Independence, following Shimony) $$\begin{aligned}
Pr_{a,b}(A|\lambda ) &=&Pr_{a}(A|\lambda )  \TCItag{6a}  \label{6a} \\
Pr_{a,b}(B|\lambda ) &=&Pr_{b}(B|\lambda )  \TCItag{6b}  \label{6b}\end{aligned}$$

Statistical sufficiency is a condition employed by statisticians in situations where considerations of locality and causality simply don’t arise. But in this application the failure of quantum theory to provide a specification of beables in region 3 such that the outcome $B$ is always redundant for determining the probability of outcome $A$ (and similarly with ‘$A$’, ‘$B$’ interchanged) has clear connections to local causality, as Seevinck and Uffink’s \[2011\] analysis has shown.

In the light of Seevinck and Uffink’s \[2011\] analysis, perhaps Bell’s local causality condition (LC) should be reformulated as follows:

> (LC$_{SU}$)A theory is said to be locally causal$_{SU}$ if it acknowledges a class $R_{\lambda }$ of beables $\lambda $ in space-time region 3 whose values may be attached independently of the choice of $a$,$b$ and are then sufficient to render $b$ functionally redundant and $B$ statistically redundant for the task of specifying the probability of $A$ in region 1.

The notions of statistical and functional redundancy appealed to here are as follows:

> For $\lambda \varepsilon R_{\lambda },$ $\lambda $ renders $B$ statistically redundant for the task ofspecifying the probability 