API

parmest

class pyomo.contrib.parmest.parmest.Estimator(experiment_list, obj_function=None, tee=False, diagnostic_mode=False, solver_options=None)

Bases: object

Parameter estimation class

Parameters:

• experiment_list (list of Experiments) – A list of experiment objects which creates one labeled model for each experiment

• obj_function (string or function (optional)) – Built in objective (currently only “SSE”) or custom function used to formulate parameter estimation objective. If no function is specified, the model is used “as is” and should be defined with a “FirstStageCost” and “SecondStageCost” expression that are used to build an objective. Default is None.

• tee (bool, optional) – If True, print the solver output to the screen. Default is False.

• diagnostic_mode (bool, optional) – If True, print diagnostics from the solver. Default is False.

• solver_options (dict, optional) – Provides options to the solver (also the name of an attribute). Default is None.

confidence_region_test(theta_values, distribution, alphas, test_theta_values=None)

Confidence region test to determine if theta values are within a rectangular, multivariate normal, or Gaussian kernel density distribution for a range of alpha values

Parameters:

• theta_values (pd.DataFrame, columns = theta_names) – Theta values used to generate a confidence region (generally returned by theta_est_bootstrap)

• distribution (string) – Statistical distribution used to define a confidence region, options = ‘MVN’ for multivariate_normal, ‘KDE’ for gaussian_kde, and ‘Rect’ for rectangular.

• alphas (list) – List of alpha values used to determine if theta values are inside or outside the region.

• test_theta_values (pd.Series or pd.DataFrame, keys/columns = theta_names, optional) – Additional theta values that are compared to the confidence region to determine if they are inside or outside.

Returns:

• training_results (pd.DataFrame) – Theta value used to generate the confidence region along with True (inside) or False (outside) for each alpha

• test_results (pd.DataFrame) – If test_theta_values is not None, returns test theta value along with True (inside) or False (outside) for each alpha

leaveNout_bootstrap_test(lNo, lNo_samples, bootstrap_samples, distribution, alphas, seed=None)

Leave-N-out bootstrap test to compare theta values where N data points are left out to a bootstrap analysis using the remaining data, results indicate if theta is within a confidence region determined by the bootstrap analysis

Parameters:

• lNo (int) – Number of data points to leave out for parameter estimation

• lNo_samples (int) – Leave-N-out sample size. If lNo_samples=None, the maximum number of combinations will be used

• bootstrap_samples (int:) – Bootstrap sample size

• distribution (string) – Statistical distribution used to define a confidence region, options = ‘MVN’ for multivariate_normal, ‘KDE’ for gaussian_kde, and ‘Rect’ for rectangular.

• alphas (list) – List of alpha values used to determine if theta values are inside or outside the region.

• seed (int or None, optional) – Random seed

Returns:

• List of tuples with one entry per lNo_sample

• * The first item in each tuple is the list of N samples that are left – out.

• * The second item in each tuple is a DataFrame of theta estimated using – the N samples.

• * The third item in each tuple is a DataFrame containing results from – the bootstrap analysis using the remaining samples.

• For each DataFrame a column is added for each value of alpha which

• indicates if the theta estimate is in (True) or out (False) of the

• alpha region for a given distribution (based on the bootstrap results)

likelihood_ratio_test(obj_at_theta, obj_value, alphas, return_thresholds=False)

Likelihood ratio test to identify theta values within a confidence region using the \(\chi^2\) distribution

Parameters:

• obj_at_theta (pd.DataFrame, columns = theta_names + 'obj') – Objective values for each theta value (returned by objective_at_theta)

• obj_value (int or float) – Objective value from parameter estimation using all data

• alphas (list) – List of alpha values to use in the chi2 test

• return_thresholds (bool, optional) – Return the threshold value for each alpha. Default is False.

Returns:

• LR (pd.DataFrame) – Objective values for each theta value along with True or False for each alpha

• thresholds (pd.Series) – If return_threshold = True, the thresholds are also returned.

objective_at_theta(theta_values=None, initialize_parmest_model=False)

Objective value for each theta

Parameters:

• theta_values (pd.DataFrame, columns=theta_names) – Values of theta used to compute the objective

• initialize_parmest_model (boolean) – If True: Solve square problem instance, build extensive form of the model for parameter estimation, and set flag model_initialized to True. Default is False.

Returns:

obj_at_theta – Objective value for each theta (infeasible solutions are omitted).

Return type:

pd.DataFrame

theta_est(solver='ef_ipopt', return_values=[], calc_cov=False, cov_n=None)

Parameter estimation using all scenarios in the data

Parameters:

• solver (string, optional) – Currently only “ef_ipopt” is supported. Default is “ef_ipopt”.

• return_values (list, optional) – List of Variable names, used to return values from the model for data reconciliation

• calc_cov (boolean, optional) – If True, calculate and return the covariance matrix (only for “ef_ipopt” solver). Default is False.

• cov_n (int, optional) – If calc_cov=True, then the user needs to supply the number of datapoints that are used in the objective function.

Returns:

• objectiveval (float) – The objective function value

• thetavals (pd.Series) – Estimated values for theta

• variable values (pd.DataFrame) – Variable values for each variable name in return_values (only for solver=’ef_ipopt’)

• cov (pd.DataFrame) – Covariance matrix of the fitted parameters (only for solver=’ef_ipopt’)

theta_est_bootstrap(bootstrap_samples, samplesize=None, replacement=True, seed=None, return_samples=False)

Parameter estimation using bootstrap resampling of the data

Parameters:

• bootstrap_samples (int) – Number of bootstrap samples to draw from the data

• samplesize (int or None, optional) – Size of each bootstrap sample. If samplesize=None, samplesize will be set to the number of samples in the data

• replacement (bool, optional) – Sample with or without replacement. Default is True.

• seed (int or None, optional) – Random seed

• return_samples (bool, optional) – Return a list of sample numbers used in each bootstrap estimation. Default is False.

Returns:

bootstrap_theta – Theta values for each sample and (if return_samples = True) the sample numbers used in each estimation

Return type:

pd.DataFrame

theta_est_leaveNout(lNo, lNo_samples=None, seed=None, return_samples=False)

Parameter estimation where N data points are left out of each sample

Parameters:

• lNo (int) – Number of data points to leave out for parameter estimation

• lNo_samples (int) – Number of leave-N-out samples. If lNo_samples=None, the maximum number of combinations will be used

• seed (int or None, optional) – Random seed

• return_samples (bool, optional) – Return a list of sample numbers that were left out. Default is False.

Returns:

lNo_theta – Theta values for each sample and (if return_samples = True) the sample numbers left out of each estimation

Return type:

pd.DataFrame

pyomo.contrib.parmest.parmest.SSE(model)

Sum of squared error between experiment_output model and data values

pyomo.contrib.parmest.parmest.ef_nonants(ef)

pyomo.contrib.parmest.parmest.group_data(data, groupby_column_name, use_mean=None)

DEPRECATED.

Group data by scenario

Parameters:

• data (DataFrame) – Data

• groupby_column_name (strings) – Name of data column which contains scenario numbers

• use_mean (list of column names or None, optional) – Name of data columns which should be reduced to a single value per scenario by taking the mean

Returns:

• grouped_data (list of dictionaries) – Grouped data

• .. deprecated:: 6.7.2 – This function (group_data) has been deprecated and may be removed in a future release.

scenariocreator

class pyomo.contrib.parmest.scenariocreator.ParmestScen(name, ThetaVals, probability)

Bases: object

A little container for scenarios; the Args are the attributes.

Parameters:

• name (str) – name for reporting; might be “”

• ThetaVals (dict) – ThetaVals[name]=val

• probability (float) – probability of occurrence “near” these ThetaVals

class pyomo.contrib.parmest.scenariocreator.ScenarioCreator(pest, solvername)

Bases: object

Create scenarios from parmest.

Parameters:

• pest (Estimator) – the parmest object

• solvername (str) – name of the solver (e.g. “ipopt”)

ScenariosFromBootstrap(addtoSet, numtomake, seed=None)

Creates new self.Scenarios list using the experiments only.

Parameters:

• addtoSet (ScenarioSet) – the scenarios will be added to this set

• numtomake (int) – number of scenarios to create

ScenariosFromExperiments(addtoSet)

Creates new self.Scenarios list using the experiments only.

Parameters:

addtoSet (ScenarioSet) – the scenarios will be added to this set

Returns:

a ScenarioSet

class pyomo.contrib.parmest.scenariocreator.ScenarioSet(name)

Bases: object

Class to hold scenario sets

Args: name (str): name of the set (might be “”)

ScenarioNumber(scennum)

Returns the scenario with the given, zero-based number

ScensIterator()

Usage: for scenario in ScensIterator()

addone(scen)

Add a scenario to the set

Parameters:

scen (ParmestScen) – the scenario to add

append_bootstrap(bootstrap_theta)

Append a bootstrap theta df to the scenario set; equally likely

Parameters:

bootstrap_theta (dataframe) – created by the bootstrap

Note: this can be cleaned up a lot with the list becomes a df,

which is why I put it in the ScenarioSet class.

write_csv(filename)

write a csv file with the scenarios in the set

Parameters:

filename (str) – full path and full name of file

graphics

pyomo.contrib.parmest.graphics.fit_kde_dist(theta_values)

Fit a Gaussian kernel-density distribution to theta values

Parameters:

theta_values (DataFrame) – Theta values, columns = variable names

Return type:

scipy.stats.gaussian_kde distribution

pyomo.contrib.parmest.graphics.fit_mvn_dist(theta_values)

Fit a multivariate normal distribution to theta values

Parameters:

theta_values (DataFrame) – Theta values, columns = variable names

Return type:

scipy.stats.multivariate_normal distribution

pyomo.contrib.parmest.graphics.fit_rect_dist(theta_values, alpha)

Fit an alpha-level rectangular distribution to theta values

Parameters:

• theta_values (DataFrame) – Theta values, columns = variable names

• alpha (float, optional) – Confidence interval value

Return type:

tuple containing lower bound and upper bound for each variable

pyomo.contrib.parmest.graphics.grouped_boxplot(data1, data2, normalize=False, group_names=['data1', 'data2'], filename=None)

Plot a grouped boxplot to compare two datasets

The datasets can be normalized by the median and standard deviation of data1.

Parameters:

• data1 (DataFrame) – Data set, columns = variable names

• data2 (DataFrame) – Data set, columns = variable names

• normalize (bool, optional) – Normalize both datasets by the median and standard deviation of data1

• group_names (list, optional) – Names used in the legend

• filename (string, optional) – Filename used to save the figure

pyomo.contrib.parmest.graphics.grouped_violinplot(data1, data2, normalize=False, group_names=['data1', 'data2'], filename=None)

Plot a grouped violinplot to compare two datasets

The datasets can be normalized by the median and standard deviation of data1.

Parameters:

• data1 (DataFrame) – Data set, columns = variable names

• data2 (DataFrame) – Data set, columns = variable names

• normalize (bool, optional) – Normalize both datasets by the median and standard deviation of data1

• group_names (list, optional) – Names used in the legend

• filename (string, optional) – Filename used to save the figure

pyomo.contrib.parmest.graphics.pairwise_plot(theta_values, theta_star=None, alpha=None, distributions=[], axis_limits=None, title=None, add_obj_contour=True, add_legend=True, filename=None)

Plot pairwise relationship for theta values, and optionally alpha-level confidence intervals and objective value contours

Parameters:

• theta_values (DataFrame or tuple) –

  • If theta_values is a DataFrame, then it contains one column for each theta variable and (optionally) an objective value column (‘obj’) and columns that contains Boolean results from confidence interval tests (labeled using the alpha value). Each row is a sample.

    • Theta variables can be computed from theta_est_bootstrap, theta_est_leaveNout, and leaveNout_bootstrap_test.

    • The objective value can be computed using the likelihood_ratio_test.

    • Results from confidence interval tests can be computed using the leaveNout_bootstrap_test, likelihood_ratio_test, and confidence_region_test.

  • If theta_values is a tuple, then it contains a mean, covariance, and number of samples (mean, cov, n) where mean is a dictionary or Series (indexed by variable name), covariance is a DataFrame (indexed by variable name, one column per variable name), and n is an integer. The mean and covariance are used to create a multivariate normal sample of n theta values. The covariance can be computed using theta_est(calc_cov=True).

• theta_star (dict or Series, optional) – Estimated value of theta. The dictionary or Series is indexed by variable name. Theta_star is used to slice higher dimensional contour intervals in 2D

• alpha (float, optional) – Confidence interval value, if an alpha value is given and the distributions list is empty, the data will be filtered by True/False values using the column name whose value equals alpha (see results from leaveNout_bootstrap_test, likelihood_ratio_test, and confidence_region_test)

• distributions (list of strings, optional) – Statistical distribution used to define a confidence region, options = ‘MVN’ for multivariate_normal, ‘KDE’ for gaussian_kde, and ‘Rect’ for rectangular. Confidence interval is a 2D slice, using linear interpolation at theta_star.

• axis_limits (dict, optional) – Axis limits in the format {variable: [min, max]}

• title (string, optional) – Plot title

• add_obj_contour (bool, optional) – Add a contour plot using the column ‘obj’ in theta_values. Contour plot is a 2D slice, using linear interpolation at theta_star.

• add_legend (bool, optional) – Add a legend to the plot

• filename (string, optional) – Filename used to save the figure