34,972 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
A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements
Multipath propagation causes major impairments to Global
Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step
Approximate Bayesian Computation for a Class of Time Series Models
In the following article we consider approximate Bayesian computation (ABC)
for certain classes of time series models. In particular, we focus upon
scenarios where the likelihoods of the observations and parameter are
intractable, by which we mean that one cannot evaluate the likelihood even
up-to a positive unbiased estimate. This paper reviews and develops a class of
approximation procedures based upon the idea of ABC, but, specifically
maintains the probabilistic structure of the original statistical model. This
idea is useful, in that it can facilitate an analysis of the bias of the
approximation and the adaptation of established computational methods for
parameter inference. Several existing results in the literature are surveyed
and novel developments with regards to computation are given
Methods Studies on System Identification from Transient Rotor Tests
Some of the more important methods are discussed that have been used or proposed for aircraft parameter identification. The methods are classified into two groups: Equation error or regression estimates and Bayesian estimates and their derivatives that are based on probabilistic concepts. In both of these two groups the cost function can be optimized either globally over the entire time span of the transient, or sequentially, leading to the formulation of optimum filters. Identifiability problems and the validation of the estimates are briefly outlined, and applications to lifting rotors are discussed
Marginal likelihoods in phylogenetics: a review of methods and applications
By providing a framework of accounting for the shared ancestry inherent to
all life, phylogenetics is becoming the statistical foundation of biology. The
importance of model choice continues to grow as phylogenetic models continue to
increase in complexity to better capture micro and macroevolutionary processes.
In a Bayesian framework, the marginal likelihood is how data update our prior
beliefs about models, which gives us an intuitive measure of comparing model
fit that is grounded in probability theory. Given the rapid increase in the
number and complexity of phylogenetic models, methods for approximating
marginal likelihoods are increasingly important. Here we try to provide an
intuitive description of marginal likelihoods and why they are important in
Bayesian model testing. We also categorize and review methods for estimating
marginal likelihoods of phylogenetic models, highlighting several recent
methods that provide well-behaved estimates. Furthermore, we review some
empirical studies that demonstrate how marginal likelihoods can be used to
learn about models of evolution from biological data. We discuss promising
alternatives that can complement marginal likelihoods for Bayesian model
choice, including posterior-predictive methods. Using simulations, we find one
alternative method based on approximate-Bayesian computation (ABC) to be
biased. We conclude by discussing the challenges of Bayesian model choice and
future directions that promise to improve the approximation of marginal
likelihoods and Bayesian phylogenetics as a whole.Comment: 33 pages, 3 figure
Resampling: an improvement of Importance Sampling in varying population size models
Sequential importance sampling algorithms have been defined to estimate
likelihoods in models of ancestral population processes. However, these
algorithms are based on features of the models with constant population size,
and become inefficient when the population size varies in time, making
likelihood-based inferences difficult in many demographic situations. In this
work, we modify a previous sequential importance sampling algorithm to improve
the efficiency of the likelihood estimation. Our procedure is still based on
features of the model with constant size, but uses a resampling technique with
a new resampling probability distribution depending on the pairwise composite
likelihood. We tested our algorithm, called sequential importance sampling with
resampling (SISR) on simulated data sets under different demographic cases. In
most cases, we divided the computational cost by two for the same accuracy of
inference, in some cases even by one hundred. This study provides the first
assessment of the impact of such resampling techniques on parameter inference
using sequential importance sampling, and extends the range of situations where
likelihood inferences can be easily performed
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