(self._free_parameters.values())]
results_table = ResultsTable(parameter_names, best_fit_values,
negative_errors, positive_errors, units)
if not quiet:
results_table.display()
return results_table.frame
def fit(self, quiet=False, compute_covariance=True, n_samples=5000):
"""
Perform a fit of the current likelihood model on the datasets
:param quiet: If True, print the results (default), otherwise do not print anything
:param compute_covariance:If True (default), compute and display the errors and the correlation matrix.
:return: a dictionary with the results on the parameters, and the values of the likelihood at the minimum
for each dataset and the total one.
"""
# Update the list of free parameters, to be safe against changes the user might do between
# the creation of this class and the calling of this method
self._update_free_parameters()
# Empty the call recorder
self._record_calls = {}
self._ncalls = 0
# Check if we have free parameters, otherwise simply return the value of the log like
if len(self._free_parameters) == 0:
custom_warnings.warn(
"There is no free parameter in the current model",
RuntimeWarning)
# Create the minimizer anyway because it will be needed by the following code
self._minimizer = self._get_minimizer(self.minus_log_like_profile,
self._free_parameters)
# Store the "minimum", which is just the current value
self._current_minimum = float(self.minus_log_like_profile())
else:
# Instance the minimizer
# If we have a global minimizer, use that first (with no covariance)
if isinstance(self._minimizer_type,
minimization.GlobalMinimization):
# Do global minimization first
global_minimizer = self._get_minimizer(
self.minus_log_like_profile, self._free_parameters)
xs, global_log_likelihood_minimum = global_minimizer.minimize(
compute_covar=False)
# Gather global results
paths = []
values = []
errors = []
units = []
for par in list(self._free_parameters.values()):
paths.append(par.path)
values.append(par.value)
errors.append(0)
units.append(par.unit)
global_results = ResultsTable(paths, values, errors, errors,
units)
if not quiet:
print(
"\n\nResults after global minimizer (before secondary optimization):"
)
global_results.display()
print("\nTotal log-likelihood minimum: %.3f\n" %
global_log_likelihood_minimum)
# Now set up secondary minimizer
self._minimizer = self._minimizer_type.get_second_minimization_instance(
self.minus_log_like_profile, self._free_parameters)
else:
# Only local minimization to be performed
self._minimizer = self._get_minimizer(
self.minus_log_like_profile, self._free_parameters)
# Perform the fit, but first flush stdout (so if we have verbose=True the messages there will follow
# what is already in the buffer)
sys.stdout.flush()
xs, log_likelihood_minimum = self._minimizer.minimize(
compute_covar=compute_covariance)
if log_likelihood_minimum == minimization.FIT_FAILED:
raise FitFailed("The fit failed to converge.")
# Store the current minimum for the -log likelihood
self._current_minimum = float(log_likelihood_minimum)
# First restore best fit (to make sure we compute the likelihood at the right point in the following)
self._minimizer.restore_best_fit()
# Now collect the values for the likelihood for the various datasets
# Fill the dictionary with the values of the -log likelihood (dataset by dataset)
minus_log_likelihood_values = collections.OrderedDict()
# Keep track of the total for a double check
total = 0
# sum up the total number of data points
total_number_of_data_points = 0
for dataset in list(self._data_list.values()):
ml = dataset.inner_fit() * (-1)
minus_log_likelihood_values[dataset.name] = ml
total += ml
total_number_of_data_points += dataset.get_number_of_data_points()
assert (
total == self._current_minimum
), "Current minimum stored after fit and current do not correspond!"
# compute additional statistics measures
statistical_measures = collections.OrderedDict()
# for MLE we can only compute the AIC and BIC as they
# are point estimates
statistical_measures["AIC"] = aic(-total, len(self._free_parameters),
total_number_of_data_points)
statistical_measures["BIC"] = bic(-total, len(self._free_parameters),
total_number_of_data_points)
# Now instance an analysis results class
self._analysis_results = MLEResults(
self.likelihood_model,
self._minimizer.covariance_matrix,
minus_log_likelihood_values,
statistical_measures=statistical_measures,
n_samples=n_samples,
)
# Show the results
if not quiet:
self._analysis_results.display()
return (
self._analysis_results.get_data_frame(),
self._analysis_results.get_statistic_frame(),
)
def _get_results_table(self, error_type, cl, covariance=None):
if error_type == "equal tail":
errors_gatherer = RandomVariates.equal_tail_interval
elif error_type == "hpd":
errors_gatherer = RandomVariates.highest_posterior_density_interval
elif error_type == "covariance":
assert covariance is not None, "If you use error_type='covariance' you have to provide a cov. matrix"
errors_gatherer = None
else:
raise ValueError(
"error_type must be either 'equal tail' or 'hpd'. Got %s" %
error_type)
# Build the data frame
parameter_paths = []
values = []
negative_errors = []
positive_errors = []
units_dict = []
for i, this_par in enumerate(self._free_parameters.values()):
parameter_paths.append(this_par.path)
this_phys_q = self.get_variates(parameter_paths[-1])
values.append(this_phys_q.value)
units_dict.append(this_par.unit)
if error_type != "covariance":
low_bound, hi_bound = errors_gatherer(this_phys_q, cl)
negative_errors.append(low_bound - values[-1])
positive_errors.append(hi_bound - values[-1])
else:
std_dev = np.sqrt(covariance[i, i])
if this_par.has_transformation():
best_fit_internal = this_par.transformation.forward(
values[-1])
_, neg_error = this_par.internal_to_external_delta(
best_fit_internal, -std_dev)
negative_errors.append(neg_error)
_, pos_error = this_par.internal_to_external_delta(
best_fit_internal, std_dev)
positive_errors.append(pos_error)
else:
negative_errors.append(-std_dev)
positive_errors.append(std_dev)
results_table = ResultsTable(parameter_paths, values, negative_errors,
positive_errors, units_dict)
return results_table