Probability Indicators: From Local Events to Global Decisions

A system asks precise local yes-or-no questions, records zero-one indicators, and combines them into a count, estimate, or action.

A sample space contains possible outcomes; an event selects outcomes of interest; the indicator reports whether the observed outcome belongs to that event.

No. After observation an indicator is exactly zero or one; before observation, probability describes uncertainty about which value it will take.

A useful event names the object, the condition, and the relevant context, such as which signal, which lane, and which time.

A self-driving system assembles several local detections into an evidence state; the decision rule, not any single indicator, determines the action.

The target quantity determines whether the natural unit is a frame, person, detection box, position, pair, or another contribution unit.

A short recommendation row exposes the same indicator architecture as a complex road scene with fewer objects and clearer counting units.

The number of documentaries in a row can be reconstructed by indexing positions or by indexing candidate titles, provided each shown documentary contributes exactly once.

A decomposition is valid when nothing is missed, nothing is duplicated, and every one has the intended meaning.

Indicators may be indexed by objects, positions, categories, times, transitions, pairs, or tuples; the smallest meaningful contribution unit is usually best.

Yes. A frame indicator counts appearances, so one pedestrian visible in 18 frames contributes 18; an identity indicator counts that pedestrian once.

The same video may count positive frames, distinct pedestrians, or pedestrian-vehicle conflicts, requiring time, object, or pair indexes respectively.

To count unsafe vehicle pairs, define one indicator per unordered pair and sum over i less than j; object indicators cannot represent a relationship faithfully.

Symmetric relations use unordered pairs and count each physical pair once; directional relations use ordered pairs because reversing the order changes the event.

For a nonnegative integer count N, the threshold indicator T_k records whether N is at least k, and N equals the sum of all crossed-level indicators.

If X is a sum of indicators, linearity gives E[X] as the sum of their event probabilities; independence is not required for this mean identity.

Covariance compares their joint probability with the product of their individual probabilities, revealing positive, negative, or near-zero association.

The variance of an indicator sum contains local variances plus pairwise covariance terms, so dependence can change uncertainty without changing the mean.

Ask what contributes exactly one unit to the target, then select an object, position, pair, group, time, or threshold indicator that matches that meaning.

Start with reality and a target, choose the natural contribution unit and index set, define a precise event, test exactly-once accounting, reconstruct the target, then analyze and decide.