METHODS AND APPARATUS TO ESTIMATE MEDIA IMPRESSION FREQUENCY DISTRIBUTIONS
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. The method further includes determining a second impression frequency distribution for the user-identified impressions and the unidentified impressions of the census impressions based on the first impression frequency distribution.
1 . A media monitoring device of an audience measurement entity, comprising:
an impression information collector to:
obtain requests from computing devices indicative of accesses to media at the computing devices, a total count of the requests corresponding to a total number of census impressions associated with the media; and
obtain a first impression frequency distribution from a database proprietor, the first impression frequency distribution corresponding to user-identified impressions of the 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, ones of the impression frequency groups representative of user-identified individuals that accessed the media a corresponding number numbers of times; and
a user-identified impression frequency data analyzer to determine a second impression frequency distribution for the user-identified impressions and the unidentified impressions of the census impressions based on the first impression frequency distribution.
2 . The media monitoring device of claim 1 , wherein the user-identified impression frequency data analyzer is to determine a total census audience size corresponding to the total number of census impressions based on the second impression frequency distribution.
3 . The media monitoring device of claim 1 , wherein the user-identified impression frequency data analyzer is to determine the second impression frequency distribution by:
calculating a user-identified probability distribution based on the first impression frequency distribution; and
calculating a census probability distribution that satisfies the principle of minimum cross entropy between the census probability distribution and the user-identified probability distribution consistent with census constraints defined by census data associated with the census impressions, the census probability distribution including probability values for corresponding frequencies in the second impression frequency distribution.
4 . The media monitoring device of claim 3 , wherein the user-identified probability distribution directly corresponds to the first impression frequency distribution.
5 . The media monitoring device of claim 3 , wherein the user-identified impression frequency data analyzer is to calculate the user-identified probability distribution based on the first impression frequency distribution by calculating probability values in the user-identified probability distribution that are consistent with user-identified constraints and that satisfy the principle of maximum entropy.
6 . The media monitoring device of claim 5 , wherein the user-identified impression frequency data analyzer is to calculate the probability values in the user-identified probability distribution that satisfy the principle of maximum entropy by determining a maximum of the negative of a summation of each probability value in the user-identified probability distribution multiplied by the log of a ratio of each corresponding probability value in the user-identified probability distribution.
7 . The media monitoring device of claim 5 , further including a constraints analyzer to generate a user-identified constraint matrix that, when multiplied by the user-identified probability distribution represented as a one-dimensional array of the probability values arranged in a first column matrix, equals a second column matrix containing user-identified constraint values defined by the user-identified constraints.
8 . The media monitoring device of claim 7 , wherein the user-identified probability distribution represents interrelationships between different dimensions of the user-identified impressions, the one-dimensional array of the probability values based on a relabeling of entries in a multi-dimensional array representing interrelationships between the different dimensions.
9 . The media monitoring device of claim 3 , wherein the user-identified impression frequency data analyzer is to calculate the census probability distribution that satisfies the principle of minimum cross entropy by determining a minimum of a summation of each probability value in the census probability distribution multiplied by the log of a ratio of each corresponding probability value in the census probability distribution to each corresponding probability value in the user-identified probability distribution.
10 . The media monitoring device of claim 3 , further including a constraints analyzer to generate a census constraint matrix that, when multiplied by the census probability distribution represented as a one-dimensional array of the probability values arranged in a first column matrix, equals a second column matrix containing census constraint values defined by the census constraints.
11 . The media monitoring device of claim 3 , wherein the census probability distribution represents interrelationships between different dimensions of the census impressions.
12 . The media monitoring device of claim 11 , wherein the different dimensions correspond to at least one of different platforms of the computing devices, different Internet sites through which the media was accessed, different geographic locations where the media was accessed, or different placements or formats of the media within websites through which the media was accessed.
13 . The media monitoring device of claim 1 , wherein a difference between a first number of the user-identified impressions and the total number of census impressions corresponds to a second number of the unidentified impressions, the unidentified impressions associated with unidentified individuals for whom second demographic information is not stored by the database proprietor.
14 . The media monitoring device of claim 1 , wherein at least one of the impressions information collector or the user identified impression frequency analyzer is implemented by a hardware processor.
15 . A method, comprising:
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, a total count of the requests corresponding to a total number of census impressions associated with the media;
obtaining a first impression frequency distribution from a database proprietor, the first impression frequency distribution corresponding to user-identified impressions of the 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, ones of the impression frequency groups representative of user-identified individuals that accessed the media a corresponding number numbers of times; and
determining, by executing an instruction with a processor, a second impression frequency distribution for the user-identified impressions and the unidentified impressions of the census impressions based on the first impression frequency distribution.
16 - 27 . (canceled)
28 . A tangible computer readable storage medium comprising instructions that, when executed, cause a machine to at least:
log 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, a total count of the requests corresponding to a total number of census impressions associated with the media;
obtain a first impression frequency distribution from a database proprietor, the first impression frequency distribution corresponding to user-identified impressions of the 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 recognizable by the database proprietor, the first impression frequency distribution including a plurality of impression frequency groups of user-identified audience sizes, ones of the impression frequency groups representative of user-identified individuals that accessed the media a corresponding number numbers of times; and
determine a second impression frequency distribution for the user-identified impressions and the unidentified impressions of the census impressions based on the first impression frequency distribution.
29 . (canceled)
30 . The storage medium of claim 28 , wherein the determining of the second impression frequency distribution includes:
calculating a user-identified probability distribution based on the first impression frequency distribution; and
calculating a census probability distribution that satisfies the principle of minimum cross entropy between the census probability distribution and the user-identified probability distribution consistent with census constraints defined by census data associated with the census impressions, the census probability distribution including probability values for corresponding frequencies in the second impression frequency distribution.
31 . (canceled)
32 . The storage medium of claim 30 , wherein the instructions further cause the machine to calculate probability values in the user-identified probability distribution that are consistent with user-identified constraints and that satisfy the principle of maximum entropy.
33 . (canceled)
34 . The storage medium of claim 32 , wherein the instructions further cause the machine to generate a user-identified constraint matrix that, when multiplied by the user-identified probability distribution represented as a one-dimensional array of the probability values arranged in a first column matrix, equals a second column matrix containing user-identified constraint values defined by the user-identified constraints.
35 . (canceled)
36 . (canceled)
37 . The storage medium of claim 30 , wherein the instructions further cause the machine to generate a census constraint matrix that, when multiplied by the census probability distribution represented as a one-dimensional array of the probability values arranged in a first column matrix, equals a second column matrix containing census constraint values defined by the census constraints.
38 - 48 . (canceled)