This module implements the MCMC class, which serves as a base class for Markov Chain Monte Carlo (MCMC) simulations.
 
The MCMC class provides methods for initializing simulations, running iterations, updating results, and converting results into different formats such as distributions or OPAD objects. It is designed to be extended by subclasses that implement specific MCMC behaviors.
 
Classes:
    MCMC: Abstract base class for MCMC simulations.

Modules
		numpy networkx pandas matplotlib.pyplot time

Classes
		structure_learning.approximators.approximator.Approximator(abc.ABC) MCMC   class MCMC(structure_learning.approximators.approximator.Approximator)     MCMC(data: pandas.core.frame.DataFrame, initial_state: ~State, max_iter: int = 30000, score_object: Union[str, structure_learning.scores.score.Score] = None, proposal_object: Union[str, structure_learning.proposals.proposal.StructureLearningProposal] = None, pc_init: bool = True, pc_significance_level=0.01, pc_ci_test='pearsonr', blacklist: numpy.ndarray = None, whitelist: numpy.ndarray = None, seed: int = None, result_type: str = 'distribution', graph_type='dag', burn_in: float = 0.1)   Base class for Markov Chain Monte Carlo (MCMC) simulations. Inheriting classes must implement the `step` method to define the behavior of a single MCMC iteration.     Method resolution order: MCMC structure_learning.approximators.approximator.Approximator abc.ABC builtins.object Methods defined here: __init__(self, data: pandas.core.frame.DataFrame, initial_state: ~State, max_iter: int = 30000, score_object: Union[str, structure_learning.scores.score.Score] = None, proposal_object: Union[str, structure_learning.proposals.proposal.StructureLearningProposal] = None, pc_init: bool = True, pc_significance_level=0.01, pc_ci_test='pearsonr', blacklist: numpy.ndarray = None, whitelist: numpy.ndarray = None, seed: int = None, result_type: str = 'distribution', graph_type='dag', burn_in: float = 0.1) Initialize the MCMC instance.   Parameters:     data (pd.DataFrame):                                        Dataset for the MCMC simulation.     initial_state (State):                                      Initial state for the simulation.     max_iter (int):                                             Maximum number of iterations. Default is 30000.     score_object (Union[str, Score]):                           Scoring object or type. Default is None.     proposal_object (Union[str, StructureLearningProposal]):    Proposal object or type. Default is None.     pc_init (bool):                                             Whether to initialize using the PC algorithm. Default is True.     pc_significance_level (float):                              Significance level for the PC algorithm. Default is 0.01.     pc_ci_test (str):                                           Conditional independence test for the PC algorithm. Default is 'pearsonr'.     blacklist (np.ndarray):                                     Mask for edges to ignore in the proposal.     whitelist (np.ndarray):                                     Mask for edges to include in the proposal.     plus1 (bool):                                               Whether to use plus1 neighborhood. Default is False.     seed (int):                                                 Random seed for reproducibility. Default is 32.     result_type (str):                                          Type of result to generate. Default is 'distribution'.     graph_type (str):                                           Type of graph ('dag' or 'cpdag'). Default is 'dag'. __str__(self) Return str(self). config(self) Get the configuration of the MCMC instance.   Returns:     dict: Configuration dictionary. get_chain_info(self, results, key='graph') Extract chain information from the MCMC results.   Parameters:     results (dict): Results of the MCMC simulation.     key (str): Key to extract information for. Default is 'graph'.   Returns:     list: Chain information. get_graphs(self, results) Retrieve a list of sampled graphs from the MCMC results.   Parameters:     results (dict): Results of the MCMC simulation.   Returns:     list: Sampled graphs. run(self, intervals=-1) -> Tuple[dict, float] Execute the MCMC simulation.   Returns:     Tuple[dict, float]: Results of the simulation and acceptance ratio. step(self) -> dict Perform one iteration of the MCMC simulation.   Returns:     dict: Information about the current iteration. to_cpdag_distribution(self) to_distribution(self) Convert the MCMC results to a distribution.   Returns:     MCMCDistribution: Distribution object. to_opad(self, plus=False) Convert the MCMC results to an OPAD object.   Parameters:     plus (bool): Whether to use the plus1 neighborhood. Default is False.   Returns:     OPAD: OPAD object. traceplot(self, ax=None) Generate a trace plot of the MCMC simulation.   Parameters:     ax (matplotlib.axes.Axes): Matplotlib axis to plot on. Default is None.   Returns:     list: Plot object. update_results(self, iteration, info) Update the results of the MCMC simulation with information from the current iteration.   Parameters:     iteration (int): Current iteration number.     info (dict): Information about the current iteration. Readonly properties defined here: trace Data and other attributes defined here: RESULT_TYPE_DIST = 'distribution' RESULT_TYPE_ITER = 'iterates' RESULT_TYPE_OPAD = 'opad' RESULT_TYPE_OPAD_PLUS = 'opad+' __abstractmethods__ = frozenset({'step'}) Methods inherited from structure_learning.approximators.approximator.Approximator: save(self, filename: str, compression='gzip') Saves the Graph object to a file.   Parameters:     filename (str): Path to the output file. Class methods inherited from structure_learning.approximators.approximator.Approximator: load(filename: str, compression='gzip') Loads a Graph object from a file.   Parameters:     filename (str): Path to the input file.   Returns:     Graph: Loaded Graph object. Data descriptors inherited from structure_learning.approximators.approximator.Approximator: __dict__ dictionary for instance variables __weakref__ list of weak references to the object

Data
		State = ~State Tuple = typing.Tuple Union = typing.Union