9,616 research outputs found
Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost
Poyiadjis et al. (2011) show how particle methods can be used to estimate
both the score and the observed information matrix for state space models.
These methods either suffer from a computational cost that is quadratic in the
number of particles, or produce estimates whose variance increases
quadratically with the amount of data. This paper introduces an alternative
approach for estimating these terms at a computational cost that is linear in
the number of particles. The method is derived using a combination of kernel
density estimation, to avoid the particle degeneracy that causes the
quadratically increasing variance, and Rao-Blackwellisation. Crucially, we show
the method is robust to the choice of bandwidth within the kernel density
estimation, as it has good asymptotic properties regardless of this choice. Our
estimates of the score and observed information matrix can be used within both
online and batch procedures for estimating parameters for state space models.
Empirical results show improved parameter estimates compared to existing
methods at a significantly reduced computational cost. Supplementary materials
including code are available.Comment: Accepted to Journal of Computational and Graphical Statistic
Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation
This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values depending on the mode of traffic operation – free flowing, congested or faulty – making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain. This study proposes an expectation-maximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inference algorithms and an online particle filter. The authors also develop an EM parameter estimation that, in combination with a time-window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator
Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm
Online variants of the Expectation Maximization (EM) algorithm have recently
been proposed to perform parameter inference with large data sets or data
streams, in independent latent models and in hidden Markov models.
Nevertheless, the convergence properties of these algorithms remain an open
problem at least in the hidden Markov case. This contribution deals with a new
online EM algorithm which updates the parameter at some deterministic times.
Some convergence results have been derived even in general latent models such
as hidden Markov models. These properties rely on the assumption that some
intermediate quantities are available in closed form or can be approximated by
Monte Carlo methods when the Monte Carlo error vanishes rapidly enough. In this
paper, we propose an algorithm which approximates these quantities using
Sequential Monte Carlo methods. The convergence of this algorithm and of an
averaged version is established and their performance is illustrated through
Monte Carlo experiments
Sequential Bayesian inference for static parameters in dynamic state space models
A method for sequential Bayesian inference of the static parameters of a
dynamic state space model is proposed. The method is based on the observation
that many dynamic state space models have a relatively small number of static
parameters (or hyper-parameters), so that in principle the posterior can be
computed and stored on a discrete grid of practical size which can be tracked
dynamically. Further to this, this approach is able to use any existing
methodology which computes the filtering and prediction distributions of the
state process. Kalman filter and its extensions to non-linear/non-Gaussian
situations have been used in this paper. This is illustrated using several
applications: linear Gaussian model, Binomial model, stochastic volatility
model and the extremely non-linear univariate non-stationary growth model.
Performance has been compared to both existing on-line method and off-line
methods
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