Methods and apparatus to estimate census level impressions and unique audience sizes across demographics

1. A computing system to determine census-based audience metrics of media across multiple demographics, the computing system comprising:

memory; and

one or more processors coupled to the memory and configured to:

determine a plurality of cross-demographic total census parameter values based on ratios of third-party impression counts and third-party audience sizes;

select a first cross-demographic total census parameter value as an upper bound constraint from the plurality of cross-demographic total census parameter values based on comparisons between ones of the plurality of cross-demographic total census parameter values;

select a second cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values based on the second cross-demographic total census parameter value being less than the upper bound constraint;

determine a first census-level audience size based on the second cross-demographic total census parameter value;

determine a first census-level impression count based on the second cross-demographic total census parameter value;

store the first census-level audience size and the first census-level impression count in the memory; and

send the first census-level audience size and the first census-level impression count to a network-connected device.

2. The computing system of claim 1 , wherein the one or more processors are configured to:

select between a finite universe audience model and an infinite universe audience model, and

determine the first census-level audience size and the first census-level impression count based on the selected one of the finite universe audience model or the infinite universe audience model.

3. The computing system of claim 1 , wherein the one or more processors are configured to determine whether the second cross-demographic total census parameter value satisfies a census-level total impression count constraint based on the first census-level impression count.

4. The computing system of claim 3 , wherein the census-level total impression count constraint is based on a census-level total impression count collected by an audience measurement entity, and the third-party impression counts and the third-party audience sizes are provided by a database proprietor, the database proprietor separate from the audience measurement entity.

5. The computing system of claim 3 , wherein, in response to the second cross-demographic total census parameter value not satisfying the census-level total impression count constraint, the one or more processors are configured to:

discard the second cross-demographic total census parameter value;

select a third cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values;

based on the third cross-demographic total census parameter value, determine a second census-level audience size and a second census-level impression count to satisfy the census-level total impression count constraint; and

store the second census-level audience size and the second census-level impression count in the memory.

6. The computing system of claim 1 , wherein the third-party impression counts and the third-party audience sizes correspond to impressions of audience members accessing a media item on corresponding client devices via the Internet.

7. The computing system of claim 1 , wherein the one or more processors are configured to select the first cross-demographic total census parameter value as a peak cross-demographic total census parameter value of the plurality of cross-demographic total census parameter values.

8. A non-transitory computer readable medium comprising instructions that, when executed, cause a computing system to at least:

determine a plurality of cross-demographic total census parameter values based on ratios of third-party impression counts and third-party audience sizes;

select a first cross-demographic total census parameter value as an upper bound constraint from the plurality of cross-demographic total census parameter values based on comparisons between ones of the plurality of cross-demographic total census parameter values;

select a second cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values based on the second cross-demographic total census parameter value being less than the upper bound constraint;

determine a first census-level audience size based on the second cross-demographic total census parameter value;

determine a first census-level impression count based on the second cross-demographic total census parameter value;

store the first census-level audience size and the first census-level impression count in a memory of the computing system; and

send the first census-level audience size and the first census-level impression count to a network-connected device.

9. The non-transitory computer readable medium of claim 8 , wherein the instructions, when executed, cause the computing system to:

select between a finite universe audience model and an infinite universe audience model, and

determine the first census-level audience size and the first census-level impression count based on the selected one of the finite universe audience model or the infinite universe audience model.

10. The non-transitory computer readable medium of claim 8 , wherein the instructions, when executed, cause the computing system to determine whether the second cross-demographic total census parameter value satisfies a census-level total impression count constraint based on the first census-level impression count.

11. The non-transitory computer readable medium of claim 10 , wherein the census-level total impression count constraint is based on a census-level total impression count collected by an audience measurement entity, and the third-party impression counts and the third-party audience sizes are provided by a database proprietor, the database proprietor separate from the audience measurement entity.

12. The non-transitory computer readable medium of claim 10 , wherein, in response to the second cross-demographic total census parameter value not satisfying the census-level total impression count constraint, the instructions, when executed, cause the computing system to:

discard the second cross-demographic total census parameter value;

select a third cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values;

based on the third cross-demographic total census parameter value, determine a second census-level audience size and a second census-level impression count to satisfy the census-level total impression count constraint; and

store the second census-level audience size and the second census-level impression count in the memory.

13. The non-transitory computer readable medium of claim 8 , wherein the third-party impression counts and the third-party audience sizes correspond to impressions of audience members accessing a media item on corresponding client devices via the Internet.

14. The non-transitory computer readable medium of claim 8 , wherein the instructions, when executed, cause the computing system to select the first cross-demographic total census parameter value as a peak cross-demographic total census parameter value of the plurality of cross-demographic total census parameter values.

15. A method, comprising:

determining, by a computing system having one or more processors, a plurality of cross-demographic total census parameter values based on ratios of third-party impression counts and third-party audience sizes;

selecting, by the computing system, a first cross-demographic total census parameter value as an upper bound constraint from the plurality of cross-demographic total census parameter values based on comparisons between ones of the plurality of cross-demographic total census parameter values;

selecting, by the computing system, a second cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values based on the second cross-demographic total census parameter value being less than the upper bound constraint;

determining, by the computing system, a first census-level audience size based on the second cross-demographic total census parameter value;

determining, by the computing system, a first census-level impression count based on the second cross-demographic total census parameter value;

storing the first census-level audience size and the first census-level impression count in a memory of the computing system; and

sending, by the computing system, the first census-level audience size and the first census-level impression count to a network-connected device.

16. The method of claim 15 , further including:

selecting between a finite universe audience model and an infinite universe audience model, and

determining the first census-level audience size and the first census-level impression count based on the selected one of the finite universe audience model or the infinite universe audience model.

17. The method of claim 15 , further including:

determining whether the second cross-demographic total census parameter value satisfies a census-level total impression count constraint based on the first census-level impression count.

18. The method of claim 17 , wherein the census-level total impression count constraint is based on a census-level total impression count collected by an audience measurement entity, and the third-party impression counts and the third-party audience sizes are provided by a database proprietor, the database proprietor separate from the audience measurement entity.

19. The method of claim 17 , further including:

in response to the second cross-demographic total census parameter value not satisfying the census-level total impression count constraint,

discarding the second cross-demographic total census parameter value;

selecting a third cross-demographic total census parameter value from the plurality of cross-demographic total census parameter values;

based on the third cross-demographic total census parameter value, determining a second census-level audience size and a second census-level impression count to satisfy the census-level total impression count constraint; and

store the second census-level audience size and the second census-level impression count in the memory.

20. The method of claim 15 , wherein the third-party impression counts and the third-party audience sizes correspond to impressions of audience members accessing a media item on corresponding client devices via the Internet.

21. The method of claim 15 , further including:

selecting the first cross-demographic total census parameter value as a peak cross-demographic total census parameter value of the plurality of cross-demographic total census parameter values.