Methods and apparatus to estimate population reach from marginal ratings

Abstract

Methods, apparatus, systems, and articles of manufacture are disclosed to to estimate population reach from marginal ratings. An example apparatus includes an interface to access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience; a reach determiner to iteratively estimate a reach of the media for the population audience based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and the interface to output the estimated reach for the population audience.

1 . An apparatus to determine reach of media from marginal ratings, the apparatus comprising:
 an interface to access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience;   a reach determiner to iteratively execute processing operations to converge on an output estimate of a reach of the media for the population audience, the reach determiner to evaluate an error between an updated population audience reach estimate determined from a current iteration of the processing operations and a prior population audience reach estimate determined from a prior iteration of the processing operation, the updated population audience reach estimate determined based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and   the interface to output the estimate of the reach for the population audience.   
     
     
         2 . The apparatus of  claim 1 , further including a pseudo universe determiner to determine, during the current iteration, a current pseudo universe estimate of a population audience corresponding to the current iteration based on a current pseudo universe estimate of a recorded audience corresponding to the current iteration;
 the reach determiner to determine the updated population audience reach estimate corresponding to the current iteration based on the current pseudo universe of the population audience;   the pseudo universe determiner to determine an updated pseudo universe estimate of a recorded audience; and   the reach determiner to execute a subsequent iteration of the processing operations, when the error between the updated population audience reach estimate and the prior population audience reach estimate does not satisfy an error threshold.   
     
     
         3 . The apparatus of  claim 2 , wherein the reach determiner is to initialize the current estimate of the reach for the population audience reach at prior to the current iteration. 
     
     
         4 . The apparatus of  claim 3 , wherein the pseudo universe determiner is to initialize the current pseudo universe estimate of the recorded audience prior to the current iteration. 
     
     
         5 . The apparatus of  claim 4 , wherein the current pseudo universe estimate of the recorded audience is initialized with a universe estimate. 
     
     
         6 . The apparatus of  claim 4 , wherein the reach determiner is to execute the subsequent iteration of the processing operations when a second error corresponding to a comparison of the updated pseudo universe of the recorded audience and the current pseudo universe of the recorded audience does not satisfy the error threshold. 
     
     
         7 . The apparatus of  claim 6 , wherein the reach determiner is to determine the estimate for the reach for the population audience to be at least one of the current population audience reach estimate or the updated population audience reach estimate when the error threshold is satisfied. 
     
     
         8 . The apparatus of  claim 2 , wherein the reach for the population audience is a reach across two or more time intervals corresponding to the marginal ratings for the population audience. 
     
     
         9 . The apparatus of  claim 8 , wherein:
 the pseudo universe estimate of the recorded audience corresponds to a first universe estimate that assumes independence among the marginal ratings for the recorded audience; and   the pseudo universe estimate of the population audience corresponds to a second universe estimate that assumes independency among the marginal ratings for the population audience.   
     
     
         10 . The apparatus of  claim 9 , wherein the reach determiner is to execute the current and subsequent iterations of the processing operations to converge the estimate of reach for the population audience to a reach number corresponding to a deduplicated number of persons exposed to 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 reach determiner is to execute a third iteration of the processing operations when an error corresponding to the subsequent iteration of the processing operations does not satisfy the error threshold, perform a third iteration. 
     
     
         13 . A method to determine reach of media from marginal ratings, the method comprising:
 accessing, by executing an instruction with a processor, marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience;   iteratively, by executing an instruction with the processor, executing processing operations to converge on an output estimate of a reach of the media for the population audience by evaluating an error between an updated population audience reach estimate determined from a current iteration of the processing operations and a prior population audience reach estimate determined from a prior iteration of the processing operations, the updated population audience reach estimate determined based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and   outputting the estimate of the reach for the population audience.   
     
     
         14 . The method of  claim 13 , wherein iteratively estimating the reach for the population audience includes:
 during the current iteration:
 determining a current pseudo universe estimate of a population audience corresponding to the current iteration based on a current pseudo universe estimate of a recorded audience corresponding to the current iteration; 
 determining the updated population audience reach estimate corresponding to the current iteration based on the current pseudo universe of the population audience; 
 determine an updated pseudo universe estimate of a recorded audience; and 
 executing a subsequent iteration of the processing operations when the error between the updated population audience reach estimate and the prior population audience reach estimate does not satisfy an error threshold. 
   
     
     
         15 . The method of  claim 14 , further including initializing the estimate of the reach for the population audience prior to the current iteration. 
     
     
         16 . The method of  claim 15 , further including initializing the current pseudo universe estimate of the recorded audience prior to the current iteration. 
     
     
         17 . The method of  claim 16 , wherein the current pseudo universe estimate of the recorded audience is initialized with a universe estimate. 
     
     
         18 . The method of  claim 16 , further including executing the subsequent iteration of the processing operations when a second error corresponding to a comparison of the updated pseudo universe of the recorded audience and the current pseudo universe of the recorded audience does not satisfy the error threshold. 
     
     
         19 . The method of  claim 18 , further including, when the error threshold is satisfied, determining the estimate for the reach for the population audience to be at least one of the current audience population reach estimate or the updated population reach audience reach estimate when the error threshold is satisfied. 
     
     
         20 . A non-transitory computer readable storage medium comprising instructions which, when executed, cause a machine to at least:
 access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience;   iteratively execute processing operations to converge on an output estimate of a reach of the media for the population audience by evaluating an error between a an updated population audience reach estimate determined from a current iteration of the processing operations and a prior population audience reach estimate determined from a prior iteration of the processing operations, the updated population audience reach estimate determined based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and   output the estimate of the reach for the population audience.