A Hybrid Second-Order Iterated Smoother

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Dao Nguyen*+
• Keywords: iterated smoothing ; SMC ; stochastic approximation ; likelihood free ; derivative free ; second order

Abstract

"Plug and play" inferences, also known as "derivative free" or "likelihood free" inferences are receiving great attention recently due to the fact that in many practical problems, the likelihood is intractable to compute directly. This paper introduce a new plug and play algorithm, namely, hybrid second-order iterated smoother. We use fixed lag smoother to reduce the high variance of the estimator. To improve the speed of convergence, an approximation of the observed information matrix is also proposed. While enjoying greater convergence rate, most observed information matrix approximation methods are computational expensive, especially in plug and play approaches. Therefore, to relax the intensive computation, we only use Hessian approximation for a few initial iterations by adapting sequential Monte Carlo approximations. Due to the special structure of iterated smoothing, we then bypass the sequential Monte Carlo approximations of the Hessian by using the last estimated smoother value at the beginning of the next iteration. In a toy example and in a real data set, we show our proposed approach outweighs the standard approaches in term of convergence rate.