Methods and apparatus to estimate audience sizes and durations of media accesses

A method comprising:

• storing, in a panel database of an audience measurement system, monitoring data representative of media to which panelists were exposed to, the monitoring data received from a plurality of panel meters located at panelist households, the plurality of panel meters comprising on-device meter systems that locally collect web browsing information;
• receiving, by an impression collection server of the audience measurement system, census impressions from a plurality of non-panelist devices;
• storing, by the impression collection server, impression-related data indicative of the census impressions in a census database, wherein execution of beacon instructions by web browsers of the non-panelist devices causes the non-panelist devices to send impression requests to the impression collection server via the internet and to provide device identifiers and media identifiers in the impression requests, wherein the media identifiers enable the audience measurement system to identify media accessed via the non-panelist devices, wherein the impression requests are implemented as hypertext transfer protocol (HTTP) requests;
• obtaining, by a computing system of the audience measurement system, panelist data corresponding to a panel audience from the panel database, the panelist data including:
• (i) a first panel audience size and a first panel event duration for a first website and (ii) a second panel audience size and a second panel event duration for a second website, the first panel audience size and the second panel audience size obtained using panel meters;
• obtaining, by the computing system, census data corresponding to a census audience from the census database, the census data including a first census event duration for the first website, a second census event duration for the second website, and a total census audience size for the first website and the second website;
• determining, by the computing system, a first census audience size for the first website and a second census audience size for the second website by:
• selecting constraint equations from a memory, the constraint equations corresponding to one or more events, the one or more events corresponding to the first website and the second website;
• and
• selecting by an auxiliary equation from the memory, the auxiliary equation including (a) the total census audience size, (b) a first universe estimate corresponding to the census audience size, and (c) the first census audience size and the second census audience size;
• causing, by the computing system, storage of the first audience size and the second audience size in a database after determining the first census audience size and the second census audience size based on the constraint equations and the auxiliary equation;
• and
• generating a report including the first audience size and the second audience size.

A non-transitory computer readable medium comprising instructions that when executed by a computing system cause the computing system to:

• store, in a panel database of an audience measurement system, monitoring data representative of media to which panelists were exposed to, the monitoring data received from a plurality of panel meters located at panelist households, the plurality of panel meters comprising on-device meter systems that locally collect web browsing information;
• receive, by an impression collection server of the audience measurement system, census impressions from a plurality of non-panelist devices;
• store, by the impression collection server, impression-related data indicative of the census impressions in a census database, wherein execution of beacon instructions by web browsers of the non-panelist devices causes the non-panelist devices to send impression requests to the impression collection server via the internet and to provide device identifiers and media identifiers in the impression requests, wherein the media identifiers enable the audience measurement system to identify media accessed via the non-panelist devices, wherein the impression requests are implemented as hypertext transfer protocol (HTTP) requests;
• obtain panelist data corresponding to a panel audience from the panel database, the panelist data including:
• (i) a first panel audience size and a first panel event duration for a first website and (ii) a second panel audience size and a second panel event duration for a second website;
• obtain census data corresponding to a census audience from the census database, the census data including a first census event duration for the first website, a second census event duration for the second website, and a total census audience size for the first website and the second website;
• determine a first census audience size for the first website and a second census audience size for the second website by:
• selecting constraint equations from computer memory, the constraint equations corresponding to one or more events, the one or more events corresponding to the first website and the second website;
• and
• selecting an auxiliary equation from the computer memory, the auxiliary equation including (a) the total census audience size, (b) a first universe estimate corresponding to the census audience size, and (c) the first census audience size and the second census audience size;
• cause storage of the first audience size and the second audience size in a database after determining the first census audience size and the second census audience size based on the constraint equations and the auxiliary equation;
• and
• generate a report including the first audience size and the second audience size.