Determining metrics characterizing numbers of unique members of media audiences
Example methods disclosed herein include accessing a query requesting a metric associated with a number of unique members of an audience of media over an aggregate monitoring interval corresponding to a plurality of component monitoring intervals. Disclosed example methods also include determining respective aggregate interval probability distributions modeling likelihoods of respective monitored individuals being exposed to the media during the aggregate monitoring interval, a first one of the aggregate interval probability distributions for a first one of the monitored individuals being determined by combining parameters of respective component interval probability distributions modeling likelihoods of the first one of the monitored individuals being exposed to the media during respective ones of the component monitoring intervals. Disclosed example methods further include evaluating an audience-level probability distribution determined from the aggregate interval probability distributions to determine the metric to transmit to the computing device in response to the query.
1. An apparatus comprising:
memory;
computer readable instructions; and
processor circuitry to execute the computer readable instructions to at least:
estimate parameters of respective sets of first probability distributions for corresponding monitored individuals based on impression data collected responsive to beacon requests from client devices that accessed instances of media, a first one of the sets of the first probability distributions to model likelihoods of exposure by a first one of the monitored individuals to ones of the instances of media during ones of a plurality of component time intervals;
parse a query from a compute device to identify a first one of the instances of media, an aggregate time interval and an audience metric to be returned in response to the query;
combine the parameters of ones of the sets of first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval to determine a second probability distribution to model exposure of an audience to the first one of the instances of media during the aggregate time interval; and
cause transmission of a response including a value of the audience metric to the compute device in response to the query, the value based on the second probability distribution.
2. The apparatus of claim 1 , wherein to combine the parameters, the processor circuitry is to:
identify a first subset of the first one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval;
combine first parameters of ones of the first probability distributions included in the first subset to determine a third probability distribution to model exposure of the first one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determine the second probability distribution based on the third probability distribution.
3. The apparatus of claim 2 , wherein to combine the parameters, the processor circuitry is to:
identify a second subset of a second one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval, the second one of the sets of the first probability distributions to model likelihoods of exposure by a second one of the monitored individuals to the ones of the instances of media during the ones of the plurality of component time intervals;
combine second parameters of ones of the first probability distributions included in the second subset to determine a fourth probability distribution to model exposure of the second one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determine the second probability distribution based on the third probability distribution and the fourth probability distribution.
4. The apparatus of claim 3 , wherein the processor circuitry is to numerically convolve the third probability distribution and the fourth probability distribution to determine the second probability distribution.
5. The apparatus of claim 1 , wherein the processor circuitry is to determine the value of the of the audience metric based on a numerical integration of the second probability distribution.
6. The apparatus of claim 5 , wherein the processor circuitry is to perform the numerical integration based on a query value included in the query.
7. The apparatus of claim 6 , wherein the query value is a first query value, and the processor circuitry is to parse the query to determine the first query value and a second query value, the second query value to identify the audience metric to be returned in response to the query, the audience metric to be one of a plurality of possible audience metrics identified by a corresponding plurality of possible values of the second query value.
8. At least one non-transitory computer readable medium comprising computer readable instructions that, when executed, cause at least one processor to at least:
estimate parameters of respective sets of first probability distributions for corresponding monitored individuals based on impression data collected responsive to beacon requests from client devices that accessed instances of media, a first one of the sets of the first probability distributions to model likelihoods of exposure by a first one of the monitored individuals to ones of the instances of media during ones of a plurality of component time intervals;
parse a query from a compute device to identify a first one of the instances of media, an aggregate time interval and an audience metric to be returned in response to the query;
combine the parameters of ones of the sets of first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval to determine a second probability distribution to model exposure of an audience to the first one of the instances of media during the aggregate time interval; and
cause transmission of a response including a value of the audience metric to the compute device in response to the query, the value based on the second probability distribution.
9. The at least one non-transitory computer readable medium of claim 8 , wherein to combine the parameters, the instructions cause the at least one processor to:
identify a first subset of the first one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval;
combine first parameters of ones of the first probability distributions included in the first subset to determine a third probability distribution to model exposure of the first one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determine the second probability distribution based on the third probability distribution.
10. The at least one non-transitory computer readable medium of claim 9 , wherein to combine the parameters, the instructions cause the at least one processor to:
identify a second subset of a second one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval, the second one of the sets of the first probability distributions to model likelihoods of exposure by a second one of the monitored individuals to the ones of the instances of media during the ones of the plurality of component time intervals;
combine second parameters of ones of the first probability distributions included in the second subset to determine a fourth probability distribution to model exposure of the second one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determine the second probability distribution based on the third probability distribution and the fourth probability distribution.
11. The at least one non-transitory computer readable medium of claim 10 , wherein the instructions cause the at least one processor to numerically convolve the third probability distribution and the fourth probability distribution to determine the second probability distribution.
12. The at least one non-transitory computer readable medium of claim 8 , wherein the instructions cause the at least one processor to determine the value of the of the audience metric based on a numerical integration of the second probability distribution.
13. The at least one non-transitory computer readable medium of claim 12 , wherein the instructions cause the at least one processor to perform the numerical integration based on a query value included in the query.
14. The at least one non-transitory computer readable medium of claim 13 , wherein the query value is a first query value, and the instructions cause the at least one processor to parse the query to determine the first query value and a second query value, the second query value to identify the audience metric to be returned in response to the query, the audience metric to be one of a plurality of possible audience metrics identified by a corresponding plurality of possible values of the second query value.
15. A method comprising:
estimating, by executing an instruction with at least one processor, parameters of respective sets of first probability distributions for corresponding monitored individuals based on impression data collected responsive to beacon requests from client devices that accessed instances of media, a first one of the sets of the first probability distributions to model likelihoods of exposure by a first one of the monitored individuals to ones of the instances of media during ones of a plurality of component time intervals;
parsing a query from a compute device to identify a first one of the instances of media, an aggregate time interval and an audience metric to be returned in response to the query;
combining, by executing an instruction with the at least one processor, the parameters of ones of the sets of first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval to determine a second probability distribution to model exposure of an audience to the first one of the instances of media during the aggregate time interval; and
transmitting a response including a value of the audience metric to the compute device in response to the query, the value based on the second probability distribution.
16. The method of claim 15 , wherein the combining includes:
identifying a first subset of the first one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval;
combining first parameters of ones of the first probability distributions included in the first subset to determine a third probability distribution to model exposure of the first one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determining the second probability distribution based on the third probability distribution.
17. The method of claim 16 , wherein the combining includes:
identifying a second subset of a second one of the sets of the first probability distributions corresponding to the first one of the instances of media and the ones of the component time intervals included in aggregate time interval, the second one of the sets of the first probability distributions to model likelihoods of exposure by a second one of the monitored individuals to the ones of the instances of media during the ones of the plurality of component time intervals;
combining second parameters of ones of the first probability distributions included in the second subset to determine a fourth probability distribution to model exposure of the second one of the monitored individuals to the first one of the instances of media during the aggregate time interval; and
determining the second probability distribution based on the third probability distribution and the fourth probability distribution.
18. The method of claim 17 , wherein the determining of the second probability distribution includes numerically convolving the third probability distribution and the fourth probability distribution to determine the second probability distribution.
19. The method of claim 15 , further including determining the value of the of the audience metric based on a numerical integration of the second probability distribution, the numerical integration based on a query value included in the query.
20. The method of claim 19 , wherein the query value is a first query value, and the parsing includes parsing the query to determine the first query value and a second query value, the second query value to identify the audience metric to be returned in response to the query, the audience metric to be one of a plurality of possible audience metrics identified by a corresponding plurality of possible values of the second query value.