METHODS AND APPARATUS TO ESTIMATE POPULATION REACH FROM MARGINAL RATINGS

1 . An apparatus to determine a reach of media for a total population audience from marginal ratings, the apparatus comprising:

means for accessing (i) first marginal ratings for a plurality of margins, the first marginal ratings representative of corresponding different portions of a recorded audience of panelists exposed to media at corresponding different periods of time, the means for accessing to access (ii) second marginal ratings provided by a media provider for the total population audience of the media, and (iii) a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins, the media divided into the different periods of time;

means for iteratively converging on an output estimate of a reach of the media for the total population audience, wherein for a first process iteration, the means for iteratively converging is to:

determine a first total population audience reach estimate for the first process iteration, the first total population audience reach estimate based on a link expression, the link expression based on a first pseudo universe estimate of the total population audience, the first pseudo universe estimate of the total population audience based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings; and

evaluate an error between the first total population audience reach estimate determined from the first process iteration and a prior second total population audience reach estimate determined from a prior second process iteration; and

means for outputting the output estimate of the reach for the total population audience.

2 . The apparatus of claim 1 , further including means for determining a second pseudo universe estimate of the recorded audience, the means for iteratively converging to execute a subsequent third process iteration when the error between the first total population audience reach estimate and the prior second total population audience reach estimate does not satisfy an error threshold.

3 . The apparatus of claim 2 , wherein the means for iteratively converging is to initialize the output estimate of the reach for the total population audience reach prior to the first iteration.

4 . The apparatus of claim 3 , wherein the means for iteratively converging is to initialize the first pseudo universe estimate of the recorded audience prior to the first iteration.

5 . The apparatus of claim 4 , wherein the first pseudo universe estimate of the recorded audience is initialized with a total population size.

6 . The apparatus of claim 4 , wherein the means for iteratively converging is to execute the subsequent third process iteration when a second error corresponding to a comparison of the second pseudo universe of the recorded audience and the first pseudo universe of the recorded audience does not satisfy the error threshold.

7 . The apparatus of claim 6 , wherein the means for iteratively converging is to determine the output estimate of the reach for the total population audience to be at least one of the first total population audience reach estimate or the prior second total population audience reach estimate when the error threshold is satisfied.

8 . The apparatus of claim 2 , wherein the reach for the total population audience is a reach across two or more time intervals corresponding to the marginal ratings for the total population audience.

9 . The apparatus of claim 8 , wherein:

the second pseudo universe estimate of the recorded audience is based on an assumed independence among the first marginal ratings for the recorded audience; and

the first pseudo universe estimate of the total population audience is based on an assumed independence among the second marginal ratings for the total population audience.

10 . The apparatus of claim 9 , wherein the means for iteratively converging is to execute the first process iteration and the subsequent third iteration to converge on the output estimate of the reach for the total population audience corresponding to a deduplicated number of persons exposed to the media across the time intervals.

11 . The apparatus of claim 10 , wherein the time intervals are quarter hours.

12 . The apparatus of claim 2 , wherein the means for iteratively converging is to execute a fourth process iteration when a second error corresponding to the subsequent third process iteration does not satisfy the error threshold.

13 . An apparatus to determine a reach of media for a total population audience from marginal ratings, the apparatus comprising:

memory;

computer readable instructions; and

processor circuitry to execute the computer readable instructions to:

access first marginal ratings for a plurality of margins, the first marginal ratings representative of corresponding different portions of a recorded audience of panelists exposed to media at corresponding different periods of time;

access second marginal ratings provided by a media provider for the total population audience of the media;

access a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins, the media divided into the different periods of time;

iteratively coverage on an output estimate of a reach of the media for the total population audience, wherein for a first process iteration, the processor circuitry is to:

determine a first total population audience reach estimate for the first process iteration, the first total population audience reach estimate based on a link expression, the link expression based on a first pseudo universe estimate of the total population audience, the first pseudo universe estimate of the total population audience based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings;

evaluate an error between the first total population audience reach estimate determined from the first process iteration and a prior second total population audience reach estimate determined from a prior second process iteration; and

output the output estimate of the reach for the total population audience.

14 . The apparatus of claim 13 , wherein the processor circuitry is to:

determine a second pseudo universe estimate of the recorded audience; and

execute a subsequent third process iteration when the error between the first population audience reach estimate and the prior second population audience reach estimate does not satisfy an error threshold.

15 . The apparatus of claim 14 , wherein the processor circuitry is to initialize the output estimate of the reach for the population audience reach prior to the first iteration.

16 . The apparatus of claim 15 , wherein the processor circuitry is to initialize the first pseudo universe estimate of the recorded audience prior to the first iteration.

17 . The apparatus of claim 16 , wherein the first pseudo universe estimate of the recorded audience is initialized with a total population size.

18 . The apparatus of claim 16 , wherein the processor circuitry is to execute the subsequent third process iteration when a second error corresponding to a comparison of the second pseudo universe of the recorded audience and the first pseudo universe of the recorded audience does not satisfy the error threshold.

19 . The apparatus of claim 18 , wherein when the error threshold is satisfied, the processor circuitry is to determine the output estimate of the reach for the population audience to be at least one of the first population audience reach estimate or the prior second population audience reach estimate.

20 . A non-transitory computer readable storage medium comprising instructions which, when executed, cause a machine to at least:

access first marginal ratings for a plurality of margins, the first marginal ratings representative of corresponding different portions of a recorded audience of panelists exposed to media at corresponding different periods of time;

access second marginal ratings provided by a media provider for a total population audience of the media;

access a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins, the media divided into the different periods of time;

iteratively converge on an output estimate of a reach of the media for the total population audience, wherein for a first process iteration, the instructions are to cause the machine to:

determine a first total population audience reach estimate for the first process iteration, the first total population audience reach estimate based on a link expression, the link expression based on a first pseudo universe estimate of the total population audience, the first pseudo universe estimate of the total population audience based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings;

evaluate an error between the first total population audience reach estimate determined from the first process iteration and a prior second total population audience reach estimate determined from a prior second process iteration; and

output the output estimate of the reach for the total population audience.