Ionides, King et al. (see e.g. Inference for nonlinear dynamical systems,
PNAS 103) have recently introduced an original approach to perform maximum
likelihood parameter estimation in state-space models which only requires being
able to simulate the latent Markov model according its prior distribution.
Their methodology relies on an approximation of the score vector for general
statistical models based upon an artificial posterior distribution and bypasses
the calculation of any derivative. Building upon this insightful work, we
provide here a simple "derivative-free" estimator of the observed information
matrix based upon this very artificial posterior distribution. However for
state-space models where sequential Monte Carlo computation is required, these
estimators have too high a variance and need to be modified. In this specific
context, we derive new derivative-free estimators of the score vector and
observed information matrix which are computed using sequential Monte Carlo
approximations of smoothed additive functionals associated with a modified
version of the original state-space model.
Description
Derivative-Free Estimation of the Score Vector and Observed Information
Matrix with Application to State-Space Models
%0 Generic
%1 doucet2013derivativefree
%A Doucet, Arnaud
%A Jacob, Pierre E.
%A Rubenthaler, Sylvain
%D 2013
%K computational
%T Derivative-Free Estimation of the Score Vector and Observed Information
Matrix with Application to State-Space Models
%U http://arxiv.org/abs/1304.5768
%X Ionides, King et al. (see e.g. Inference for nonlinear dynamical systems,
PNAS 103) have recently introduced an original approach to perform maximum
likelihood parameter estimation in state-space models which only requires being
able to simulate the latent Markov model according its prior distribution.
Their methodology relies on an approximation of the score vector for general
statistical models based upon an artificial posterior distribution and bypasses
the calculation of any derivative. Building upon this insightful work, we
provide here a simple "derivative-free" estimator of the observed information
matrix based upon this very artificial posterior distribution. However for
state-space models where sequential Monte Carlo computation is required, these
estimators have too high a variance and need to be modified. In this specific
context, we derive new derivative-free estimators of the score vector and
observed information matrix which are computed using sequential Monte Carlo
approximations of smoothed additive functionals associated with a modified
version of the original state-space model.
@misc{doucet2013derivativefree,
abstract = {Ionides, King et al. (see e.g. Inference for nonlinear dynamical systems,
PNAS 103) have recently introduced an original approach to perform maximum
likelihood parameter estimation in state-space models which only requires being
able to simulate the latent Markov model according its prior distribution.
Their methodology relies on an approximation of the score vector for general
statistical models based upon an artificial posterior distribution and bypasses
the calculation of any derivative. Building upon this insightful work, we
provide here a simple "derivative-free" estimator of the observed information
matrix based upon this very artificial posterior distribution. However for
state-space models where sequential Monte Carlo computation is required, these
estimators have too high a variance and need to be modified. In this specific
context, we derive new derivative-free estimators of the score vector and
observed information matrix which are computed using sequential Monte Carlo
approximations of smoothed additive functionals associated with a modified
version of the original state-space model.},
added-at = {2013-04-25T15:51:51.000+0200},
author = {Doucet, Arnaud and Jacob, Pierre E. and Rubenthaler, Sylvain},
biburl = {https://www.bibsonomy.org/bibtex/2420107d186575cc57ef3b53f970443ba/julyanarbel},
description = {Derivative-Free Estimation of the Score Vector and Observed Information
Matrix with Application to State-Space Models},
interhash = {55650bd378fa7a3b24a05a7d2345880d},
intrahash = {420107d186575cc57ef3b53f970443ba},
keywords = {computational},
note = {cite arxiv:1304.5768Comment: Technical report, 18 pages},
timestamp = {2013-04-25T15:51:52.000+0200},
title = {Derivative-Free Estimation of the Score Vector and Observed Information
Matrix with Application to State-Space Models},
url = {http://arxiv.org/abs/1304.5768},
year = 2013
}