Abstract: Methods, apparatus, and systems are disclosed for estimating panel attrition. An example apparatus includes at least one memory, machine readable instructions, and processor circuitry to execute the machine readable instructions to determine a beta distribution of a non-parametric survival curve estimate based on panel meter data associated with a cohort of panelists, determine confidence intervals for a set of beta distribution parameters associated with the survival curve estimate, and output a panelist attrition estimate generated based on the confidence intervals for the survival curve estimate, the panelist attrition estimate to represent panelist retention over time based on an installation date of the panel meter.

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: The disclosed computer-implemented method may include systems for generating personalized avatar reactions during live video broadcasts. For example, the systems and methods described herein can access a social networking system user's profile to identify an avatar associated with the social networking system user. The systems and methods can generate an avatar reaction by modifying one or more features of the avatar based on a corresponding emoticon reaction. Once generated, the social networking system user can select the avatar reaction for addition to an ephemeral reaction stream associated with a live video broadcast. Various other methods, systems, and computer-readable media are also disclosed.

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 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: 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: A magnetic insertion meter is disclosed herein. Disclosed insertion meters include in some examples, a sensor head tube having a textured front surface and at least two electrodes. Disclosed insertion meters include a textured front surface adapted to move the separation point of a fluid flowing over the sensor head tube towards the upstream surface as compared to the same sensor head tube without the textured front surface. Methods of measuring flow are also disclosed herein using example magnetic insertion meters.

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 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, 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, and articles of manufacture are disclosed to estimate an audience population. An example apparatus includes processor circuitry; characteristic identifier instructions to be executed by the processor circuitry to determine whether respective ones of respondents are associated with a characteristic; recapture probability estimator instructions to be executed by the processor circuitry to select a recapture probability of the respective ones of respondents; and population estimator instructions to be executed by the processor circuitry to in response to the recapture probability satisfying a recapture threshold, determine a population estimate having the characteristics based on a first model; and in response to the recapture probability not satisfying the recapture threshold, determine the population estimate having the characteristics based on a second model, the second model different than the first model.

Abstract: A hydraulic unit is for use in a multi zone heating system. The hydraulic unit comprises a variable output pump; a plurality of independently controllable valves, each valve being associated with one heating zone; and at least one temperature sensor. Each heating zone receives a heated water supply from a common heat source via the pump. The heating system includes a controller comprising a processor which receives signals from the at least one temperature sensor which processes the signals in accordance with control software. Command signals are sent to the pump and the plurality of independently controllable valves, to vary the flow rate of water from the common heat source to each of the heating zones independently one to another. Remote fault diagnosis and control is also provided.

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: 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: 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 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, 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 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 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.