Poisson likelihood without uncertainty implementation

docs/api.rst

@@ -109,6 +109,14 @@ Default PDFs
     third_moment.third_moment_expansion
     third_moment.compute_third_moments
 
+Simple PDFs
+~~~~~~~~~~~
+
+.. autosummary:: 
+    :toctree: _generated/
+
+    simple_pdf.Poisson
+
 
 Exceptions
 ----------

docs/plugins.rst

@@ -283,6 +283,38 @@ Once again, the exclusion limit can be computed as
  * ``analysis`` (optional): Unique identifier for the analysis.
  * ``xsection`` (optional): Cross-section value for the signal hypothesis. Units determined by the user.
 
+``'default_pdf.poisson'``
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Simple Poisson implementation without uncertainties which can be described as follows;
+
+.. math::
+
+    \mathcal{L}(\mu) = \prod_{i\in{\rm bins}}{\rm Poiss}(n^i|\mu n_s^i + n_b^i)
+
+It can take any number of yields.
+
+.. code-block:: python3
+    :linenos:
+
+    >>> pdf_wrapper = spey.get_backend("default_pdf.poisson")
+    >>> statistical_model = pdf_wrapper(
+    ...     signal_yields=[12.0, 15.0],
+    ...     background_yields=[50.0,48.0],
+    ...     data=[36, 33],
+    ...     analysis="example",
+    ...     xsection=0.123,
+    ... )
+
+**Arguments:**
+
+ * ``signal_yields``: keyword for signal yields. It can take one or more values as a list or NumPy array.
+ * ``background_yields``: keyword for background-only expectations. It can take one or more values as a list or NumPy array.
+ * ``data``: keyword for observations. It can take one or more values as a list or NumPy array.
+ * ``analysis`` (optional): Unique identifier for the analysis.
+ * ``xsection`` (optional): Cross-section value for the signal hypothesis. Units determined by the user.
+
+
 External Plug-ins
 -----------------
 

docs/releases/changelog-v0.1.md

@@ -1,4 +1,4 @@
-# Release notes v0.1.2
+# Release notes v0.1.3
 
 ## New features since last release
 
@@ -9,6 +9,10 @@
 * $\chi^2$ function has been extended to compute background + signal vs background only model.
   ([#17](https://github.com/SpeysideHEP/spey/pull/17))
 
+* Poisson based likelihood constructor without uncertainties has been added
+  (Request by Veronica Sanz for EFT studies).
+  ([#22](https://github.com/SpeysideHEP/spey/pull/22))
+
 ## Improvements
 
 * Backend inspection has been added for the models that act like intermediate functions.
@@ -23,6 +27,9 @@
   chi-square computer. See issue [#19](https://github.com/SpeysideHEP/spey/issues/19).
   ([#20](https://github.com/SpeysideHEP/spey/pull/20))
 
+* Execution error fix during likelihood computation for models with single nuisance parameter.
+  ([#22](https://github.com/SpeysideHEP/spey/pull/22))
+
 ## Contributors
 
 This release contains contributions from (in alphabetical order):

setup.py

@@ -19,6 +19,7 @@
     "default_pdf.correlated_background = spey.backends.default_pdf:CorrelatedBackground",
     "default_pdf.third_moment_expansion = spey.backends.default_pdf:ThirdMomentExpansion",
     "default_pdf.effective_sigma = spey.backends.default_pdf:EffectiveSigma",
+    "default_pdf.poisson = spey.backends.default_pdf.simple_pdf:Poisson",
 ]
 
 setup(

src/spey/_version.py

@@ -1,3 +1,3 @@
 """Version number (major.minor.patch[-label])"""
 
-__version__ = "0.1.2"
+__version__ = "0.1.3"

src/spey/backends/default_pdf/simple_pdf.py

@@ -0,0 +1,289 @@
+"""This file contains basic likelihood implementations"""
+
+from typing import Callable, List, Optional, Text, Tuple, Union
+
+from autograd import grad, hessian
+from autograd import numpy as np
+
+from spey._version import __version__
+from spey.backends.distributions import MainModel
+from spey.base import BackendBase, ModelConfig
+from spey.utils import ExpectationType
+
+# pylint: disable=E1101,E1120,W0613
+
+
+class Poisson(BackendBase):
+    r"""
+    Poisson distribution without uncertainty implementation.
+
+    .. math::
+
+        \mathcal{L}(\mu) = \prod_{i\in{\rm bins}}{\rm Poiss}(n^i|\mu n_s^i + n_b^i)
+
+    where :math:`n_{s,b}` are signal and background yields and :math:`n` are the observations.
+
+    Args:
+        signal_yields (``List[float]``): signal yields
+        background_yields (``List[float]``): background yields
+        data (``List[int]``): data
+    """
+
+    name: Text = "default_pdf.poisson"
+    """Name of the backend"""
+    version: Text = __version__
+    """Version of the backend"""
+    author: Text = "SpeysideHEP"
+    """Author of the backend"""
+    spey_requires: Text = __version__
+    """Spey version required for the backend"""
+
+    __slots__ = ["_model", "_main_model"]
+
+    def __init__(
+        self,
+        signal_yields: List[float],
+        background_yields: List[float],
+        data: List[int],
+    ):
+        self.data = np.array(data, dtype=np.float64)
+        self.signal_yields = np.array(signal_yields, dtype=np.float64)
+        self.background_yields = np.array(background_yields, dtype=np.float64)
+
+        minimum_poi = -np.inf
+        if self.is_alive:
+            minimum_poi = -np.min(
+                self.background_yields[self.signal_yields > 0.0]
+                / self.signal_yields[self.signal_yields > 0.0]
+            )
+
+        self._main_model = None
+
+        self._config = ModelConfig(
+            poi_index=0,
+            minimum_poi=minimum_poi,
+            suggested_init=[1.0],
+            suggested_bounds=[(minimum_poi, 10)],
+        )
+
+    @property
+    def is_alive(self) -> bool:
+        """Returns True if at least one bin has non-zero signal yield."""
+        return np.any(self.signal_yields > 0.0)
+
+    def config(
+        self, allow_negative_signal: bool = True, poi_upper_bound: float = 10.0
+    ) -> ModelConfig:
+        r"""
+        Model configuration.
+
+        Args:
+            allow_negative_signal (``bool``, default ``True``): If ``True`` :math:`\hat\mu`
+              value will be allowed to be negative.
+            poi_upper_bound (``float``, default ``40.0``): upper bound for parameter
+              of interest, :math:`\mu`.
+
+        Returns:
+            ~spey.base.ModelConfig:
+            Model configuration. Information regarding the position of POI in
+            parameter list, suggested input and bounds.
+        """
+        if allow_negative_signal and poi_upper_bound == 10.0:
+            return self._config
+
+        return ModelConfig(
+            self._config.poi_index,
+            self._config.minimum_poi,
+            self._config.suggested_init,
+            [(0, poi_upper_bound)],
+        )
+
+    @property
+    def main_model(self) -> MainModel:
+        """retreive the main model distribution"""
+        if self._main_model is None:
+
+            def lam(pars: np.ndarray) -> np.ndarray:
+                """
+                Compute lambda for Main model with third moment expansion.
+                For details see above eq 2.6 in :xref:`1809.05548`
+
+                Args:
+                    pars (``np.ndarray``): nuisance parameters
+
+                Returns:
+                    ``np.ndarray``:
+                    expectation value of the poisson distribution with respect to
+                    nuisance parameters.
+                """
+                return pars[0] * self.signal_yields + self.background_yields
+
+            self._main_model = MainModel(lam)
+
+        return self._main_model
+
+    def get_objective_function(
+        self,
+        expected: ExpectationType = ExpectationType.observed,
+        data: Optional[np.ndarray] = None,
+        do_grad: bool = True,
+    ) -> Callable[[np.ndarray], Union[Tuple[float, np.ndarray], float]]:
+        r"""
+        Objective function i.e. negative log-likelihood, :math:`-\log\mathcal{L}(\mu, \theta)`
+
+        Args:
+            expected (~spey.ExpectationType): Sets which values the fitting algorithm should focus and
+              p-values to be computed.
+
+              * :obj:`~spey.ExpectationType.observed`: Computes the p-values with via post-fit
+                prescriotion which means that the experimental data will be assumed to be the truth
+                (default).
+              * :obj:`~spey.ExpectationType.aposteriori`: Computes the expected p-values with via
+                post-fit prescriotion which means that the experimental data will be assumed to be
+                the truth.
+              * :obj:`~spey.ExpectationType.apriori`: Computes the expected p-values with via pre-fit
+                prescription which means that the SM will be assumed to be the truth.
+            data (``np.ndarray``, default ``None``): input data that to fit
+            do_grad (``bool``, default ``True``): If ``True`` return objective and its gradient
+              as ``tuple`` if ``False`` only returns objective function.
+
+        Returns:
+            ``Callable[[np.ndarray], Union[float, Tuple[float, np.ndarray]]]``:
+            Function which takes fit parameters (:math:`\mu` and :math:`\theta`) and returns either
+            objective or objective and its gradient.
+        """
+        current_data = (
+            self.background_yields if expected == ExpectationType.apriori else self.data
+        )
+        data = current_data if data is None else data
+
+        def negative_loglikelihood(pars: np.ndarray) -> np.ndarray:
+            """Compute twice negative log-likelihood"""
+            return -self.main_model.log_prob(pars, data)
+
+        if do_grad:
+            grad_negative_loglikelihood = grad(negative_loglikelihood, argnum=0)
+            return lambda pars: (
+                negative_loglikelihood(pars),
+                grad_negative_loglikelihood(pars),
+            )
+
+        return negative_loglikelihood
+
+    def get_logpdf_func(
+        self,
+        expected: ExpectationType = ExpectationType.observed,
+        data: Optional[np.array] = None,
+    ) -> Callable[[np.ndarray, np.ndarray], float]:
+        r"""
+        Generate function to compute :math:`\log\mathcal{L}(\mu, \theta)` where :math:`\mu` is the
+        parameter of interest and :math:`\theta` are nuisance parameters.
+
+        Args:
+            expected (~spey.ExpectationType): Sets which values the fitting algorithm should focus and
+              p-values to be computed.
+
+              * :obj:`~spey.ExpectationType.observed`: Computes the p-values with via post-fit
+                prescriotion which means that the experimental data will be assumed to be the truth
+                (default).
+              * :obj:`~spey.ExpectationType.aposteriori`: Computes the expected p-values with via
+                post-fit prescriotion which means that the experimental data will be assumed to be
+                the truth.
+              * :obj:`~spey.ExpectationType.apriori`: Computes the expected p-values with via pre-fit
+                prescription which means that the SM will be assumed to be the truth.
+            data (``np.array``, default ``None``): input data that to fit
+
+        Returns:
+            ``Callable[[np.ndarray], float]``:
+            Function that takes fit parameters (:math:`\mu` and :math:`\theta`) and computes
+            :math:`\log\mathcal{L}(\mu, \theta)`.
+        """
+        current_data = (
+            self.background_yields if expected == ExpectationType.apriori else self.data
+        )
+        data = current_data if data is None else data
+
+        return lambda pars: self.main_model.log_prob(pars, data)
+
+    def get_hessian_logpdf_func(
+        self,
+        expected: ExpectationType = ExpectationType.observed,
+        data: Optional[np.ndarray] = None,
+    ) -> Callable[[np.ndarray], float]:
+        r"""
+        Currently Hessian of :math:`\log\mathcal{L}(\mu, \theta)` is only used to compute
+        variance on :math:`\mu`. This method returns a callable function which takes fit
+        parameters (:math:`\mu` and :math:`\theta`) and returns Hessian.
+
+        Args:
+            expected (~spey.ExpectationType): Sets which values the fitting algorithm should focus and
+              p-values to be computed.
+
+              * :obj:`~spey.ExpectationType.observed`: Computes the p-values with via post-fit
+                prescriotion which means that the experimental data will be assumed to be the truth
+                (default).
+              * :obj:`~spey.ExpectationType.aposteriori`: Computes the expected p-values with via
+                post-fit prescriotion which means that the experimental data will be assumed to be
+                the truth.
+              * :obj:`~spey.ExpectationType.apriori`: Computes the expected p-values with via pre-fit
+                prescription which means that the SM will be assumed to be the truth.
+            data (``np.ndarray``, default ``None``): input data that to fit
+
+        Returns:
+            ``Callable[[np.ndarray], float]``:
+            Function that takes fit parameters (:math:`\mu` and :math:`\theta`) and
+            returns Hessian of :math:`\log\mathcal{L}(\mu, \theta)`.
+        """
+        current_data = (
+            self.background_yields if expected == ExpectationType.apriori else self.data
+        )
+        data = current_data if data is None else data
+
+        def log_prob(pars: np.ndarray) -> np.ndarray:
+            """Compute log-probability"""
+            return self.main_model.log_prob(pars, data)
+
+        return hessian(log_prob, argnum=0)
+
+    def get_sampler(self, pars: np.ndarray) -> Callable[[int], np.ndarray]:
+        r"""
+        Retreives the function to sample from.
+
+        Args:
+            pars (``np.ndarray``): fit parameters (:math:`\mu` and :math:`\theta`)
+            include_auxiliary (``bool``): wether or not to include auxiliary data
+              coming from the constraint model.
+
+        Returns:
+            ``Callable[[int, bool], np.ndarray]``:
+            Function that takes ``number_of_samples`` as input and draws as many samples
+            from the statistical model.
+        """
+
+        def sampler(sample_size: int, *args, **kwargs) -> np.ndarray:
+            """
+            Fucntion to generate samples.
+
+            Args:
+                sample_size (``int``): number of samples to be generated.
+
+            Returns:
+                ``np.ndarray``:
+                generated samples
+            """
+            return self.main_model.sample(pars, sample_size)
+
+        return sampler
+
+    def expected_data(self, pars: List[float], **kwargs) -> List[float]:
+        r"""
+        Compute the expected value of the statistical model
+
+        Args:
+            pars (``List[float]``): nuisance, :math:`\theta` and parameter of interest,
+
+        Returns:
+            ``List[float]``:
+            Expected data of the statistical model
+        """
+        return self.main_model.expected_data(pars)