# Source code for pymc.distributions.censored

```
# Copyright 2023 The PyMC Developers
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
import pytensor.tensor as pt
from pytensor.tensor import TensorVariable
from pytensor.tensor.random.op import RandomVariable
from pymc.distributions.distribution import (
Distribution,
SymbolicRandomVariable,
_moment,
)
from pymc.distributions.shape_utils import _change_dist_size, change_dist_size
from pymc.util import check_dist_not_registered
class CensoredRV(SymbolicRandomVariable):
"""Censored random variable"""
inline_logprob = True
_print_name = ("Censored", "\\operatorname{Censored}")
[docs]class Censored(Distribution):
r"""
Censored distribution
The pdf of a censored distribution is
.. math::
\begin{cases}
0 & \text{for } x < lower, \\
\text{CDF}(lower, dist) & \text{for } x = lower, \\
\text{PDF}(x, dist) & \text{for } lower < x < upper, \\
1-\text{CDF}(upper, dist) & \text {for} x = upper, \\
0 & \text{for } x > upper,
\end{cases}
Parameters
----------
dist : unnamed_distribution
Univariate distribution which will be censored.
This distribution must have a logcdf method implemented for sampling.
.. warning:: dist will be cloned, rendering it independent of the one passed as input.
lower : float or None
Lower (left) censoring point. If `None` the distribution will not be left censored
upper : float or None
Upper (right) censoring point. If `None`, the distribution will not be right censored.
Warnings
--------
Continuous censored distributions should only be used as likelihoods.
Continuous censored distributions are a form of discrete-continuous mixture
and as such cannot be sampled properly without a custom step sampler.
If you wish to sample such a distribution, you can add the latent uncensored
distribution to the model and then wrap it in a :class:`~pymc.Deterministic`
:func:`~pymc.math.clip`.
Examples
--------
.. code-block:: python
with pm.Model():
normal_dist = pm.Normal.dist(mu=0.0, sigma=1.0)
censored_normal = pm.Censored("censored_normal", normal_dist, lower=-1, upper=1)
"""
rv_type = CensoredRV
[docs] @classmethod
def dist(cls, dist, lower, upper, **kwargs):
if not isinstance(dist, TensorVariable) or not isinstance(
dist.owner.op, (RandomVariable, SymbolicRandomVariable)
):
raise ValueError(
f"Censoring dist must be a distribution created via the `.dist()` API, got {type(dist)}"
)
if dist.owner.op.ndim_supp > 0:
raise NotImplementedError(
"Censoring of multivariate distributions has not been implemented yet"
)
check_dist_not_registered(dist)
return super().dist([dist, lower, upper], **kwargs)
@classmethod
def rv_op(cls, dist, lower=None, upper=None, size=None):
lower = pt.constant(-np.inf) if lower is None else pt.as_tensor_variable(lower)
upper = pt.constant(np.inf) if upper is None else pt.as_tensor_variable(upper)
# When size is not specified, dist may have to be broadcasted according to lower/upper
dist_shape = size if size is not None else pt.broadcast_shape(dist, lower, upper)
dist = change_dist_size(dist, dist_shape)
# Censoring is achieved by clipping the base distribution between lower and upper
dist_, lower_, upper_ = dist.type(), lower.type(), upper.type()
censored_rv_ = pt.clip(dist_, lower_, upper_)
return CensoredRV(
inputs=[dist_, lower_, upper_],
outputs=[censored_rv_],
ndim_supp=0,
)(dist, lower, upper)
@_change_dist_size.register(CensoredRV)
def change_censored_size(cls, dist, new_size, expand=False):
uncensored_dist, lower, upper = dist.owner.inputs
if expand:
new_size = tuple(new_size) + tuple(uncensored_dist.shape)
return Censored.rv_op(uncensored_dist, lower, upper, size=new_size)
@_moment.register(CensoredRV)
def moment_censored(op, rv, dist, lower, upper):
moment = pt.switch(
pt.eq(lower, -np.inf),
pt.switch(
pt.isinf(upper),
# lower = -inf, upper = inf
0,
# lower = -inf, upper = x
upper - 1,
),
pt.switch(
pt.eq(upper, np.inf),
# lower = x, upper = inf
lower + 1,
# lower = x, upper = x
(lower + upper) / 2,
),
)
moment = pt.full_like(dist, moment)
return moment
```