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 to estimate cardinality of users represented in arbitrarily distributed bloom filter arrays are disclosed. A system includes a communication interface to: access a first Bloom filter array representative of first entries in a first database, the first entries allocated to ones of first elements in the first Bloom filter array based on a non-uniform distribution of outputs of a hash function applied to the first entries, and access a second Bloom filter array representative of second entries in a second database. The system also includes machine readable instructions to cause one or more processors to estimate a cardinality of a union of the first and second entries based on the non-uniform distribution of the outputs of the hash function.

Abstract: Methods and systems are provided for operating a vehicle in a mode to free the vehicle from being stuck in sand are presented. In one example, a speed of an electric machine is adjusted to determine when wheel jitter occurs. The electric machine speed may be maintained at a speed where wheel jitter occurs while the vehicle is stuck.

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: 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: 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: 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 and apparatus to model on/off states of media presentation devices based on return path data are disclosed. An apparatus includes a memory and processor circuitry to execute instructions stored in the memory to: generate a probability distribution of actual durations of first tuning segments, the first tuning segments representative of lengths of time during which panelists accessed first media; modify the lengths associated with ones of the first tuning segments to generate second tuning segments having second durations; and estimate a time when a media device associated with a return path data (RPD) device is powered on based on (i) the probability distribution, (ii) the second tuning segments, and (iii) a third tuning segment during which the RPD device accessed second media, the third tuning segment reported from the RPD device.

Abstract: Methods and apparatus to calibrate media ratings based on return path data are disclosed. An apparatus includes a processor and memory including instructions that, when executed, cause the processor to: determine an initial rating for the media provided in a first geographic area based on return path data (RPD) tuning information obtained from RPD devices in subscriber households in the first geographic area; determine a first panelist rating for the media provided in a second geographic area based on first panel tuning information obtained from first metering devices in a first subset of panelist households in the second geographic area; determine a nonsubscriber calibration factor based on the first panelist rating; and determine a final rating for the media in the first geographic area by modifying the initial rating based on the nonsubscriber calibration factor.

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 and apparatus to model on/off states of media presentation devices based on return path data are disclosed. An apparatus includes a memory and processor circuitry to execute instructions stored in the memory to: generate a probability distribution of actual durations of first tuning segments, the first tuning segments representative of lengths of time during which panelists accessed first media; modify the lengths associated with ones of the first tuning segments to generate second tuning segments having second durations; and estimate a time when a media device associated with a return path data (RPD) device is powered on based on (i) the probability distribution, (ii) the second tuning segments, and (iii) a third tuning segment during which the RPD device accessed second media, the third tuning segment reported from the RPD device.

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: 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: Methods, apparatus, systems, and articles of manufacture are disclosed to determine unique audience size via clustered data. An example apparatus includes memory, machine readable instructions, and processor circuitry to at least one of execute or instantiate the machine readable instructions. The example processor circuitry is to form a first matrix identifying matching and non-matching instances of first values of respective demographics of an audience of media and second values of the respective demographics. Also, the processor circuitry is to normalize the first matrix to generate an account sharing adjustment matrix. Additionally, the processor circuitry is to apply the account sharing adjustment matrix to a vector of one or more counts of impressions of the media to correct for one or more members of the audience that share a user account registered with a database proprietor, the one or more counts of the impressions corresponding to the respective demographics.

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, 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: Disclosed examples access data from a database, the data stored across multiple registers of the database; determine (a) a maximum rank for each of the multiple registers and (b) a maximum rank count for each of the multiple registers; determine a frequency distribution based on the maximum ranks and the maximum rank counts; and generate a report including at least one of the frequency distribution, the maximum ranks, or the maximum rank counts.

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.