Methods and apparatus to estimate population reach from marginals
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.
1. An audience measurement system comprising:
a plurality of meters configured to monitor operation of first media devices in households; and
a computing system comprising a processor and a memory, the computing system configured to:
receive, via the Internet, media presentation data associated with operation of the first media devices monitored by the plurality of meters;
receive, from a service provider via the Internet, return path data associated with operation of second media devices;
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, the first audience exposure values and the first de-duplicated audience value based on the media presentation data;
determine a first intermediate range based on (i) a largest second audience exposure value of a plurality of second audience exposure values for a population audience of the media, (ii) a sum of the second audience exposure values, and (iii) the audience relationship value, the second audience exposure values based on the return path data;
determine a second intermediate range based on the largest second audience exposure value and the sum of the second audience exposure values;
determine bounds of a pseudo universe estimate of the population audience of the media based on a set intersection of the first intermediate range and the second intermediate range;
iteratively determine the pseudo universe estimate of the population audience and a second de-duplicated audience value for the population audience of the media by iteratively updating an initial pseudo universe estimate based on the audience relationship value and the second audience exposure values to converge to a final pseudo universe estimate of the population audience that is within the bounds; and
output the second de-duplicated audience value and the audience relationship value to an application that is to perform an operation based on at least one of the second de-duplicated audience value or the audience relationship value.
2. The audience measurement system of claim 1 , wherein the computing system is configured to iteratively converge on a pseudo universe estimate of the recorded audience of the media based on (A) the first de-duplicated audience value for the recorded audience of the media and (B) the first audience exposure values.
3. The audience measurement system of claim 2 , wherein the computing system is configured to determine the audience relationship value based on the pseudo universe estimate of the recorded audience.
4. The audience measurement system of claim 1 , wherein the computing system is configured to iteratively converge on an upper bound of the second intermediate range.
5. At least one non-transitory computer readable medium comprising instructions that, when executed, cause at least one processor to at least:
receive, from a plurality of meters via the Internet, media presentation data associated with operation of first media devices monitored by the plurality of meters;
receive, from a service provider via the Internet, return path data associated with operation of second media devices;
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, the first audience exposure values and the first de-duplicated audience value based on the media presentation data;
determine a first intermediate range based on (i) a largest second audience exposure value of a plurality of second audience exposure values for a population audience of the media, (ii) a sum of the second audience exposure values, and (iii) the audience relationship value, the second audience exposure values based on the return path data;
determine a second intermediate range based on the largest second audience exposure value and the sum of the second audience exposure values;
determine bounds of a pseudo universe estimate of the population audience of the media based on a set intersection of the first intermediate range and the second intermediate range;
iteratively determine the pseudo universe estimate of the population audience and a second de-duplicated audience value for the population audience of the media by iteratively updating an initial pseudo universe estimate based on the audience relationship value and the second audience exposure values to converge to a final pseudo universe estimate of the population audience that is within the bounds; and
output the second de-duplicated audience value and the audience relationship value to an application that is to perform an operation based on at least one of the second de-duplicated audience value or the audience relationship value.
6. The at least one non-transitory computer readable medium of claim 5 , wherein the instructions cause the at least one processor to iteratively converge on a pseudo universe estimate of the recorded audience of the media based on (A) the first de-duplicated audience value for the recorded audience of the media and (B) the first audience exposure values.
7. The at least one non-transitory computer readable medium of claim 5 , wherein the instructions cause the at least one processor to determine the audience relationship value based on the pseudo universe estimate of the recorded audience.
8. The at least one non-transitory computer readable medium of claim 5 , wherein the instructions cause the at least one processor to iteratively converge on an upper bound of the second intermediate range.
9. A method comprising:
receiving, from a plurality of meters via the Internet, media presentation data associated with operation of first media devices monitored by the plurality of meters;
receiving, from a service provider via the Internet, return path data associated with operation of second media devices;
determining, by executing an instruction with at least one processor, 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, the first audience exposure values and the first de-duplicated audience value based on the media presentation data;
determining, by executing an instruction with the at least one processor, a first intermediate range based on (i) a largest second audience exposure value of a plurality of second audience exposure values for a population audience of the media, (ii) a sum of the second audience exposure values, and (iii) the audience relationship value, the second audience exposure values based on the return path data;
determining, by executing an instruction with the at least one processor, a second intermediate range based on the largest second audience exposure value and the sum of the second audience exposure values;
determining, by executing an instruction with the at least one processor, bounds of a pseudo universe estimate of the population audience of the media based a set intersection of the first intermediate range and the second intermediate range;
iteratively determining, by executing an instruction with the at least one processor, the pseudo universe estimate of the population audience and a second deduplicated audience value for the population audience of the media by iteratively updating an initial pseudo universe estimate based on the audience relationship value and the second audience exposure values to converge to a final pseudo universe estimate of the population audience that is within the bounds; and
outputting the second de-duplicated audience value and the audience relationship value to an application that is to perform an operation based on at least one of the second de-duplicated audience value or the audience relationship value.
10. The method of claim 9 , further including iteratively converging, by executing an instruction with the at least one processor, on a pseudo universe estimate of the recorded audience of the media based on (A) the first de-duplicated audience value for the recorded audience of the media and (B) the first audience exposure values.
11. The method of claim 9 , further including determining, by executing an instruction with the at least one processor, the audience relationship value based on the pseudo universe estimate of the recorded audience.
12. The method of claim 9 , further including iteratively converging, by executing an instruction with the at least one processor, on an upper bound of the second intermediate range.
13. The audience measurement system of claim 1 , wherein the application is select a targeted commercial to be provided to at least one of the first media devices or the second media devices.
14. The audience measurement system of claim 1 , wherein the application is select secondary media to be provided to a secondary media device associated with at least one of the first media devices or the second media devices.
15. The at least one non-transitory computer readable medium of claim 5 , wherein the application is select a targeted commercial to be provided to at least one of the first media devices or the second media devices.
16. The at least one non-transitory computer readable medium of claim 5 , wherein the application is select secondary media to be provided to a secondary media device associated with at least one of the first media devices or the second media devices.
17. The at least one non-transitory computer readable medium of claim 5 , wherein the instructions cause the at least one processor to execute the application.
18. The method of claim 9 , wherein the application is select a targeted commercial to be provided to at least one of the first media devices or the second media devices.
19. The method of claim 9 , wherein the application is select secondary media to be provided to a secondary media device associated with at least one of the first media devices or the second media devices.
20. The method of claim 9 , further including executing the application with the at least one processor.