Methods and apparatus to estimate population reach from marginals

Abstract

Methods, apparatus, systems, and articles of manufacture are disclosed to estimate population reach from marginals. An example apparatus includes memory including computer readable instructions; and a processor to execute the instructions to: iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media; determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.

What is claimed is: 
     
         1 . An apparatus to determine reach of media from marginal ratings, the apparatus comprising:
 memory including computer readable instructions; and   a processor to execute the instructions to:
 iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media; 
 determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and 
 iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media. 
   
     
     
         2 . The apparatus of  claim 1 , wherein the processor is to output the estimate of the reach of the second media for the population audience and the panel representation value to an application that is to perform an operation based on at least one of the estimate of the reach of the second media for the population audience or the panel representation value. 
     
     
         3 . The apparatus of  claim 1 , wherein the processor is to converge on the output estimate of the reach of the second media for the population audience by:
 determining a subsequent population audience reach estimate from a subsequent iteration, the subsequent population audience reach estimate based on the second marginal ratings for the population audience and the pseudo universe estimate of the population audience of the second media; and   evaluating an error between the subsequent population audience reach estimate determined from the subsequent iteration and an initial population audience reach estimate determined from an initial iteration prior the subsequent iteration.   
     
     
         4 . The apparatus of  claim 3 , wherein the processor is to:
 determine, during the subsequent iteration, a first pseudo universe estimate of the population audience of the second media corresponding to the subsequent iteration based on the panel representation value; and   execute a second subsequent iteration when the error between the subsequent population audience reach estimate and the initial population audience reach estimate does not satisfy an error threshold.   
     
     
         5 . The apparatus of  claim 4 , wherein the processor is to initialize (a) the estimate of the reach for the population audience prior to the initial iteration and (b) the first pseudo universe estimate of the recorded audience prior to the initial iteration. 
     
     
         6 . The apparatus of  claim 5 , wherein the processor is to determine the estimate for the reach for the population audience to be at least one of the subsequent population audience reach estimate or the initial population audience reach estimate when the error threshold is satisfied. 
     
     
         7 . The apparatus of  claim 4 , wherein the reach for the population audience is a reach across two or more time intervals corresponding to the second marginal ratings for the population audience. 
     
     
         8 . The apparatus of  claim 7 , wherein the processor is to execute the subsequent iteration and the second subsequent iteration to converge the estimate of the reach for the population audience to a reach number corresponding to a deduplicated number of persons exposed to the second media across the time intervals. 
     
     
         9 . The apparatus of  claim 8 , wherein the time intervals are quarter hours. 
     
     
         10 . The apparatus of  claim 4 , wherein the processor is to execute a third subsequent iteration when a second error determined during the second subsequent iteration does not satisfy the error threshold. 
     
     
         11 . The apparatus of  claim 1 , wherein the recorded reach for the recorded audience and the first marginal ratings for the recorded audience is provided by a first media provider and the second marginal ratings for the population audience of the second media are provided by a second media provider. 
     
     
         12 . The apparatus of  claim 11 , wherein at least one of (a) the second marginal ratings are different than the first marginal ratings, (b) the second media provider is different from the first media provider, (c) for a second population audience is different from the population audience, or (d) the second media is different from the first media. 
     
     
         13 . A non-transitory computer readable storage medium comprising instructions which, when executed cause one or more processors to at least:
 iteratively converge on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media;   determine a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and   iteratively converge on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.   
     
     
         14 . The computer readable storage medium of  claim 1 , wherein the instructions cause the one or more processors to output the estimate of the reach of the second media for the population audience and the panel representation value to an application that is to perform an operation based on at least one of the estimate of the reach of the second media for the population audience or the panel representation value. 
     
     
         15 . The computer readable storage medium of  claim 1 , wherein the instructions cause the one or more processors to converge on the output estimate of the reach of the second media for the population audience by:
 determining a subsequent population audience reach estimate from a subsequent iteration, the subsequent population audience reach estimate based on the second marginal ratings for the population audience and the pseudo universe estimate of the population audience of the second media; and   evaluating an error between the subsequent population audience reach estimate determined from the subsequent iteration and an initial population audience reach estimate determined from an initial iteration prior the subsequent iteration.   
     
     
         16 . The computer readable storage medium of  claim 3 , wherein the instructions cause the one or more processors to:
 determine, during the subsequent iteration, a first pseudo universe estimate of the population audience of the second media corresponding to the subsequent iteration based on the panel representation value; and   execute a second subsequent iteration when the error between the subsequent population audience reach estimate and the initial population audience reach estimate does not satisfy an error threshold.   
     
     
         17 . The computer readable storage medium of  claim 4 , wherein the instructions cause the one or more processors to initialize (a) the estimate of the reach for the population audience prior to the initial iteration and (b) the first pseudo universe estimate of the recorded audience prior to the initial iteration. 
     
     
         18 . The computer readable storage medium of  claim 5 , wherein the instructions cause the one or more processors to determine the estimate for the reach for the population audience to be at least one of the subsequent population audience reach estimate or the initial population audience reach estimate when the error threshold is satisfied. 
     
     
         19 . The computer readable storage medium of  claim 4 , wherein the reach for the population audience is a reach across two or more time intervals corresponding to the second marginal ratings for the population audience. 
     
     
         20 . A method to determine reach of media from marginal ratings, the method comprising:
 iteratively converging on an output estimate of a pseudo universe estimate of a recorded audience of first media based on (A) a recorded reach for the recorded audience of the first media and (B) first marginal ratings for the recorded audience of the first media;   determining a panel representation value based on the pseudo universe estimate of the recorded audience of the first media; and   iteratively converging on an output estimate of a final reach of second media for a population audience based on the panel representation value and second marginal ratings for the population audience of the second media.