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Documentation patch for PR424 #458

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Merged
chriseclectic merged 2 commits into from
Oct 25, 2021
Merged

Documentation patch for PR424 #458

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Update nodes.py
Oct 25, 2021
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Oct 25, 2021
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17 changes: 9 additions & 8 deletions qiskit_experiments/data_processing/nodes.py
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Expand Up @@ -395,22 +395,23 @@ class Probability(DataAction):
r"""Compute the mean probability of a single measurement outcome from counts.

This node returns the mean and standard deviation of a single measurement
outcome probability $p$ estimated from the observed counts. The mean and
outcome probability :math:`p` estimated from the observed counts. The mean and
variance are computed from the posterior Beta distribution
$B(\alpha_0^\prime,\alpha_1^\prime)$ estimated from a Bayesian update
of a prior Beta distribution $B(\alpha_0, \alpha_1)$ given the observed
:math:`B(\alpha_0^\prime,\alpha_1^\prime)` estimated from a Bayesian update
of a prior Beta distribution :math:`B(\alpha_0, \alpha_1)` given the observed
counts.

The mean and variance of the Beta distribution $B(\alpha_0, \alpha_1)$ are:
The mean and variance of the Beta distribution :math:`B(\alpha_0, \alpha_1)` are:

.. math::

\text{E}[p] = \frac{\alpha_0}{\alpha_0 + \alpha_1}, \quad
\text{Var}[p] = \frac{\text{E}[p] (1 - \text{E}[p])}{\alpha_0 + \alpha_1 + 1}

Given a prior Beta distribution $B(\alpha_0, \alpha_1)$, the posterior
distribution for the observation of $F$ counts of a given
outcome out of $N$ total shots is a $B(\alpha_0^\prime,\alpha_1^\prime)$ with
Given a prior Beta distribution :math:`B(\alpha_0, \alpha_1)`, the posterior
distribution for the observation of :math:`F` counts of a given
outcome out of :math:`N` total shots is a
:math:`B(\alpha_0^\prime,\alpha_1^\prime):math:` with

.. math::
\alpha_0^\prime = \alpha_0 + F, \quad
Expand All @@ -419,7 +420,7 @@ class Probability(DataAction):
.. note::

The default value for the prior distribution is *Jeffery's Prior*
$\alpha_0 = \alpha_1 = 0.5$ which represents ignorance about the true
:math:`\alpha_0 = \alpha_1 = 0.5` which represents ignorance about the true
probability value. Note that for this prior the mean probability estimate
from a finite number of counts can never be exactly 0 or 1. The estimated
mean and variance are given by
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