Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to determine a duration of media presentation based on tuning session duration. Example apparatus a receiver to obtain a first tuning session duration indicative of an amount of time between channel changes of a first media presentation device at a first media presentation location, a presentation session estimator to select a model from storage, the model selected based on a match of the first tuning session duration and a second tuning session duration, the model including a relation between the second tuning session duration and a first presentation session duration of media presented on a second media presentation device at a second media presentation location, and estimate a second presentation session duration of media presented within the first tuning session duration based on the model.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to determine a duration of media presentation based on tuning session duration. Example apparatus a receiver to obtain a first tuning session duration indicative of an amount of time between channel changes of a first media presentation device at a first media presentation location, a presentation session estimator to select a model from storage, the model selected based on a match of the first tuning session duration and a second tuning session duration, the model including a relation between the second tuning session duration and a first presentation session duration of media presented on a second media presentation device at a second media presentation location, and estimate a second presentation session duration of media presented within the first tuning session duration based on the model.

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 for determining a unique audience exposed to media while reducing memory resources of a computing device are disclosed herein. An example apparatus includes memory; instructions in the apparatus; and processor circuitry to execute the instruction to, based on impression requests from a plurality of client devices via a network, log a plurality of impressions corresponding to media accessed at the client devices; generate a product by multiplying a count of the impressions by a square of a count of registered users of a database proprietor exposed to the media; generate a quotient by dividing the product by a count of demographic impressions logged by the database proprietor; and determine a unique audience size based on a square root of the quotient.

Abstract: Methods and apparatus to model on/off states of media presentation devices based on return path data are disclosed. An apparatus includes a memory and processor circuitry to execute instructions stored in the memory to: generate a first probability distribution indicative of actual durations of panel tuning segments, the panel tuning segments corresponding to time periods during which panelists were exposed to first media; generate a second probability distribution indicative of modelled durations of modelled tuning segments, the modelled tuning segments corresponding to modified lengths of the panel tuning segments; and estimate a set-on time for a media set associated with an RPD device based on RPD tuning information and the first and second probability distributions, the RPD tuning information reported from the RPD device, the RPD tuning information indicative of a reported RPD tuning segment during which the RPD device was accessing second media.

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 population reach from marginal ratings. An example apparatus includes means for iteratively converging on an output estimate of a reach of media for a total population audience and means for outputting the estimate of the reach for the total population audience.

Abstract: Methods and apparatus to correct for deterioration of a demographic model to associate demographic information with media impression information are disclosed. An example method includes estimating first and second ages of audience members based on demographic information; estimating a third age of an audience member who is not included in the audience members; applying a window function to the second ages to determine a distribution of ages based on the third age; multiplying window values by the first ages to determine corrected first age components; dividing a total of the corrected first age components by a sum of the window values to determine an estimated age of the audience member at a first time; and determining the corrected age of the audience member at a second time based on the estimated age of the audience member at the first time and a time difference between the first and second times.

Abstract: Methods and apparatus to adjust media impressions based on media impression notification loss rates in network communications are disclosed.

Abstract: Example methods and apparatus to replicate panelists using a local minimum solution of an integer least squares problem are disclosed. An example apparatus includes memory; and processor circuitry to execute computer readable instructions to: determine weight adjustments based on a ratio of (A) a first dot product of (i) attribute data and (ii) a difference between first aggregate panelist data and second seed panelist data, and (B) a second dot product of the attribute data and the attribute data, the first aggregate panelist data based on the attribute data, the attribute data corresponding to a seed panel; determine weight estimates based on the weight adjustments, the weight estimates to replicate respective seed panelists in the seed panel; and replicate respective ones of the seed panelists based on the weight estimates to generate a synthetic audience representative of return path data reported by a plurality of media devices.

Abstract: Methods and apparatus to partition data are disclosed. An example apparatus to partition panelist data includes an indicator matrix generator to determine an indicator matrix including panelist vectors for panelists based on panelist data associated with the panelists, a first one of the panelist vectors for a first one of the panelists to indicate whether the first one of the panelists: has a first characteristic, meets a first criterion based on the first characteristic and a second characteristic, has a third characteristic, and meets a second criterion based on the third characteristic and a fourth characteristic. The example apparatus further includes a matrix reducer to reduce the indicator matrix to a set of unique panelist vectors that represent partitions of the panelist data, the partitions of the panelist data to utilize less storage capacity than the panelist data.

Abstract: Processor systems to estimate audience sizes and impression counts for different frequency intervals are disclosed. An example processor system includes a memory management unit (MMU) to assign requests from computing devices indicative of accesses to media to a first block of memory and to assign user-identified impression data corresponding to user-identified impressions to a second block of memory. The processor system including an arithmetic logic unit (ALU) to determine multipliers relating a first probability distribution for the user-identified impressions to a second probability distribution for census impressions. The multipliers based on probability constraints defined by weighted probabilities associated with the second probability distribution, where different ones of the probabilities weighted based on estimated populations for corresponding ones of the different demographics.

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: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach for different unions based on marginal ratings. An example method includes performing first parallel computations to determine first multipliers corresponding to a total number of panelists exposed to media at (a) a first margin of time, (b) a second margin of time, and (c) a union corresponding to the first and second margins of time, keeping a subset of the first multipliers corresponding to unknown census data; performing second parallel computation to determine second multipliers corresponding to a total audience exposed to the media at the first margin of time and the second margin of time, the second parallel computations to be performed by solving second equations corresponding to a tree association; and determining an estimate for a population reach of the union based on the second multipliers.

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, systems and articles of manufacture are disclosed that estimate the second frequency moment. An example apparatus includes a hashing generator to input a first audience member identifier and a second audience member identifier of the media impression data through a hashing function, an output of the hashing generator being a first bit-value representation of the first audience member identifier and a second bit-value representation of the second audience member identifier, a vector generator to increment first and second values of corresponding first and second positions in a vector based on the first and second bit-value representations, respectively, a second frequency moment generator to estimate the second frequency moment of the media impression data using the vector, and a comparator to, using the second frequency moment, determine whether a computer can complete a query request of the media impression data based on query processing constraints.

Abstract: Example methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to assign respondents to geographic locations for audience measurement are disclosed. Example apparatus disclosed herein are to determine a set of constraints based on aggregate values of demographic features associated with respective ones of the geographic locations. Disclosed example apparatus are also to construct a model to return probabilities that respective ones the respondents are associated with the respective ones of the geographic locations, the model to have a set of parameters, respective ones of the parameters to be associated with respective ones of the constraints. Disclosed example apparatus are further to evaluate the model based on values of the set of parameters and values of the demographic features for a first one of the respondents to determine a set of probabilities that the first respondent is to be assigned to respective ones of the geographic locations.

Abstract: Example methods and apparatus disclosed herein include campaign mapping for total audience measurement. An example apparatus includes processor circuitry to train a machine learning model to determine first and second estimated duplication factors for respective first and second reference media campaigns; and determine, using the machine learning model, third estimated duplication factors for a query media campaign based on total exposure metrics associated with individual ones of media platforms for the query media campaign. The processor circuitry to select one of the first and second reference media campaigns based on a comparison of the third estimated duplication factors with each of the first and second estimated duplication factors; and determine fourth estimated duplication factors for the query media campaign based on (a) the respective first or second estimated duplication factors associated with the selected one of the first and second reference media campaigns and (b) the total exposure metrics.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. Example apparatus disclosed herein are to identify locations corresponding to monitored panelists, and when a first one of the identified locations corresponds to two or more affiliates, sum tuning minutes of the two or more affiliates. Disclosed example apparatus are also to generate an affiliate probability based on the sum, and convert first data of households in the first one of the locations to a candidate receivability session based on the affiliate probability. Disclosed apparatus are further to generate a seed panel, the seed panel to include at least one of the monitored panelists selected based on a population associated with return path data, and donate second data associated with a donor pool of first panelists to second panelists included in the seed panel, the second panelists associated with faulty media monitoring equipment.