Lower Previsions

• Polyhedral Lower Previsions
• Lower Probabilities
• Belief Functions
• Linear Vacuous Mixtures
• Probability Measures
• More Examples

class improb.lowprev.LowPrev

Abstract base class for working with arbitrary lower previsions.

dominates(gamble, other_gamble, event=True, algorithm=None)

Does gamble dominate other_gamble in lower prevision?

Parameters:

• gamble (dict or similar; see Gambles) – The left hand side gamble.
• other_gamble (dict or similar; see Gambles) – The right hand side gamble.
• event (list or similar; see Events) – The event to condition on.
• algorithm (str) – The algorithm to use (the default value uses the most efficient algorithm).

Returns:

True if gamble dominates other_gamble, False otherwise.

Return type:

bool

get_extend_domain()

Get largest possible domain to which the lower prevision can be extended.

get_lower(gamble, event=True, algorithm=None)

Return the lower expectation for gamble conditional on event via natural extension.

Parameters:

• gamble (dict or similar; see Gambles) – The gamble whose upper expectation to find.
• event (list or similar; see Events) – The event to condition on.
• algorithm (str) – The algorithm to use (the default value uses the most efficient algorithm).

Returns:

The lower bound for this expectation, i.e. the natural extension of the gamble.

Return type:

float or Fraction

get_upper(gamble, event=True, algorithm=None)

Return the upper expectation for gamble conditional on event via natural extension.

Parameters:

• gamble (dict or similar; see Gambles) – The gamble whose upper expectation to find.
• event (list or similar; see Events) – The event to condition on.
• algorithm (str) – The algorithm to use (None for the most efficient algorithm).

Returns:

The upper bound for this expectation, i.e. the natural extension of the gamble.

Return type:

float or Fraction

is_avoiding_sure_loss(algorithm=None)

No Dutch book? Does the lower prevision avoid sure loss?

Returns:True if avoids sure loss, False otherwise. Return type:bool

is_coherent(algorithm=None)

Do all assessments coincide with their natural extension? Is the lower prevision coherent?

Parameters:algorithm (str) – The algorithm to use (the default value uses the most efficient algorithm). Returns:True if coherent, False otherwise. Return type:bool

is_linear(algorithm=None)

Is the lower prevision a linear prevision? More precisely, we check that the natural extension is linear on the linear span of the domain of the lower prevision.

Parameters:algorithm (str) – The algorithm to use (the default value uses the most efficient algorithm). Returns:True if linear, False otherwise. Return type:bool

pspace

An PSpace representing the possibility space.