6,630 research outputs found
Risk-sensitive filtering and smoothing for continuous-time Markov processes
Ā© 2005 IEEE.We consider risk sensitive filtering and smoothing for a dynamical system whose output is a vector process in 2. The components of the observation process are a Markov process observed through a Brownian motion and a Markov process observed through a Poisson process. Risk-sensitive filters for the robust estimation of an indirectly observed Markov state processes are given. These filters are stochastic partial differential equations for which robust discretizations are obtained. Computer simulations are given which demonstrate the benefits of risk sensitive filtering.W. Paul Malcolm, Robert J. Elliott, and Matthew R. James
Active Classification for POMDPs: a Kalman-like State Estimator
The problem of state tracking with active observation control is considered
for a system modeled by a discrete-time, finite-state Markov chain observed
through conditionally Gaussian measurement vectors. The measurement model
statistics are shaped by the underlying state and an exogenous control input,
which influence the observations' quality. Exploiting an innovations approach,
an approximate minimum mean-squared error (MMSE) filter is derived to estimate
the Markov chain system state. To optimize the control strategy, the associated
mean-squared error is used as an optimization criterion in a partially
observable Markov decision process formulation. A stochastic dynamic
programming algorithm is proposed to solve for the optimal solution. To enhance
the quality of system state estimates, approximate MMSE smoothing estimators
are also derived. Finally, the performance of the proposed framework is
illustrated on the problem of physical activity detection in wireless body
sensing networks. The power of the proposed framework lies within its ability
to accommodate a broad spectrum of active classification applications including
sensor management for object classification and tracking, estimation of sparse
signals and radar scheduling.Comment: 38 pages, 6 figure
Mismatched Quantum Filtering and Entropic Information
Quantum filtering is a signal processing technique that estimates the
posterior state of a quantum system under continuous measurements and has
become a standard tool in quantum information processing, with applications in
quantum state preparation, quantum metrology, and quantum control. If the
filter assumes a nominal model that differs from reality, however, the
estimation accuracy is bound to suffer. Here I derive identities that relate
the excess error caused by quantum filter mismatch to the relative entropy
between the true and nominal observation probability measures, with one
identity for Gaussian measurements, such as optical homodyne detection, and
another for Poissonian measurements, such as photon counting. These identities
generalize recent seminal results in classical information theory and provide
new operational meanings to relative entropy, mutual information, and channel
capacity in the context of quantum experiments.Comment: v1: first draft, 8 pages, v2: added introduction and more results on
mutual information and channel capacity, 12 pages, v3: minor updates, v4:
updated the presentatio
Evaluating Structural Models for the U.S. Short Rate Using EMM and Particle Filters
We combine the efficient method of moments with appropriate algorithms from the optimal filtering literature to study a collection of models for the U.S. short rate. Our models include two continuous-time stochastic volatility models and two regime switching models, which provided the best fit in previous work that examined a large collection of models. The continuous-time stochastic volatility models fall into the class of nonlinear, non-Gaussian state space models for which we apply particle filtering and smoothing algorithms. Our results demonstrate the effectiveness of the particle filter for continuous-time processes. Our analysis also provides an alternative and complementary approach to the reprojection technique of Gallant and Tauchen (1998) for studying the dynamics of volatility.
Locally adaptive smoothing with Markov random fields and shrinkage priors
We present a locally adaptive nonparametric curve fitting method that
operates within a fully Bayesian framework. This method uses shrinkage priors
to induce sparsity in order-k differences in the latent trend function,
providing a combination of local adaptation and global control. Using a scale
mixture of normals representation of shrinkage priors, we make explicit
connections between our method and kth order Gaussian Markov random field
smoothing. We call the resulting processes shrinkage prior Markov random fields
(SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior
distribution of model parameters because this method provides superior
performance in the presence of the high dimensionality and strong parameter
correlations exhibited by our models. We compare the performance of three prior
formulations using simulated data and find the horseshoe prior provides the
best compromise between bias and precision. We apply SPMRF models to two
benchmark data examples frequently used to test nonparametric methods. We find
that this method is flexible enough to accommodate a variety of data generating
models and offers the adaptive properties and computational tractability to
make it a useful addition to the Bayesian nonparametric toolbox.Comment: 38 pages, to appear in Bayesian Analysi
- ā¦