Abstract: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach for different unions based on marginal ratings.

Abstract: Example methods, apparatus, and articles of manufacture are disclosed to estimate population reach. An example apparatus includes an association controller to generate a tree association corresponding to a union of a first margin of media and a second margin of the media; and one or more commercial solvers to determine first multipliers by solving first equations corresponding to panelist impressions and panelist audience totals, the second margin, or the union; perform first parallel computations with a processor to determine second multipliers to solve second equations corresponding to the tree association using the first multipliers; discard the first multipliers; perform second parallel computations to determine third multipliers by solving third equations corresponding to the tree association using database proprietor impression totals; and determine an estimate for a population reach of the media for at least one of the first margin, the second margin, or the union based on the third multipliers.

Abstract: Methods, apparatus, systems and articles of manufacture to perform identity matching across audience measurement systems are disclosed.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to improve reach calculation efficiency. An example method includes estimating, with a processor, a sample distribution of marketing data to generate a maximum entropy distribution, generating, with the processor, a geometric distribution based on estimating a minimum cross entropy of (a) the maximum entropy distribution and (b) the sample distribution of marketing data, and improving calculation efficiency of the public reach of the sample distribution of marketing data by generating, with the processor, conserved quantity expressions of the geometric distribution.

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 to correct for bias in ratings data are disclosed. Example methods disclosed herein include accessing information specifying a set of population strata having corresponding strata demographic statistics capable of being combined to determine a first set of baseline demographic statistics for a sample population that corresponds to a second set of baseline demographic statistics for a target population. Disclosed example methods also include determining a set of weights corresponding respectively to the set of population strata that reduces bias between the second set of baseline demographic statistics for the target population and the first set of baseline demographic statistics for the sample population when the set of weights is applied to the strata demographic statistics to determine the first set of baseline demographic statistics for the sample population.

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 a data organizer to determine, by executing an instruction with a processor, estimated aggregate panelist data based on attribute data corresponding to a seed panel and weight estimates used to replicate respective seed panelists in the seed panel; and a weight determiner to iteratively adjust, by executing an instruction with the processor, the weight estimates based on comparisons of the estimated aggregate panelist data as determined based on the adjusted weight estimates and input aggregate panelist data to generate final weight estimates; and replicate, by executing an instruction with the processor, respective ones of the seed panelists based on final weight estimates to generate a synthetic audience representative of return path data reported by a plurality of media devices.

Abstract: Methods and apparatus for determining a unique audience exposed to media while reducing memory resources of a computing device are disclosed herein. Example instructions cause a machine to at least, 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; obtain a count of demographic impressions logged by a database proprietor; obtain a count of registered users of the database proprietor exposed to the media; and execute a process to determine a unique audience size by multiplying a count of the plurality of impressions by a square of the count of the registered users to generate a product; dividing the product by the count of the demographic impressions to generate a quotient; and determining the unique audience size based on a square root of the quotient.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to rectify false set top box tuning data. Disclosed examples methods include identifying in return path data a first group of set top boxes classified as likely to exhibit machine events in tuning data of the return path data more frequently than a second group of set top boxes represented in the return path data. Additionally, in some examples, the method includes determining whether the first group of set top boxes includes a machine event based on a pattern of the tuning data in the return path data for respective ones of the first group of set top boxes and improving an accuracy of return path data by rectifying the machine event.

Abstract: Apparatus, systems, and articles of manufacture are disclosed to categorize audience members by age. An example apparatus includes memory including instructions, and a processor to execute the instructions to split audience member records from an initial node into child nodes based on comparisons of attribute-value pairs of the audience member records to a first value threshold, the attribute-value pairs representative of database subscriber activity data of audience members subscribed to a database proprietor, designate a first child node of the child nodes as a terminal node when a quantity of the audience member records of the first child node of the child nodes does not satisfy a minimum leaf size, generate an age-correction model based on the terminal node, and correct, based on the age-correction model, the age characteristic associated with the media impression, the media impression indicative of a person exposed to media presented by a media presentation device.

Abstract: Methods and apparatus to calculate granular data of a region based on another region for media audience measurement are disclosed. An example method for calculating, via a processor, granular data of a region includes determining aggregate behavioral data associated with a media audience measurement of a target region. The example method includes determining, via the processor, aggregate demographics data of the target region. The example method includes determining, via the processor, granular data of a source region. The example method includes calculating, via the processor, granular data of the target region to measure a media audience of the target region by apportioning the aggregate demographics data and the aggregate behavioral data of the target region based on the granular data of the source region.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. An example apparatus includes: a comparator to compare a target rating to a computed rating to determine a comparison result, the computed rating determined based on a seed panel, the seed panel including monitored panelists associated with return path data; a seed panelist data adjuster to adjust the seed panel based on the comparison result to reduce an error between the target rating and the computed rating; and a household data adjuster to add tuning without viewing data to households of the adjusted seed panel, the tuning without viewing data for a first one of the households to represent monitored data corresponding to a media presentation device of the first one of the households being on while a media output device in communication with the media presentation device is off.

Abstract: An example apparatus includes a misattribution matrix generator to generate a misattribution matrix based on panelist data corresponding to audience measurement panelists. The misattribution matrix representing a panelist media impression as misattributed to a first demographic group by a database proprietor when the panelist media impression corresponds to a second demographic group. The apparatus also includes a census distribution analyzer to determine, based on the misattribution matrix, probability values that different census distribution models correspond to a true census distribution for census media impressions indicated in a misattributed census distribution. The true census distribution indicating a distribution of the census media impressions across the first and second demographic groups and accounting for misattribution by the database proprietor in the misattributed census distribution.

Abstract: Methods and apparatus to assign demographic information to panelists are disclosed. An example disclosed method includes generating decoy database proprietor identifiers to protect privacies of members of panelist households corresponding to panelist database proprietor identifiers, the decoy database proprietor identifiers to be determined based on a probability density function so that a quantity of the decoy database proprietor identifiers is less than would be used if the decoy database proprietor identifiers were selected by a random selection process. The example method also includes querying a server at a database proprietor using the panelist database proprietor identifiers and the decoy database proprietor identifiers, to obtain demographic information and assigning, by executing an instruction with a processor, the panelist database proprietor identifiers to panelists in the panelist households based on the demographic information obtained from the server at the database proprietor.

Abstract: Example methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach for different unions based on marginal ratings. An example apparatus includes a reach determiner to estimate a population reach of a union of time intervals for which media ratings data is available; a pseudo universe determiner to determine a pseudo universe estimate of a recorded audience corresponding to the union; determine a pseudo universe estimate of a population audience corresponding to the union based on the pseudo universe estimate of the recorded audience; and determine an error of the population reach estimate of the union based on the pseudo universe of the population audience corresponding to the union; and the reach determiner to when the error does not satisfy a threshold, adjust the population reach estimate; and when the error does satisfy the threshold, determine the population reach of the union based on the population reach estimate.

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 to impute media consumption behavior are disclosed. An example apparatus includes a localized event engine implemented with hardware or at least one processor to, in response to a difference satisfying a first threshold, determine that a first subset of tuning data exhibits local bias, the difference to be between (i) a first percentage of exposure minutes determined from the tuning data, and (ii) a second percentage of exposure minutes determined from viewing data, determine that a second subset of the viewing data represents heavy viewing in response to (1) a first number of households satisfying a second threshold and (2) a third percentage of exposure minutes satisfying a third threshold, and a localized event selector implemented with hardware or the at least one processor to impute the second subset of the viewing data for the first subset of the tuning data.

Abstract: An electric axle drive utilizes an electric motor to propel both half-shafts via final drive gearing and a differential. Torque vectoring gearing alters the torque distribution by transmitting power from one of the half shafts to the motor or from the motor to the half-shaft in response to engagement of brakes. Both the final drive gearing and the torque vectoring gearing are implemented using stepped planetary gear sets. The final drive gearing and differential are located on one end of the electric motor. The torque vectoring gearing is located on the opposite end of the electric motor.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to determine a duration of media presentation based on tuning session duration. Example apparatus include a tuning session determiner to determine a first tuning session based on a period of time between channel changes of a first media presentation device; a presentation session determiner to determine first presentation session data within the determined first tuning session; a modeler to determine a model by relating the first tuning session with the first presentation session data; a receiver to determine a second tuning session for tuning data from a second media presentation device; and a presentation session estimator to: select the model for the second tuning session, based on a match of a first duration of the second tuning session and a second duration associated with the model, and estimate second presentation session data for the second tuning session based on the model.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to to estimate population reach from marginal ratings. An example apparatus includes an interface to access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience; a reach determiner to iteratively estimate a reach of the media for the population audience based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and the interface to output the estimated reach for the population audience.