# Towards Automatic Calibration of the Number of State Particles Within the SMC^2 Algorithm

by N. Chopin, J. Ridgway, M. Gerber & O. Papaspiliopoulos

SMC2 is an efficient algorithm for sequential estimation and state inference of state-space models. It generates Nθ parameter particles θm, and, for each θm, it runs a particle filter of size Nx (i.e. at each time step, Nx particles are generated in the state space ). We discuss how to automatically calibrate Nx in the course of the algorithm. Our approach relies on conditional Sequential Monte Carlo updates, monitoring the state of the pseudo random number generator and on an estimator of the variance of the unbiased estimate of the likelihood that is produced by the particle filters, which is obtained using nonparametric regression techniques. We observe that our approach is both less CPU intensive and with smaller Monte Carlo errors than the initial version of SMC2.