Abstract: Methods and apparatus to estimate census-level audience sizes and duration data across dimensions and/or demographics are disclosed. An example apparatus includes constraint equation control circuitry to select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members, constraint parameter estimation circuitry to solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events, and output generation circuitry to determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.

Abstract: Methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to estimate and use nested merge ratios (e.g., nested Fréchet ratios) for audience measurement are disclosed herein. Example apparatus disclosed herein are to identify a first merged media event for which a first census audience value is to be determined, the first merged media event based on a union including a second merged media event. Disclosed example apparatus are also to determine whether the first merged media event satisfies a mutual exclusivity condition. Disclosed example apparatus are further to, in response to the first merged media event satisfying the mutual exclusivity condition, estimate the first census audience value for the first merged media event based on at least a merge ratio and a second census audience value previously estimated for the second merged media event.

Abstract: A disclosed example includes determining a plurality of cross-demographic total census parameter values based on ratios of third-party impression counts and third-party audience sizes, selecting a first cross-demographic total census parameter value as an upper bound constraint from the plurality of cross-demographic total census parameter values based on comparisons between ones of the plurality of cross-demographic total census parameter values, selecting a second cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values based on the second cross-demographic total census parameter value being less than the upper bound constraint, determining a first census-level audience size based on the second cross-demographic total census parameter value, and determining a first census-level impression count based on the second cross-demographic total census parameter value.

Abstract: An example apparatus to determine census-based audience metrics of media across multiple demographics includes an audience size determiner to determine a first census-level audience size based on a third-party audience size, a third-party impression count, and a first cross-demographic total census parameter value; an impression counts determiner to determine a first census-level impression count based on the third-party audience size, the third-party impression count, and the first cross demographic total census parameter value; and a verifier to determine whether the first cross-demographic total census parameter value satisfies a constraint based on the first census-level impression count; and when the constraint is not satisfied the verifier to: (a) discard the first cross-demographic total census parameter value, and (b) select a second cross-demographic total census parameter value, the second cross-demographic total census parameter value to determine a second census-level audience size and a second ce

Abstract: Methods, apparatus, and systems are disclosed for determining census-level audience metrics across demographics.

Abstract: Methods, apparatus, and systems are disclosed for determining census-level audience metrics across demographics. An example apparatus disclosed herein includes a distribution parameter solver to initialize distribution parameter values for a probability of an individual within a demographic being included in a subscriber audience for the demographic and having a first average impression duration, the subscriber audience having a first subscriber audience size, a divergence parameter solver to determine divergence parameter values between (i) the subscriber audience size and the first impression duration and (ii) a census-level audience size and a second impression duration based on the initialized distribution parameter values, and a search space identifier to identify a search space within bounds based on a census-level total impression count and a census-level total impression duration, the search space to define a range including an equality constraint.

Abstract: Methods, apparatus, systems and articles of manufacture to de-duplicate partially-tagged entities are disclosed. An example method includes identifying a tagged audience for a first sub-entity, identifying a panel audience for the second sub-entity, determining a panel duplication between the first sub-entity and a second sub-entity, determining a duplicated audience based on the tagged audience, the panel audience, and the panel duplication, and determining a de-duplicated audience for the partially-tagged entity based on the duplicated audience and a total audience, the total audience including the tagged audience for the first sub-entity and the panel audience for the second sub-entity.

Abstract: An example apparatus to determine census-based audience metrics of media across multiple demographics includes an audience size determiner to determine a first census-level audience size based on a third-party audience size, a third-party impression count, and a first cross-demographic total census parameter value; an impression counts determiner to determine a first census-level impression count based on the third-party audience size, the third-party impression count, and the first cross demographic total census parameter value; and a verifier to determine whether the first cross-demographic total census parameter value satisfies a constraint based on the first census-level impression count; and when the constraint is not satisfied the verifier to: (a) discard the first cross-demographic total census parameter value, and (b) select a second cross-demographic total census parameter value, the second cross-demographic total census parameter value to determine a second census-level audience size and a second ce

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to store first impression counts of first media impressions corresponding to panelists in a population that accessed media via one or more of a plurality of media access platforms; and store marginal impression counts for second media impressions corresponding to audience members in the population that accessed the media via the plurality of media access platforms, ones of the marginal impression counts indicative of a total number of impressions of the media accessed via corresponding ones of the plurality of media access platforms; calculate multipliers relating a first probability distribution of the first media impressions to a second probability distribution of the second media impressions, the multipliers calculated based on constraints defined by the marginal impression counts for the second media impressions; and calculate second impression counts of the second media impressions based on the multipliers.

Abstract: Methods, apparatus, systems and articles of manufacture to de-duplicate partially-tagged entities are disclosed. An example method includes identifying a tagged audience for a first sub-entity, identifying a panel audience for the second sub-entity, determining a panel duplication between the first sub-entity and a second sub-entity, determining a duplicated audience based on the tagged audience, the panel audience, and the panel duplication, and determining a de-duplicated audience for the partially-tagged entity based on the duplicated audience and a total audience, the total audience including the tagged audience for the first sub-entity and the panel audience for the second sub-entity.