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, a total count of the requests corresponding to a total number of census impressions. The MMU to assign user-identified impression data corresponding to user-identified impressions to a second block of memory, the user-identified impressions associated with user-identified individuals for whom first demographic information is stored by a database proprietor.

Abstract: Methods, systems, apparatus and articles of manufacture to determine causal effects are disclosed herein. An example apparatus includes a weighting engine to calculate a first set of weights for a first set of covariates corresponding to a treatment dataset and a second set of weights for a second set of covariates corresponding to a control dataset using maximum entropy, the first set of weights to equal the second set of weights.

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: Methods and apparatus for estimating a Lorenz curve for a dataset based on a frequency value associated with the dataset are disclosed. An example apparatus for estimating a Lorenz curve for a dataset representing a distribution of products for individual members of a population includes a frequency identifier and a Lorenz curve generator. The frequency identifier is to access a frequency value associated with the dataset. The frequency value is derived from an occurrence value associated with the products of the dataset and a population value associated with the individual members of the population of the dataset. The frequency identifier is to access the frequency value without directly accessing the occurrence value and the population value. The Lorenz curve generator is to generate an estimated Lorenz curve for the dataset using a Lorenz curve estimation function including the frequency value.

Abstract: Methods, systems, apparatus and articles of manufacture to generate projection factors are disclosed. An apparatus to reduce panel imbalance errors includes a data analyzer to identify a retailer in a geographic region indicative of shopping bias. The data analyzer also is to identify households of interest in the geographic region having combined panel data, the combined panel data representing core panelist data and auxiliary data. The apparatus also includes a modeling engine to calculate potential spending of each household at one or more stores of the retailer. The potential spending is based on observed spending. The apparatus also includes a projection engine to reduce panel imbalance errors by calculating projection weights for the combined panel based on (a) the potential spending at the one or more stores and (b) social or demographic representation data of the combined panel.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to store first impression counts of first media impressions corresponding to panelists in a population that accessed media via one or more of a plurality of media access platforms; and store marginal impression counts for second media impressions corresponding to audience members in the population that accessed the media via the plurality of media access platforms, ones of the marginal impression counts indicative of a total number of impressions of the media accessed via corresponding ones of the plurality of media access platforms; calculate multipliers relating a first probability distribution of the first media impressions to a second probability distribution of the second media impressions, the multipliers calculated based on constraints defined by the marginal impression counts for the second media impressions; and calculate second impression counts of the second media impressions based on the multipliers.

Abstract: Methods and apparatus to estimate media impression frequency distributions are disclosed. An example method includes logging a plurality of requests in a database, the plurality of requests obtained from a plurality of network communications from computing devices, the plurality of requests indicative of accesses to media at the computing devices. The method further includes obtaining a first impression frequency distribution from a database proprietor. The first impression frequency distribution corresponding to user-identified impressions of census impressions and exclusive of unidentified impressions of the census impressions. The user-identified impressions corresponding to user-identified individuals for whom first demographic information is stored by the database proprietor. The first impression frequency distribution including a plurality of impression frequency groups of user-identified audience sizes.

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 a reach determiner to estimate a population reach of a union of time intervals for which media ratings data is available; a pseudo universe determiner to determine a pseudo universe estimate of a recorded audience corresponding to the union; determine a pseudo universe estimate of a population audience corresponding to the union based on the pseudo universe estimate of the recorded audience; and determine an error of the population reach estimate of the union based on the pseudo universe of the population audience corresponding to the union; and the reach determiner to when the error does not satisfy a threshold, adjust the population reach estimate; and when the error does satisfy the threshold, determine the population reach of the union based on the population reach estimate.

Abstract: Methods, apparatus, systems, and articles of manufacture are disclosed to to estimate population reach from marginal ratings. An example apparatus includes an interface to access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience; a reach determiner to iteratively estimate a reach of the media for the population audience based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and the interface to output the estimated reach for the population audience.

Abstract: Methods and apparatus to determine reach with time dependent weights are disclosed. An example method disclosed herein includes determining a first subset of panelists exposed to media at a first time; determining a second subset of the panelists exposed to the media at a second time; applying a first plurality of weights to the first subset of panelists to generate first weighted exposures; applying a second plurality of weights to the second subset of the panelists to generate second weighted exposures; for a first panelist in the first and second subsets, determining a first cumulative weighted exposure by determining which of the first and second weighted exposures is largest for each of the first panelist; for a second panelist in one of the first and second subsets, determining a second cumulative weighted exposure by based on the weight applied to the second panelist; and determining a reach of the media for the first and second times by combining the first and second cumulative weighted exposures.

Abstract: Methods and apparatus for estimating a Lorenz curve for a dataset based on a frequency value associated with the dataset are disclosed. A Lorenz curve estimation apparatus includes a frequency identifier to determine a frequency value associated with a dataset. The Lorenz curve estimation apparatus further includes a Lorenz curve generator to generate an estimated Lorenz curve for the dataset based on a Lorenz curve estimation function including the frequency value.

Abstract: Methods, systems and apparatus to improve the efficiency of calculating a customer retention rate are disclosed herein.

Abstract: Methods, apparatus, systems and articles of manufacture are disclosed to improve multi-demographic modeling efficiency. An example apparatus includes a feature set aggregator to segregate training data based on feature sets of interest, and to identify households that participate in at least one of the feature sets of interest, a class enumerator to reduce multi-demographic model iterations by enumerating demographic combinations for the identified households, the enumerated demographic combinations including a single identifier to represent a combination of two or more demographic categories, and a modeling engine to generate training coefficients associated with respective ones of the enumerated demographic combinations.

Abstract: Methods, apparatus, and articles of manufacture to measure geographical features using an image of a geographical location are disclosed. An example method includes dividing an image of a geographic area of interest into geographical zones, the geographical zones being representative of different physical geographical areas; modifying boundaries of a first one of the geographical zones to more closely conform to an observable landmark or a geographical location observable by a person located in the first one of the geographical zones; storing descriptions for the geographical zones in a computer memory based on the modified boundaries of the first one of the geographical zones; and storing a value representative of a geographical feature represented in the image for the first one of the geographical zones.

Abstract: Methods, apparatus, and articles of manufacture to measure geographical features using an image of a geographical location are disclosed. An example method includes dividing, with a processor, an image of a geographic area of interest into a plurality of geographical zones, the geographical zones being representative of different geographical areas having approximately equal physical areas, measuring, with the processor, a geographical feature represented in the image for corresponding ones of the plurality of geographical zones, storing descriptions for the geographical zones in a computer memory, and storing values representative of the geographical feature of the geographical zones.

Abstract: Methods, apparatus, and articles of manufacture to measure geographical features using an image of a geographical location are disclosed. An example method includes dividing an image of a geographic area of interest into geographical zones, the geographical zones being representative of different physical geographical areas; modifying boundaries of a first one of the geographical zones to more closely conform to an observable landmark or a geographical location observable by a person located in the first one of the geographical zones; storing descriptions for the geographical zones in a computer memory based on the modified boundaries of the first one of the geographical zones; and storing a value representative of a geographical feature represented in the image for the first one of the geographical zones.

Abstract: Methods and apparatus are disclosed to align panelist data with retailer sales data. An example method includes calculating a panelist reporting period for a panelist dataset having a first number of occasions, the panelist dataset having a household resolution, applying trip weights to a retailer dataset, the retailer dataset including a second number of occasions during a market research reporting period, the retailer dataset having a trip resolution, and minimizing a gap between the household resolution and the trip resolution.

Abstract: Methods, apparatus, and articles of manufacture to measure geographical features using an image of a geographical location are disclosed. An example method includes dividing, with a processor, an image of a geographic area of interest into a plurality of geographical zones, the geographical zones being representative of different geographical areas having approximately equal physical areas, measuring, with the processor, a geographical feature represented in the image for corresponding ones of the plurality of geographical zones, storing descriptions for the geographical zones in a computer memory, and storing values representative of the geographical feature of the geographical zones.