Context-Aware Computing

3.4.2.3Probabilities of Correlated Context Events

Table 3.15 illustrates the influence of correlation between two basic context events on the probability Prob(e1 ∧ e2).

For conjunctions of literals with basic context events in the following inclusion-exclusion formula [50]:

$\begin{array}{l}Prob\left(E_1\vee E_2\vee \cdot \cdot \cdot \vee E_m\right)\\ ={\displaystyle \sum _{i=1}^{m}Prob\left(E_i\right)}-{\displaystyle \sum _{i<j}Prob\left(E_i\wedge E_j\wedge E_k\right)-}\\ {\displaystyle \sum _{i<j<r<s}Prob\left(E_i\wedge E_j\wedge E_r\wedge E_s\right)+\cdot \cdot \cdot +{\left(-1\right)}^{\left(m+1\right)}Prob\left(E_1\wedge E_2\wedge \cdot \cdot \cdot \wedge E_m\right)}\end{array}$

The above correlations can be taken into account by comparing each event with all other events in the same conjunction. Let e1 and e2 be two basic events, and let E be either a basic or complex event expression, the implications of correlation ...