Abstract: An example apparatus includes an association controller to generate a tree structure association for a total audience size that accessed a plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size, a matrix generator to generate a matrix by selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item and storing the sum of probabilities value in an element of the matrix, and a commercial solver to estimate a deduplicated audience size of the total audience size using the matrix.

Abstract: Methods and apparatus to calibrate media ratings based on return path data are disclosed. An apparatus includes a processor and memory including instructions that, when executed, cause the processor to: determine an initial rating for the media provided in a first geographic area based on return path data (RPD) tuning information obtained from RPD devices in subscriber households in the first geographic area; determine a first panelist rating for the media provided in a second geographic area based on first panel tuning information obtained from first metering devices in a first subset of panelist households in the second geographic area; determine a nonsubscriber calibration factor based on the first panelist rating; and determine a final rating for the media in the first geographic area by modifying the initial rating based on the nonsubscriber calibration factor.

Abstract: Methods, apparatus, and articles of manufacture are disclosed to estimate population reach from marginal ratings with missing information. An example apparatus includes a pseudo universe calculator to (i) determine a first pseudo universe estimate for a first audience of media corresponding to a first union of first margins, the first margins corresponding to known audience totals, and (ii) determine a second pseudo universe estimate for a second audience of the media corresponding to a second union of second margins, the determination based on an audience constant, the second margins including a margin corresponding to an unknown audience total. The example apparatus also includes a reach calculator to (i) determine an estimate of the unknown audience total of the second audience based on the second pseudo universe estimate for the second audience, and (ii) determine a reach estimate for the second union based on the first and second pseudo universe estimates.

Abstract: Methods, apparatus, and systems are disclosed for estimating panel attrition. An example apparatus includes at least one memory, machine readable instructions, and processor circuitry to execute the machine readable instructions to determine a beta distribution of a non-parametric survival curve estimate based on panel meter data associated with a cohort of panelists, determine confidence intervals for a set of beta distribution parameters associated with the survival curve estimate, and output a panelist attrition estimate generated based on the confidence intervals for the survival curve estimate, the panelist attrition estimate to represent panelist retention over time based on an installation date of the panel meter.

Abstract: A disclosed example includes at least one memory, programmable circuitry, and instructions to cause the programmable circuitry to increment a first value corresponding to a first position in a vector based on a first bit value representation, the first bit value representation corresponding to a first audience member identifier; increment a second value corresponding to a second position in the vector based on a second bit value representation, the second bit value representation corresponding to a second audience member identifier; estimate the second frequency moment of the media impression data using the vector; determine the variance of the second frequency moment; and based on the second frequency moment, schedule a query of the media impression data to be processed by a computer at a future time.

Abstract: Methods, apparatus, and systems are disclosed for audience-based deduplication using vector-of-counts (VOC) central moments. An example system to determine an audience size for media based on vector of counts sketch data, the system including memory, programmable circuitry, and instructions to cause the programmable circuitry to apply a hash function to first vector of counts sketch data, second vector of counts sketch data, and third vector of counts sketch data to remove personally identifiable information, determine a first covariance matrix associated with intersection cardinalities of at least two of the first, second, or third vector of counts, determine a second covariance matrix associated with disjoint cardinalities of the at least two of the first, second, or third vector of counts, and determine the audience size based on the first covariance matrix or the second covariance matrix.

Abstract: Example methods, apparatus, systems and articles of manufacture to implement under-addressable advertisement measurement are disclosed. Example apparatus disclosed herein determine a tuned under-addressable advertisement duration and a total tuned advertisement duration for a first television broadcast at a first monitored site, the tuned under-addressable advertisement duration and the total tuned advertisement duration determined based on (i) return-path tuning data associated with the first monitored site, (ii) linear advertisement log data associated with a broadcast area including the first monitored site, and (iii) addressable advertisement log data associated with the first monitored site.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to estimate an audience population. An example apparatus includes at least one memory; instructions in the apparatus; and processor circuitry to execute the instructions to: determine whether respective ones of respondents are associated with a characteristic; detect unique instances of the respective ones of the respondents; in response to the respective ones of the respondents being associated with the characteristic, increase a sample capture count by one; in response to detecting the unique instances of the respective ones of the respondents exhibiting the characteristic, increase a unique capture count by one; determine a seed population estimate based on the unique capture count; and determine a population estimate having the characteristic based on the sample capture count, the unique capture count, the seed population estimate, and a number of available samples.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to rectify false set top box tuning data. Disclosed examples methods include identifying, by executing an instruction with a processor, in the return path data, first tuning data corresponding to a first group of set top boxes, the first group of set top boxes classified as associated with machine events, determining, by executing an instruction with a processor, a ratio between first tuning events in the return path data and second tuning events in the return path data, the first tuning events attributed to the first group of the set top boxes, the second tuning events attributed to a second group of the set top boxes classified at not associated with machine events, and in response to the ratio satisfying a threshold during a time interval, removing second tuning data associated with the time interval from the first tuning data.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to estimate an audience population. An example apparatus includes processor circuitry; characteristic identifier instructions to be executed by the processor circuitry to determine whether respective ones of respondents are associated with a characteristic; recapture probability estimator instructions to be executed by the processor circuitry to select a recapture probability of the respective ones of respondents; and population estimator instructions to be executed by the processor circuitry to in response to the recapture probability satisfying a recapture threshold, determine a population estimate having the characteristics based on a first model; and in response to the recapture probability not satisfying the recapture threshold, determine the population estimate having the characteristics based on a second model, the second model different than the first model.

Abstract: Methods, apparatus, systems and articles of manufacture to impute media consumption behavior are disclosed. An example system includes one or more media meters to obtain tuning data, one or more people meters to obtain viewing data, and one or more servers to, in response to a determination that a difference satisfies a first threshold, determine that a first subset of the tuning data associated with first panelist households having tuned to first media in a first area exhibits local bias, determine that a second subset of the viewing data associated with second panelist households having viewed the first media in the second area represents heavy viewing, and impute the second subset of the viewing data for the first subset of the tuning data in response to the second subset of the viewing data representing heavy viewing.

Abstract: Methods, apparatus, systems and articles of manufacture to estimate and deduplicate audiences are disclosed herein. An example apparatus includes a controller to determine a subunion of at least first and second marginal audiences of media based on of panel data and census data, the panel data including a panel impression count and a panel audience size, and the census data including a census impression count, an audience size calculator to determine a census audience size of the at least the first and second marginal audiences based on the panel impression count and the panel audience size and determine a subunion census audience size, the subunion census audience size corresponding to an overlap between the at least the first and second marginal audiences; and a report generator to generate a report including the census audience size and the subunion census audience size.

Abstract: Example methods, apparatus, systems and articles of manufacture to implement an addressable measurement framework are disclosed. Example apparatus disclosed herein perform a common homes analysis of provider data and panel data to determine a coverage footprint associated with the provider data, the provider data including at least one of return path data reported by a plurality of set-top boxes or automatic content recognition data reported by a plurality of smart media devices, and the panel data reported by media device meters. Disclosed example apparatus also weight a portion of the provider data based on the common homes analysis, weight a portion of the panel data based on the common homes analysis, and calculate an addressable advertisement rating based on the weighted portion of the provider data and the weighted portion of the panel data.

Abstract: Methods, apparatus, systems and articles of manufacture to assign viewers to media meter data are disclosed. An apparatus includes processor circuitry to execute computer readable instructions to at least: identify a candidate household from a plurality of second households to associate with a first household based on an analysis of a first duration of time first media was presented by a first media presentation device and a second duration of time second media was presented by second media presentation devices; match different ones of first panelists of the first household with matching ones of second panelists of the candidate household; and impute respective portions of the first duration of time to the different ones of the first panelists based on portions of the second duration of time for which the matching ones of the second panelists of the candidate household were exposed to the second media.

Abstract: A disclosed example includes at least one memory, programmable circuitry, and instructions to cause the programmable circuitry to increment a first value corresponding to a first position in a vector based on a first bit value representation, the first bit value representation corresponding to a first audience member identifier; increment a second value corresponding to a second position in the vector based on a second bit value representation, the second bit value representation corresponding to a second audience member identifier; estimate the second frequency moment of the media impression data using the vector; determine the variance of the second frequency moment; and based on the second frequency moment, schedule a query of the media impression data to be processed by a computer at a future time.

Abstract: Methods and apparatus to estimate audience sizes using deduplication based on vector of counts sketch data are disclosed. An example apparatus to determine an audience size for media based on vector of counts sketch data includes: a coefficient analyzer to determine coefficient values of a polynomial based on variances, a covariance, and cardinalities corresponding to a first vector of counts from a first database and a second vector of counts from a second database; an overlap analyzer to determine a real root of the polynomial, the real root corresponding to an estimate of an overlap between the first vector of counts and the second vector of counts; and a report generator to estimate the audience size based on the estimate of the overlap and the cardinalities of the first vector of counts and the second vector of counts.

Abstract: Methods, apparatus, and articles of manufacture are disclosed to estimate population reach from marginal ratings with missing information. An example apparatus includes a pseudo universe calculator to (i) determine a first pseudo universe estimate for a first audience of media corresponding to a first union of first margins, the first margins corresponding to known audience totals, and (ii) determine a second pseudo universe estimate for a second audience of the media corresponding to a second union of second margins, the determination based on an audience constant, the second margins including a margin corresponding to an unknown audience total. The example apparatus also includes a reach calculator to (i) determine an estimate of the unknown audience total of the second audience based on the second pseudo universe estimate for the second audience, and (ii) determine a reach estimate for the second union based on the first and second pseudo universe estimates.

Abstract: Example methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to deduplicate common devices across multiple data sources are disclosed. An example apparatus includes instructions to identify a first device in a first data source and a second device in a second data source as a possible common device, calculate at least one of a station duration metric, a time match metric or a station path metric, the station duration metric, the time match metric based times of day that the first device tuned to a second set of stations and times of day that the second device tuned to the second set of stations, determine a score based on the at least one of the station duration metric, the time match metric, or the station path metric, and determine when the first device and the second device are a common device based on the score.

Abstract: Methods and apparatus to estimate cardinality across multiple datasets represented using Bloom filter arrays are disclosed. Disclosed examples include processor circuitry to execute and/or instantiate instructions to determine an inclusion-exclusion expression that defines an audience size for a user group of interest. Terms in the inclusion-exclusion expression corresponding to either a first cardinality of a first one of at least three Bloom filter arrays or a second cardinality of a union of two or more of the Bloom filter arrays. Different ones of the Bloom filter arrays representative of different sets of users who accessed media. The at least one processor further to estimate, based on the inclusion-exclusion expression, the audience size of the user group of interest.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to estimate an audience population.