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: 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: 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.

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 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.

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 and apparatus to estimate audience sizes using deduplication based on binomial sketch data are disclosed. An apparatus to estimate an audience size for media based on binomial sketch data includes a coefficient analyzer to determine coefficient values of a polynomial based on variances, a covariance, and cardinalities corresponding to first binomial sketch data from a first database and second binomial sketch data from a second database. The apparatus also includes an overlap analyzer to determine a real root of the polynomial. The real root corresponds to an estimate of an overlap between the first binomial sketch data and the second binomial sketch data. The apparatus further includes a report generator to estimate the audience size based on the estimate of the overlap and the cardinalities of the first and second binomial sketch 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: A heating device includes a flexible housing that defines a plurality of heater segments. Each heater segment includes a first compartment containing a first reactant, a second compartment containing a second reactant, and a frangible seal between the first compartment and the second compartment. The first reactant and the second reactant are configured to react exothermically upon contact with one another.

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: An example apparatus includes at least one memory, instructions in the apparatus, and processor circuitry to execute the instructions to generate a reference demographic impression distribution based on first impressions of logged impressions at a first server corresponding to first client devices, access an inaccurate demographic impression distribution based on second impressions corresponding to second client devices, determine an estimated demographic impression distribution based on an inaccurate demographic impression distribution, the estimated demographic impression distribution representative of the second impressions distributed across the different demographic segments, determine a matrix based on a reference demographic impression distribution and Lagrange multiplier values, determine an error indicator value based on the matrix, generate, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution, and store, in the at least one memory

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, 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, systems to determine a conditional probability based on audience member probability distributions for media audience measurement are disclosed. Disclosed example methods for media audience measurement include determining a first audience probability distribution for a first member of a household and determining a second audience probability distribution for a second member of the household. Disclosed example methods also include calculating probabilities for audience combinations of the first member and the second member of the household based on the first audience probability distribution and the second audience probability distribution. Disclosed example methods further include determining a household audience characteristic probability based on the calculated probabilities of the audience combinations of the household. The household audience characteristic indicates likelihoods of different possible audience compositions of the household for a media event.

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 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; a pseudo universe determiner to 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 iteratively update the pseudo universe estimate of the population audience to reduce an error; and a consistency checker to adjust the population reach estimate, the reach determiner to output the population reach estimate of the union.

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 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 population reach from marginals. Example apparatus disclosed herein are to determine an audience relationship value based on first audience exposure values for a recorded audience of a media and a first de-duplicated audience value for the recorded audience of the media, determine bounds of a pseudo universe estimate of a population audience of the media based on the audience relationship value and second audience exposure values for the population audience of the media, and iteratively determine the pseudo universe estimate of the population audience and a second de-duplicated audience value for the population audience of the media based on the audience relationship value and the second audience exposure values, the pseudo universe estimate of the population audience to be within the bounds.

Abstract: An example apparatus includes a matrix processor in circuit with a probability generator to determine a first matrix representative of element-wise multiplication between a constraint matrix and a first transpose matrix of the estimated demographic impression distribution, the constraint matrix based on the reference demographic impression distribution and determine a second matrix by multiplying the first matrix with a second transpose matrix of the constraint matrix. The apparatus further includes an error determiner in circuit with the matrix processor, the error determiner to determine an error indicator value based on the second matrix, the error indicator value indicative of an error associated with the estimated demographic impression distribution, and a probability generator to generate, in response to the error indicator value satisfying a threshold, an accuracy-improved demographic impression distribution.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to monitor media presentation to determine a period of media presentation based on tuning session period are disclosed. Example methods disclosed herein include determining a first tuning session based on a period of time between channel changes of a first media presentation device, determining first presentation session data within the determined first tuning session, determining a model relating the first tuning session with the first presentation session data, determine a second tuning session for tuning data from a second media presentation device, selecting 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 estimating second presentation session data for the second tuning session based on the model.