Sequential Monte Carlo Methods

Abstract

Algorithm 1 Bootstrap particle filter (for i = 1, . . . , N) 1. Initialization (t = 0): (a) Sample x i 0 ∼ p(x0). (b) Set initial weights: w i 0 = 1/N. 2. for t = 1 to T do (a) Resample: sample ancestor indices ai t ∼ C({w j t−1}j=1). (b) Propagate: sample x i t ∼ p(xt | x ai t t−1). x i 0:t = {x ai t 0:t−1, x i t}. (c) Weight: compute w̃ i t = p(yt | x i t) and normalize w i t = w̃ i t/ ∑N j=1 w̃ j t . The ancestor indices {ai t}i=1 allow us to keep track of exactly what happens in each resampling step. Note the bookkeeping added to the propagation step 2b. 2/22 Bookkeeping – ancestral path