Abstract: Methods and apparatus to determine reach with time dependent weights are disclosed. An example method disclosed herein includes determining a first subset of panelists exposed to media at a first time; determining a second subset of the panelists exposed to the media at a second time; applying a first plurality of weights to the first subset of panelists to generate first weighted exposures; applying a second plurality of weights to the second subset of the panelists to generate second weighted exposures; for a first panelist in the first and second subsets, determining a first cumulative weighted exposure by determining which of the first and second weighted exposures is largest for each of the first panelist; for a second panelist in one of the first and second subsets, determining a second cumulative weighted exposure by based on the weight applied to the second panelist; and determining a reach of the media for the first and second times by combining the first and second cumulative weighted exposures.

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: 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: 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 memory and processor circuitry to determine a population reach estimate of a union of time intervals for which media ratings data is available, the population reach estimate based on a pseudo universe estimate of a population audience corresponding to the union of the time intervals; determine a pseudo universe estimate of a recorded audience corresponding to the union of the time intervals; determine the pseudo universe estimate of the population audience based on the pseudo universe estimate of the recorded audience; and in response to a decision to update the pseudo universe estimate of the population audience to reduce an error of the population reach estimate output the population reach estimate of the union when the error of the population reach estimate satisfies a threshold.

Abstract: Methods, systems and apparatus to improve the efficiency of calculating a customer retention rate are disclosed herein.

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: 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, 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: 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 memory and processor circuitry to determine a population reach estimate of a union of time intervals for which media ratings data is available, the population reach estimate based on a pseudo universe estimate of a population audience corresponding to the union of the time intervals; determine a pseudo universe estimate of a recorded audience corresponding to the union of the time intervals; determine the pseudo universe estimate of the population audience based on the pseudo universe estimate of the recorded audience; and in response to a decision to update the pseudo universe estimate of the population audience to reduce an error of the population reach estimate output the population reach estimate of the union when the error of the population reach estimate satisfies a threshold.

Abstract: Example methods, apparatus, and articles of manufacture are disclosed to estimate population reach. An example apparatus includes processor circuitry to determine first multipliers corresponding to a panelist impression count and panelist audience size totals of at least one of a first margin of media, a second margin of the media, or a union of the first margin and the second margin, the first margin, the second margin, and the union included in a tree association; concurrently determine second multipliers using the tree association and the first multipliers; determine third multipliers corresponding to a total audience size exposed to the media at at least one of the first margin, the second margin, or the union based on the tree association using database proprietor impression totals; and determine, based on the third multipliers, an estimate for the population reach of the media for at least one of the first margin, the second margin, or the union.

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 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: 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, apparatus, systems, and articles of manufacture are disclosed to estimate population reach from marginals. An example apparatus includes memory including computer readable instructions; and a processor to execute the instructions to: iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media; determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.

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

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, systems, apparatus, and articles of manufacture to determine causal effects are disclosed herein. An example apparatus includes a weighting engine to calculate a first set of weights corresponding to a first treatment dataset, a second set of weights corresponding to a second treatment dataset, and a third set of weights corresponding to a control dataset, the weighting engine to increase an operational efficiency of the apparatus by calculating the first set of weights, second set of weights, and third set of weights independently, a weighting response engine to calculate a first weighted response for the first treatment dataset, a second weighted response for the second treatment dataset, and determine a causal effect between the first treatment dataset and the second treatment dataset based on a difference between the first weighted response and the second weighted response, and a report generator to transmit a report to an audience measurement entity.

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: 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, systems, apparatus and articles of manufacture to determine causal effects are disclosed herein. An example apparatus includes a weighting engine to calculate a first set of weights corresponding to a first treatment dataset, a second set of weights corresponding to a second treatment dataset, and a third set of weights corresponding to a control dataset, the weighting engine to increase an operational efficiency of the apparatus by calculating the first set of weights, second set of weights, and third set of weights independently, a weighting response engine to calculate a first weighted response for the first treatment dataset, a second weighted response for the second treatment dataset, and determine a causal effect between the first treatment dataset and the second treatment dataset based on a difference between the first weighted response and the second weighted response, and a report generator to transmit a report to an audience measurement entity.