"Submission to the review on “Higher Education Funding and Student Finance”

Neil Shephard
	Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6EE, UK
	and Department of Economics, University of Oxford


Abstract

A key ingredient of many particle filters is the use of the sampling importance resampling
algorithm (SIR), which transforms a sample of weighted draws from a prior distribution into
equally weighted draws from a posterior distribution. We give a novel analysis of the SIR
algorithm and analyse the jittered generalisation of SIR, showing that existing implementations
of jittering lead to marked inferior behaviour over the basic SIR algorithm. We show how
jittering can be designed to improve the performance of the SIR.

Keywords: Importance sampling, particle Żlter, random numbers, sampling importance resam-
pling, state space models

JEL Classifications: C01, C14, C32