Bayesian Nets

Bayesian nets can be used for general, causal analysis or in combination with Entropy Pooling for causal and predictive views / stress-testing. Methods for storing Entropy Pooling views and computing appropriately weighted Entropy Pooling posterior probabilities are integrated into the BayesianNet class, making it straightforward to perform these complex analyses.

The entropy_pooling_probability method accepts options for a particular Entropy Pooling computation. Besides the control parameters that are available for the Entropy Pooling class, these options can contain parameters for the compute_posterior_probability method, i.e., heuristic and verbose parameters. Finally, it is possible to specify that the intermediate Entropy Pooling probabilities are returned using the 'return_all' key:

post_prob, intermediate_probs = bnet.entropy_pooling_probability(R, options={'return_all': True})

class BayesianNet(name=None)

Bayesian net class.

Parameters:: name (str) – Name of the Bayesian net.

add_edge(parent, child)

Method for adding an edge between two nodes in the Bayesian net.

Parameters:

parent (str) – Name of parent node.
child (str) – Name of child node.

Raises:

ValueError – If parent or child node has not been defined.

add_node(name, states)

Method for adding a node to the Bayesian net.

Parameters:

name (str) – Name of the new node.
states (List[str]) – A list of possible states for the new node.

Raises:

TypeError – If name or one of the states is not a string.
TypeError – If states is not a list.
ValueError – If states is empty.

build(): Method for building the Bayesian net.

entropy_pooling_probability(R, p=None, observations=None, **kwargs)

Method for computing Entropy Pooling probabilities given the leaf nodes specification.

Parameters:

R (DataFrame) – P&L / risk factor simulation with shape (S, I).
p (ndarray) – Prior probability vector with shape (S,) for the S scenarios in R. Set to np.ones(S) / S by default.
observations (dict) – Dictionary containing observations.
kwargs (dict) – Entropy Pooling options.

Return type:

Union[ndarray, Tuple[ndarray, ndarray]]

Returns:

Vector with shape (S,) containing weighted posterior probabilities or a tuple containing the weighted posterior probabilities as well as a matrix with shape (S, num_joint_states) containing the unweighted posterior probabilities for the individual joint states if return_all is set to True.

Raises:

ValueError – If p is not a vector of shape (S,) containing strictly positive elements that sum to 1.
ValueError – If no view is specified for some node and state.
ValueError – If observations contains a node which is not a part of the network.
ValueError – If a state is invalid for a particular node.

get_entropy_pooling_views()

Method for getting the current Entropy Pooling views dictionary.

Return type:: dict
Returns:: Current Entropy Pooling views dictionary.
Raises:: AttributeError – If no Entropy Pooling views have been specified.

get_parent(node=None)

Method for getting the parent(s) of node(s).

Parameters:: node (str) – Name of the node that parents should be extracted for. If given None (default), parents of all nodes will be returned.
Return type:: Union[DataFrame, dict]
Returns:: Parent(s) of node(s).
Raises:: ValueError – If the node is not a part of the network.

get_probability(node=None)

Method for extracting the current probability table(s) of node(s).

Parameters:: node (str) – Name of the node that the probability table should be extracted for. If given None (default), probability tables of all nodes are returned.
Return type:: Union[DataFrame, dict]
Returns:: Current probability table(s) of the node(s).
Raises:: ValueError – If the node does not exist or the probability table has not been initialized.

initialize_probability_tables(): Method for initializing probability tables.

joint_probability(observations=None)

Method for computing joint probabilities of the leaf nodes.

Parameters:

observations (dict) – Dictionary containing observations.

Return type:

DataFrame

Returns:

pd.DataFrame containing the joint probabilities of the leaf nodes.

Raises:

ValueError – If a node is not part of the network.
ValueError – If a state is invalid for a particular node.

marginal_probability(observations=None)

Method for computing marginal probabilities.

Parameters:

observations (dict) – Dictionary containing observations.

Return type:

dict[DataFrame]

Returns:

Dictionary of pd.DataFrames containing the probabilities of each node.

Raises:

ValueError – If a node is not a part of the network.
ValueError – If a state is invalid for a particular node.

plot(figsize=None)

Method for plotting the Bayesian net.

Parameters:: figsize (Tuple) – Figure size of the plot. Default: (9, 6).
Raises:: ValueError – If figsize is not a tuple of length two containing integers or floats.

set_entropy_pooling_view(node, state, view_lists)

Method for setting Entropy Pooling views for a particular leaf node and state.

Parameters:

node (str) – Name of the leaf node.
state (str) – Name of the state.
view_lists (list) – List of lists containing views. See documentation for Entropy Pooling add_view and add_rank_view.

Raises:

ValueError – If node is not a leaf node.
ValueError – If state does not exist for the node.
ValueError – If the first index of a list in view_lists is not in {‘regular’, ‘rank’}.

set_probability(node, probability)

Method for setting the probability of a node.

Parameters:

node (str) – Name of the node that probabilities are set for.
probability (Union[List, ndarray]) – Probability table containing the (conditional) state probabilities.

Raises:

ValueError – If node is not part of the network.
ValueError – If the probability tables have not been initialized.
ValueError – If any probabilities are negative.
ValueError – If the elements in a row sum to more than 1.
ValueError – If any given bounds do not lie in the interval [0, 1].
ValueError – If probability contains a list that does not have exactly 2 elements.
ValueError – If probability contains a list where the lower bound is greater than the upper bound.
ValueError – If the lower bounds sum to more than 1, or the upper bounds sum to less than 1.
ValueError – If the dimensionality of probability is different from the initialized probability table.