A restaurant process with a cocktail bar
A talk in the Keine Reihe series by
Martin Möhle
| Abstract: | The Chinese restaurant process (CRP) has applications in several disciplines,
for example in Bayesian statistics and in mathematical population genetics.
In addition to the features of the two-parameter CRP, the restaurant under
consideration has a cocktail bar and hence allows for a wider range of (bar
and table) occupancy mechanisms. The model depends on three real parameters
$\alpha$, $\theta_1$ and $\theta_2$ fulfilling certain conditions. Results known for the two-parameter CRP are carried over to this model. We study the number of
customers at the cocktail bar, the number of customers at each table and the
number of occupied tables after $n$ customers have entered the restaurant. For
$\alpha>0$ the number of occupied tables, properly scaled, is asymptotically
three-parameter Mittag-Leffler distributed as n tends to infinity. We provide
representations for the two- and three-parameter Mittag-Leffer distribution
leading to efficient random number generators for these distributions. The proofs draw heavily from methods known for exchangeable random partitions, martingale methods known for generalized Pólya urns and results known for the two-parameter CRP. Registration vi via email to popgen.conference@techfak.de |