統計学輪講（第１５回）

統計学輪講（第15回）
日時      2013年10月08日(火)    14時50分～15時40分
場所      経済学部新棟３階第３教室
講演者    李 勝恵 (経済M1)
演題      SMC^2: an efficient algorithm for sequential analysis of state space model

概要
In the state space models, likelihood increments are intractable in most cases, 
but they may be unbiasedly estimated by a particle filter in the x-dimension, 
for any fixed parameter.
This motivates the SMC^2 algorithm that is proposed in the paper: a sequential 
Monte Carlo algorithm, defined in the theta-dimension, which propagates and 
resamples many particle filters in the x-dimension.
In contrast, the particle MCMC framework thata has been developed by Andrieu 
allow us to design appropriate MCMC rejuvenation steps. Thus, the theta-particles 
target the correct posterior distribution at each iteration t, despite the 
intractability of the likelihood increments.

We will mainly talk about SMC^2 algorithm in both sequential and non-sequential applications.
and we contrast SMC^2 with various competing methods, both conceptually and emprically 
through a detailed simulation study, and based on particularly challenging examples.