Abstract of "Satiety Estimation for Social Gatherings: Applications to Sunday Game Night"

From: Nathan
To: Game Friends

The number of attendees at an event can be expressed by integrating the attendee flux (people/m²) over the surface of the venue. This can be converted to a volume integral over the apartment (or whatever venue) using the divergence theorem, i.e. the number of attendees of a Game Night (let’s just say that’s the event in question) is equal to the volume integral over the venue (let’s presume, without loss of generality, it’s my apartment) of the divergence of the attendee flow, a representation that admits construction of a finite-element model to predict the change of the attendee number over time, as well as the local concentration of attendees within the apartment.

Local attendee flows are modeled from first principles and updated using Bayesian methods. Each attendee is assigned a prior probability of attendance based on a ratio of invitation events to attendance events; when new data becomes available, such as a positive or negative RSVP or the weekend weather forecast, each attendee’s attendance probability is recomputed using Bayes’ theorem, with the conditional probabilities assigned based on previous iterations of the event. The estimated peak attendee number is continuously updated from the time of invitation to the time of dispersion, i.e. when the attendee number drops down to its baseline value; however, the attendance estimate typically reaches steady-state well before the start of the event this Sunday at 5pm.

The key application of this attendance estimator is to predict the minimum quantity of nachos that must be produced to satisfy every attendee. Future work will involve modeling the type and quantity of each attendee’s snack and/or drink contribution to the event to produce a more accurate nacho estimate.