Abstract: Methods and apparatus to estimate cardinality across multiple datasets represented using Bloom filter arrays are disclosed. Disclosed examples include processor circuitry to execute and/or instantiate instructions to determine an inclusion-exclusion expression that defines an audience size for a user group of interest. Terms in the inclusion-exclusion expression corresponding to either a first cardinality of a first one of at least three Bloom filter arrays or a second cardinality of a union of two or more of the Bloom filter arrays. Different ones of the Bloom filter arrays representative of different sets of users who accessed media. The at least one processor further to estimate, based on the inclusion-exclusion expression, the audience size of the user group of interest.

Abstract: Methods and apparatus to determine probabilistic media viewing metrics are disclosed herein. An example apparatus includes memory including machine reachable instructions; and processor circuitry to execute the instructions to calculate a first probability for respective ones of a plurality of panelists as having viewed media based on viewing data, the viewing data including incomplete viewing data for one or more of the panelists relative to the media; identify respective ones of a plurality of panelists as included in a demographic subgroup based on demographic data for the panelists; assign a sampling weight to the respective ones of the plurality of panelists based on the demographic data; and calculate a second probability of the demographic subgroup having viewed the media based on the first probabilities and the sampling weights for the respective ones of the plurality of panelists in the demographic subgroup.

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: Example apparatus disclosed herein include a return path data classifier to classify a first viewing period associated with segments of return path data received from a set top box into tuning classifications based on the segments of the return path data; calculate a total reported tuning duration for the first viewing period when the first viewing period is classified as live or playback tuning; and compare the total reported tuning duration to a duration threshold to determine whether the segments of return path data associated with the first viewing period are valid. The example apparatus also includes a return path data rectifier to rectify missing tuning data associated with a second viewing period based on tuning data included in the segments of return path data associated with the first viewing period when the segments of the return path data associated with the first viewing period are determined to be valid.

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: 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 and systems 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: An example apparatus disclosed herein includes a data input interface to access different sets of initial adjustment factors, the initial adjustment factors generated to correct at least one of misattribution or non-coverage of media impressions logged by a database proprietor, a grouping controller to identify a first set of the initial adjustment factors as a set of donor adjustment factors based on (a) first audience members associated with the set of donor adjustment factors satisfying a first threshold and (b) first impressions associated with the first audience members satisfying a second threshold, and identify a second set of the initial adjustment factors as a set of recipient adjustment factors, and an imputation factor generator to generate imputation factors to correct ones of the recipient adjustment factors based on ones of the donor adjustment factors.

Abstract: Example methods, apparatus, systems, and articles of manufacture to facilitate analysis and adjustment of demographic information for monitored audience members are disclosed. Disclosed example methods include receiving a data set including media exposure data and associated data from at least one of a panelist database and a user account database. Disclosed example methods include measuring the data set to determine a probability distribution of user age in the data set according to a first model. Disclosed example methods include comparing the probability distribution of user age to a threshold. Disclosed example methods include adjusting, based on the comparison of the probability distribution of user age to the threshold, the probability distribution to an adjusted probability distribution by replacing the probability distribution with a degenerate distribution.

Abstract: Methods and apparatus to calibrate media ratings based on return path data are disclosed. An apparatus includes programmable circuitry to execute machine readable instructions to: determine a subscriber calibration factor for media based on first panel tuning information obtained from first metering devices in first panelist households that subscribe to a content provider that provides media through return path data (RPD) devices; determine a nonsubscriber calibration factor for the media based on second panel tuning information obtained from second metering devices in second panelist households that do not subscribe to the content provider; and determine a final rating for the media based on an initial rating and at least one of the subscriber calibration factor or the nonsubscriber calibration factor, the initial rating based on RPD tuning information obtained from RPD devices in subscriber households that subscribe to the content provider.

Abstract: Methods and apparatus to determine probabilistic media viewing metrics are disclosed herein. An example apparatus includes memory including machine reachable instructions; and processor circuitry to execute the instructions to calculate a first probability for respective ones of a plurality of panelists as having viewed media based on viewing data, the viewing data including incomplete viewing data for one or more of the panelists relative to the media; identify respective ones of a plurality of panelists as included in a demographic subgroup based on demographic data for the panelists; assign a sampling weight to the respective ones of the plurality of panelists based on the demographic data; and calculate a second probability of the demographic subgroup having viewed the media based on the first probabilities and the sampling weights for the respective ones of the plurality of panelists in the demographic subgroup.

Abstract: Disclosed examples access media impression data via one or more wireless communications, the media impression data including panel data obtained from a meter and impression information obtained after an access of media at a computing device; determine an audience deduplication based on the panel data; determine odds ratios for platform combinations based on the audience deduplication; determine posterior distributions for the media based on the odds ratios; perform a sequential odds ratio insertion technique based on the posterior distributions to determine unique audience sizes; align the unique audience sizes based on a constraint; and generate a report including the aligned unique audience sizes.

Abstract: Example apparatus disclosed herein include a return path data classifier to classify a first viewing period associated with segments of return path data received from a set top box into tuning classifications based on the segments of the return path data; calculate a total reported tuning duration for the first viewing period when the first viewing period is classified as live or playback tuning; and compare the total reported tuning duration to a duration threshold to determine whether the segments of return path data associated with the first viewing period are valid. The example apparatus also includes a return path data rectifier to rectify missing tuning data associated with a second viewing period based on tuning data included in the segments of return path data associated with the first viewing period when the segments of the return path data associated with the first viewing period are determined to be valid.

Abstract: Methods and apparatus to estimate demographics of a household are disclosed. An example method to determine demographics for non-panelist households includes calculating a first demographic constraint average and a second demographic constraint average based on a first demographic distribution of a first tuning event of a household and a second demographic distribution of a second tuning event of the household. The household is a non-panelist household. The example method also includes, based on the first demographic constraint average, determining a first likelihood of the household being associated with a first demographic constraint. The example method also includes, based on the second demographic constraint average, determining a second likelihood of the household being associated with a second demographic constraint. The example method also includes estimating a household characteristic of the household based on the first likelihood and the second likelihood.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to rectify false set top box tuning data. Disclosed examples methods include identifying, by executing an instruction with a processor, in the return path data, first tuning data corresponding to a first group of set top boxes, the first group of set top boxes classified as associated with machine events, determining, by executing an instruction with a processor, a ratio between first tuning events in the return path data and second tuning events in the return path data, the first tuning events attributed to the first group of the set top boxes, the second tuning events attributed to a second group of the set top boxes classified at not associated with machine events, and in response to the ratio satisfying a threshold during a time interval, removing second tuning data associated with the time interval from the first tuning data.

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: A method of controlling a vehicle may include determining a proximity to a stuck condition based on measured vehicle motion parameters and a wheel speed measured by a wheel speed sensor associated with one or more wheels of the vehicle. The method may further include generating a notification to a driver of the vehicle in response to the proximity to the stuck condition indicating that the vehicle is either in a stuck condition or a nearly stuck condition, and responsive to driver selection of an unstuck mode, executing an unstuck algorithm to automatically control operation of the vehicle to achieve a free condition.

Abstract: An example includes splitting audience member records into child nodes based on comparisons of first ones of attribute-value pairs of the audience member records to a first threshold, the attribute-value pairs representative of database subscriber activity data of corresponding audience members; in response to a quantity of ones of the audience member records in a first child node not satisfying the minimum leaf size, storing a terminal node value to indicate the first child node as a terminal node associated with one age category; in response to the quantity of the ones of the audience member records in the first child node satisfying the minimum leaf size, storing an intermediate node value to indicate the first child node as an intermediate node; and generating an age-correction model based on terminal nodes to facilitate correcting a database subscriber age characteristic associated with a media impression that is logged by a server.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to generate synthetic respondent level data. An example apparatus includes at least one memory; processor circuitry to execute instructions to: identify locations corresponding to monitored panelists; when a location of the identified locations corresponds to two or more affiliates, sum tuning minutes of the two or more affiliates; generate an affiliate probability based on the sum; convert first data of households in the location to a candidate receivability session based on the affiliate probability; 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 when the second panelists are included in the seed panel, the second panelists corresponds to faulty media monitoring equipment.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to identify co-relationships between media using social media. An example apparatus includes an audience estimator to: estimate a first audience of first media based on a first set of media-exposure social media messages corresponding to client devices referencing the first media, and estimate a second audience of second media based on a second set of media-exposure social media messages corresponding to the client devices referencing the second media.