class BrokenPowerLawAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "BrokenPowerLawAuxSampler"
xmin = AuxiliaryParameter(vmin=0)
alpha = AuxiliaryParameter()
xbreak = AuxiliaryParameter(vmin=0)
beta = AuxiliaryParameter()
xmax = AuxiliaryParameter(vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A broken power law distribution sampler,
where property ~ x^``alpha`` for x < ``xbreak``,
and property ~ x^``beta`` for x > ``xbreak``.
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param xmin: Minimum value of the broken power law
:type xmin: :class:`AuxiliaryParameter`
:param xmax: Maximum value of the broken power law
:type xmax: :class:``AuxiliaryParameter
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(BrokenPowerLawAuxSampler, self).__init__(name=name,
observed=observed)
def true_sampler(self, size: int):
u = np.atleast_1d(np.random.uniform(size=size))
self._true_values = bpl(u, self.xmin, self.xbreak, self.xmax,
self.alpha, self.beta)
def observation_sampler(self, size: int):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
class ViewingAngleSampler(NonObservedAuxSampler):
_auxiliary_sampler_name = "ViewingAngleSampler"
max_angle = AuxiliaryParameter(default=90, vmin=0, vmax=180)
def __init__(self):
"""
A viewing angle sampler that samples
from 0 to ``max_angle``. Unlike other samplers,
it assumes that this is NOT an observed property
:param max_angle: The maximum angle to which to
sample in degrees
:type max_angle: :class:`AuxiliaryParameter`
"""
super(ViewingAngleSampler, self).__init__(name="va", )
def true_sampler(self, size: int) -> None:
"""
Sample the viewing angle by inverse CDF
:param size: Number of samples
:type size: int
"""
theta_inverse = np.random.uniform(0.0,
1 -
np.cos(np.deg2rad(self.max_angle)),
size=size)
self._true_values = np.arccos(1.0 - theta_inverse)
class PowerLawAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "PowerLawAuxSampler"
xmin = AuxiliaryParameter(default=1, vmin=0)
xmax = AuxiliaryParameter(default=2, vmin=0)
alpha = AuxiliaryParameter(default=1)
sigma = AuxiliaryParameter(default=1, vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A bounded power law distribution sampler,
where property ~ x^``alpha``.
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param xmin: Minimum value of the power law
:type xmin: :class:`AuxiliaryParameter`
:param xmax: Maximum value of the power law
:type xmax: :class:``AuxiliaryParameter
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(PowerLawAuxSampler, self).__init__(name=name, observed=observed)
def true_sampler(self, size: int):
self._true_values = _sample_power_law(self.xmin, self.xmax, self.alpha,
size)
def observation_sampler(self, size: int):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
class NormalAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "NormalAuxSampler"
mu = AuxiliaryParameter(default=0)
tau = AuxiliaryParameter(default=1, vmin=0)
sigma = AuxiliaryParameter(default=1, vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A normal distribution sampler,
where property ~ N(``mu``, ``sigma``).
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param mu: Mean of the normal
:type mu: :class:`AuxiliaryParameter`
:param tau: Standard deviation of the normal
:type tau: :class:`AuxiliaryParameter`
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(NormalAuxSampler, self).__init__(name=name, observed=observed)
def true_sampler(self, size: int):
self._true_values = stats.norm.rvs(loc=self.mu,
scale=self.tau,
size=size)
def observation_sampler(self, size: int):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
class ParetoAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "ParetoAuxSampler"
xmin = AuxiliaryParameter(default=1, vmin=0)
alpha = AuxiliaryParameter(default=1, vmin=0)
sigma = AuxiliaryParameter(default=1, vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A pareto distribution sampler,
where property ~ 1 / x^(``alpha`` + 1).
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param xmin: Minimum value of the pareto
:type xmin: :class:`AuxiliaryParameter`
:param alpha: Index of the pareto
:type alpha: :class:`AuxiliaryParameter`
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(ParetoAuxSampler, self).__init__(name=name, observed=observed)
def true_sampler(self, size: int):
self._true_values = (np.random.pareto(self.alpha, size) +
1) * self.xmin
def observation_sampler(self, size: int):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
class DeltaAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "DeltaAuxSampler"
xp = AuxiliaryParameter(default=0)
sigma = AuxiliaryParameter(default=1, vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A delta-function sampler for which the true value
is fixed at ``xp``. Assumes property is observed by default,
in which case the observed value is sampled from
the true value with some normally-distributed error, ``sigma``.
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param xp: Value at which delta function is located
:type xp: :class:`AuxiliaryParameter`
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(DeltaAuxSampler, self).__init__(name=name, observed=observed)
def true_sampler(self, size: int):
self._true_values = np.repeat(self.xp, repeats=size)
def observation_sampler(self, size: int):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
class TruncatedNormalAuxSampler(AuxiliarySampler):
_auxiliary_sampler_name = "TruncatedNormalAuxSampler"
mu = AuxiliaryParameter(default=0)
tau = AuxiliaryParameter(default=1, vmin=0)
lower = AuxiliaryParameter()
upper = AuxiliaryParameter()
sigma = AuxiliaryParameter(default=1, vmin=0)
def __init__(self, name: str, observed: bool = True):
"""
A truncated normal sampler,
where property ~ N(``mu``, ``sigma``), between
``lower`` and ``upper``.
:param name: Name of the property
:type name: str
:param observed: `True` if the property is observed,
`False` if it is latent. Defaults to `True`
:type observed: bool
:param mu: Mean of the normal
:type mu: :class:`AuxiliaryParameter`
:param tau: Standard deviation of the normal
:type tau: :class:`AuxiliaryParameter`
:param lower: Lower bound of the truncation
:type lower: :class:`AuxiliaryParameter`
:param upper: Upper bound of the truncation
:type upper: :class:`AuxiliaryParameter`
:param sigma: Standard deviation of normal distribution
from which observed values are sampled, if ``observed``
is `True`
:type sigma: :class:`AuxiliaryParameter`
"""
super(TruncatedNormalAuxSampler, self).__init__(name=name,
observed=observed)
def true_sampler(self, size):
l = (self.lower - self.mu) / self.tau
u = (self.upper - self.mu) / self.tau
self._true_values = stats.truncnorm.rvs(
l,
u,
loc=self.mu,
scale=self.tau,
size=size,
)
assert np.alltrue(self._true_values >= self.lower)
assert np.alltrue(self._true_values <= self.upper)
def observation_sampler(self, size):
if self._is_observed:
self._obs_values = stats.norm.rvs(loc=self._true_values,
scale=self.sigma,
size=size)
else:
self._obs_values = self._true_values
