Discipline: 
Mathematics
Status: 
Available
Level: 
Honours Project
Level: 
Summer Project
Supervisor(s): 
Dr Thomas Taimre

Mixture models are a powerful tool for many statistical applications, including density estimation from data.  
This project focuses on using mixture models in sequential or on-line importance sampling.  A specific application of interest is to the estimation of rare events, which can be viewed as a sequence of non-rare events with respect to a sequence of importance sampling distributions via the chain rule.  It is of interest to explore such schemes, particularly for high-dimensional problems, and provide insight into the type of mixture models suitable, number of mixing components required, and updating rules for mixture parameters which maintain efficiency throughout the sequence of estimation steps.