Abstract: Methods, apparatus, systems, and articles of manufacture to identify inconsistencies in audience measurement data are disclosed. Example apparatus disclosed herein are to compare ones of a first set of cumulative audience metrics with one or more limits based on a second set of event-level audience metrics to detect an inconsistency in at least one of the first set of cumulative audience metrics or the second set of event-level audience metrics. Disclosed example apparatus are further to generate a report of the inconsistency in the at least one of the first set of event-level audience metrics or the second set of cumulative audience metrics.

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: Disclosed examples determine a unique audience exposed to media while reducing memory resources of a computing device. Example instructions program programmable circuitry to log a plurality of impressions corresponding to media accessed at client devices; generate a first value based on a count of the impressions and a count of users of a database proprietor that accessed the media; generate a second value based on the first value and a count of demographic impressions logged by the database proprietor; and determine a unique audience size based on the second value.

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 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 (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 and apparatus to estimate audience sizes using deduplication based on binomial sketch data are disclosed. An apparatus includes processor circuitry to instantiate coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in the first sketch data and second sketch data, (ii) a first cardinality of the first sketch data, and (iii) a second cardinality of the second sketch data. The processor circuitry to instantiate overlap analyzer circuitry to determine a real root of the polynomial, the real root corresponding to the quantity of the second subscribers that are duplicates of the first subscribers. The processor circuitry to instantiate report generator circuitry to estimate a deduplicated audience size based on the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and the first and second cardinalities.

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, apparatus, systems and articles of manufacture (e.g., physical storage media) to estimate and use nested merge ratios (e.g., nested Fréchet ratios) for audience measurement are disclosed herein. Example apparatus disclosed herein are to identify a first merged media event for which a first census audience value is to be determined, the first merged media event based on a union including a second merged media event. Disclosed example apparatus are also to determine whether the first merged media event satisfies a mutual exclusivity condition. Disclosed example apparatus are further to, in response to the first merged media event satisfying the mutual exclusivity condition, estimate the first census audience value for the first merged media event based on at least a merge ratio and a second census audience value previously estimated for the second merged media event.

Abstract: A computer-implemented method for efficiently estimating the number of unique elements in a collection of elements comprises generating, via hash logic, hash values associated with the elements. The hash values specify bit positions within an array of bits. Hash values output from the hash logic conform to a geometric distribution such that bit positions of the array of bits corresponding to lower orders bits are more likely to be generated than bit positions corresponding to higher-order bits. Bits of the array of bits corresponding to the bit positions are set. The number of bits of the array of bits that are set is counted. Estimation logic estimates the number of unique elements of the collection of elements as a function of the number of bits of the array of bits that are set.

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: A computer-implemented method for efficiently estimating the number of unique elements in a collection of elements comprises generating, via hash logic, hash values for each element of the collection of elements. The method further comprises specifying, in a sketch-frequency table, a set of discrete statistical values associated with the hash values and, for each discrete statistical value of the set of discrete statistical values, information indicative of a frequency at which binary representations of the hash values are associated with the discrete statistical value. The cardinality of the collection of elements is estimated based on the sketch-frequency table.

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: Methods and apparatus to estimate cardinality of users represented across multiple bloom filter arrays are disclosed. Examples includes processor circuitry to execute and/or instantiate instructions to generate a first composite Bloom filter array based on first and second Bloom filter arrays. The processor circuitry is to generate a final composite Bloom filter array based on the first composite Bloom filter array and a third Bloom filter array. Different ones of the first, second, and third Bloom filter arrays representative of different sets of users who accessed media. The first, second, and third Bloom filter arrays including differential privacy noise. The processor circuitry to estimate a cardinality of a union of the first, second, and third Bloom filter arrays based on the final composite Bloom filter array.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. Example apparatus disclosed herein include means for generating a synthetic panel corresponding to a duration of time, the means for generating the synthetic panel to: generate a transition matrix corresponding to a first sub-duration of the duration of time and a second sub-duration of the duration of time; generate, based on the transition matrix, a plurality of synthetic panelists and associated viewing data; remove first ones of the synthetic panelists associated with one or more weights that do not satisfy a threshold to generate the synthetic panel corresponding to the duration of time, the synthetic panel representative of audiences of media presented by a plurality of media devices during the duration of time; and generate synthetic respondent level data based on the viewing data associated with remaining second ones of the synthetic panelists.

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 and apparatus to estimate audience sizes using deduplication based on vector of counts sketch data are disclosed. A system includes hardware circuitry to instantiate: coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in a first vector of counts and a second vector of counts, (ii) a first cardinality of the first vector of counts, and (iii) a second cardinality of the second vector of counts; and overlap analyzer circuitry to: determine a real root of the polynomial; and report generator circuitry to estimate a deduplicated audience size based on (i) the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and (ii) the first and second cardinalities. The system includes communication circuitry to transmit a network communication to a third party entity, the second network communication including a report based on the deduplicated audience size.

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 estimate audience sizes using deduplication based on binomial sketch data are disclosed. An apparatus includes processor circuitry to instantiate coefficient analyzer circuitry to determine coefficient values of a polynomial based on (i) variances in values in the first sketch data and second sketch data, (ii) a first cardinality of the first sketch data, and (iii) a second cardinality of the second sketch data. The processor circuitry to instantiate overlap analyzer circuitry to determine a real root of the polynomial, the real root corresponding to the quantity of the second subscribers that are duplicates of the first subscribers. The processor circuitry to instantiate report generator circuitry to estimate a deduplicated audience size based on the estimate of the quantity of the second subscribers that are duplicates of the first subscribers and the first and second cardinalities.

Abstract: A computer-implemented method for efficiently estimating the number of unique elements in a collection of elements comprises generating, via hash logic, hash values associated with the elements. The hash values specify bit positions within an array of bits. Hash values output from the hash logic conform to a geometric distribution such that bit positions of the array of bits corresponding to lower orders bits are more likely to be generated than bit positions corresponding to higher-order bits. Bits of the array of bits corresponding to the bit positions are set. The number of bits of the array of bits that are set is counted. Estimation logic estimates the number of unique elements of the collection of elements as a function of the number of bits of the array of bits that are set.