Abstract: Example technical solutions to determine census-level audience metrics across demographics are disclosed. Disclosed example apparatus include a distribution parameter solver to initialize distribution parameter values for a probability of an individual within a demographic being (i) included in a subscriber audience for the demographic and (ii) having a first impression duration, the subscriber audience having a first subscriber audience size. Disclosed example apparatus also include a divergence parameter solver to determine divergence parameter values between (i) the first subscriber audience size and the first impression duration and (ii) a census-level audience size and a second impression duration based on the initialized distribution parameter values.

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: Methods, apparatus, systems and articles of manufacture to estimate and deduplicate audiences are disclosed herein. An example apparatus includes a controller to determine a subunion of at least first and second marginal audiences of media based on of panel data and census data, the panel data including a panel impression count and a panel audience size, and the census data including a census impression count, an audience size calculator to determine a census audience size of the at least the first and second marginal audiences based on the panel impression count and the panel audience size and determine a subunion census audience size, the subunion census audience size corresponding to an overlap between the at least the first and second marginal audiences; and a report generator to generate a report including the census audience size and the subunion census audience size.

Abstract: An example apparatus includes audience metrics collecting circuitry to access first audience metrics from a server, and access second audience metrics from the server, matrix building circuitry to build a matrix of the first audience metrics and the second audience metrics, missing values of the matrix corresponding to the second audience metrics, data transforming circuitry to transform the first audience metrics and the second audience metrics in the matrix, missing value calculating circuitry to determine imputed transformed values of the missing values using a recommender system, and the data transforming circuitry to recover imputed values of the missing values based on the imputed transformed values.

Abstract: Methods, apparatus, systems and articles of manufacture (e.g., physical storage media) to estimate and use duplication factors for audience measurement are disclosed. Example apparatus disclosed herein are to access first marginal ratings values that represent respective portions of a first population associated with corresponding ones of a plurality of media segments, estimate the duplication factor based on a difference between a sum of the first marginal ratings values and a largest one of the first marginal ratings values, access second marginal ratings values that represent respective portions of a second population associated with corresponding ones of the media segments, and output, based on the duplication factor and the second marginal ratings values, a reach value for a union of the media segments, the reach value to represent a number of unique individuals of the second population associated with at least one of the media segments.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed for audience measurement analysis including at least one memory, instructions, and processor circuitry to execute the instructions to scale at least one of subscriber duration values or total census-level duration values to generate a scaled duration value that corresponds to an impression count of at least a threshold amount of duration time, determine cross-demographic total census parameter values based on the scaled duration value, determine a search space of possible cross-demographic total census parameter values, the search space to include the determined cross-demographic total census parameter values, determine census-level metrics based on the determined cross-demographic total census parameter values, the census-level metrics including demographic census-level audience size data and demographic census duration values, output a report of the census-level metrics.

Abstract: Methods and apparatus to estimate census level audience sizes, impression counts, and duration data are disclosed. Example instructions cause one or more processor to at least set up a system of equations based on first census data; select a census parameter value based on a constraint for census parameter selection, the constraint based on media access represented in panel data; iteratively solve for second census data that satisfies the system of equations using the panel data and the census parameter value, the second census data including an audience size value, an impression count value, and a duration value for a media item accessed by anonymous audience members in a demographic group; and generate a report including the second census data.

Abstract: An example apparatus includes an audience size calculator circuitry to determine a first census-level audience size, and an impression count calculator circuitry to determine a first census-level impression count.

Abstract: Methods and apparatus to determine census information of events.

Abstract: Methods, apparatus, systems, and articles of manufacture to estimate audience measurement metrics based on users represented in Bloom filter arrays are disclosed. An apparatus includes a communications interface to receive a first Bloom filter array from a first computer of a first database proprietor. The first Bloom filter array is representative of first users who accessed media. The first users are registered with the first database proprietor. The first Bloom filter array includes a first array of first elements. Values of respective ones of the first elements are either a 0 or a 1 based on whether quantities of the first users allocated to the respective ones of the first elements are even or odd. The apparatus further includes a Bloom filter array analyzer to estimate a first cardinality for the first Bloom filter array. The first cardinality is indicative of a total number of the first users who accessed the media.

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 to estimate cardinality of users represented in arbitrarily distributed bloom filter arrays are disclosed. An apparatus includes a communications interface to obtain a first Bloom filter array generated by a first computer of a first database proprietor and obtain a second Bloom filter array generated by a second computer of a second database proprietor. The apparatus includes a cardinality analyzer to estimate a total number of unique users included in a union of corresponding ones of the first and second users represented in the first and second Bloom filter arrays regardless of whether the first and second users are mapped, based on a first distribution or a second distribution different than the first distribution, to the corresponding first and second Bloom filter arrays.