Probability

class Probability(outcome, alpha_prior=0.5, validate=True)

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 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 counts.

The mean and variance of the Beta distribution $B({\alpha }_0,{\alpha }_1)$ are:

$$\text{E}[p]=\frac{{\alpha }_0}{{\alpha }_0+{\alpha }_1},\text{Var}[p]=\frac{\text{E}[p](1-\text{E}[p])}{{\alpha }_0+{\alpha }_1+1}$$

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 $B({\alpha }_0^{\prime },{\alpha }_1^{\prime }):math:$ with

$${\alpha }_0^{\prime }={\alpha }_0+F,{\alpha }_1^{\prime }={\alpha }_1+N-F.$$

Note

The default value for the prior distribution is Jeffery’s Prior ${\alpha }_0={\alpha }_1=0.5$ 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

$$\text{E}[p]=\frac{F+0.5}{N+1},\text{Var}[p]=\frac{\text{E}[p](1-\text{E}[p])}{N+2}$$

This node will deprecate standard error provided by the previous node.

Initialize a counts to probability data conversion.

Parameters:

• outcome (str) – The bitstring for which to return the probability and variance.

• alpha_prior (float | Sequence[float]) – A prior Beta distribution parameter [alpha0, alpha1]. If specified as float this will use the same value for alpha0 and alpha1 (Default: 0.5).

• validate (bool) – If set to False the DataAction will not validate its input.

Raises:

DataProcessorError – When the dimension of the prior and expected parameter vector do not match.

Methods

__call__(data)

Call the data action of this node on the data.

Parameters:

data (ndarray) – A numpy array with arbitrary dtype. If the elements are ufloat objects consisting of a nominal value and a standard error, then the error propagation is done automatically.

Returns:

The processed data.

Return type:

ndarray