Methods and apparatus to estimate population reach from different marginal rating unions

A non-transitory computer readable medium comprising instructions which, when executed cause one or more processors to at least:

• determine a population reach estimate of a union of time intervals for which media ratings data is available, the population reach estimate based on a pseudo universe estimate of a population audience corresponding to the union of the time intervals;
• determine a pseudo universe estimate of a recorded audience corresponding to the union of the time intervals;
• determine the pseudo universe estimate of the population audience based on the pseudo universe estimate of the recorded audience;
• and
• in response to a decision to update the pseudo universe estimate of the population audience to reduce an error of the population reach estimate:
• adjust the population reach estimate of the union;
• apply a correction to the population reach estimate of the union to maintain a condition associated with the population reach estimate;
• and
• output the population reach estimate of the union when the error of the population reach estimate satisfies a threshold.

A method comprising:

• determining, by executing an instruction with one or more processors, a population reach estimate of a union of time intervals for which media ratings data is available, the population reach estimate based on a pseudo universe estimate of a population audience corresponding to the union of the time intervals;
• determining, by executing an instruction with the one or more processors, a pseudo universe estimate of a recorded audience corresponding to the union of the time intervals;
• determining, by executing an instruction with the one or more processors, the pseudo universe estimate of the population audience based on the pseudo universe estimate of the recorded audience;
• and
• in response to a decision to update the pseudo universe estimate of the population audience to reduce an error of the population reach estimate:
• adjusting, by executing an instruction with the one or more processors, the population reach estimate of the union;
• applying, by executing an instruction with the one or more processors, a correction to the population reach estimate of the union to maintain a condition associated with the population reach estimate;
• and
• outputting, by executing an instruction with the one or more processors, the population reach estimate of the union when the error of the population reach estimate satisfies a threshold.