def extend(self, keys=None, lower=True, upper=True, algorithm='linear'):
# default algorithm
if algorithm is None:
algorithm = 'linear'
# other algorithms?
if algorithm != 'linear':
LinVac.extend(self, keys, lower, upper, algorithm)
return
# number of undefined singletons?
num_undefined = len(self.pspace) - len(self)
if num_undefined == 0:
# nothing to do
return
# sum probabilities over all defined singletons
mass = sum(
self.get(({
omega: 1
}, True), (0, 0))[0] for omega in self.pspace)
# distribute remaining probability over remaining events
remaining_mass = (1 - mass) / num_undefined
value = (remaining_mass, remaining_mass)
for omega in self.pspace:
key = ({omega: 1}, True)
if key not in self:
self[key] = value
def get_linvac(self, epsilon):
"""Convert probability into a linear vacuous mixture:
.. math::
\underline{E}(f)=(1-\epsilon)E(f)+\epsilon\inf f"""
epsilon = self.make_number(epsilon)
return LinVac(self.pspace,
lprob=[(1 - epsilon) * self[{
omega: 1
}, True][0] for omega in self.pspace],
number_type=self.number_type)
def extend(self, keys=None, lower=True, upper=True, algorithm='linear'):
# default algorithm
if algorithm is None:
algorithm = 'linear'
# other algorithms?
if algorithm != 'linear':
LinVac.extend(self, keys, lower, upper, algorithm)
return
# number of undefined singletons?
num_undefined = len(self.pspace) - len(self)
if num_undefined == 0:
# nothing to do
return
# sum probabilities over all defined singletons
mass = sum(self.get(({omega: 1}, True), (0, 0))[0]
for omega in self.pspace)
# distribute remaining probability over remaining events
remaining_mass = (1 - mass) / num_undefined
value = (remaining_mass, remaining_mass)
for omega in self.pspace:
key = ({omega: 1}, True)
if key not in self:
self[key] = value
def get_precise(self, gamble, event=True, algorithm='linear'):
r"""Calculate the conditional expectation,
.. math::
E(f|A)=
\frac{
\sum_{\omega\in A}p(\omega)f(\omega)
}{
\sum_{\omega\in A}p(\omega)
}
where :math:`p(\omega)` is simply the probability of the
singleton :math:`\omega`::
self[{omega: 1}, True][0]
"""
# default algorithm
if algorithm is None:
algorithm = 'linear'
# other algorithms?
if algorithm != 'linear':
return LinVac.get_lower(self, gamble, event, algorithm)
self.is_valid(raise_error=True)
gamble = self.make_gamble(gamble)
if event is True or (isinstance(event, Event) and event.is_true()):
# self[{omega: 1}, True][0] is the lower probability ([0])
# of the indicator gamble of omega ({omega: 1}),
# unconditionally (True).
return sum(self[{
omega: 1
}, True][0] * gamble[omega] for omega in self.pspace)
else:
event = self.pspace.make_event(event)
event_prob = self.get_precise(event.indicator(self.number_type))
if event_prob == 0:
raise ZeroDivisionError(
"cannot condition on event with zero probability")
return self.get_precise(gamble * event) / event_prob
def get_precise(self, gamble, event=True, algorithm='linear'):
r"""Calculate the conditional expectation,
.. math::
E(f|A)=
\frac{
\sum_{\omega\in A}p(\omega)f(\omega)
}{
\sum_{\omega\in A}p(\omega)
}
where :math:`p(\omega)` is simply the probability of the
singleton :math:`\omega`::
self[{omega: 1}, True][0]
"""
# default algorithm
if algorithm is None:
algorithm = 'linear'
# other algorithms?
if algorithm != 'linear':
return LinVac.get_lower(self, gamble, event, algorithm)
self.is_valid(raise_error=True)
gamble = self.make_gamble(gamble)
if event is True or (isinstance(event, Event) and event.is_true()):
# self[{omega: 1}, True][0] is the lower probability ([0])
# of the indicator gamble of omega ({omega: 1}),
# unconditionally (True).
return sum(self[{omega: 1}, True][0] * gamble[omega]
for omega in self.pspace)
else:
event = self.pspace.make_event(event)
event_prob = self.get_precise(event.indicator(self.number_type))
if event_prob == 0:
raise ZeroDivisionError(
"cannot condition on event with zero probability")
return self.get_precise(gamble * event) / event_prob