23,475 research outputs found
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
Cramer-Rao Bounds for Joint RSS/DoA-Based Primary-User Localization in Cognitive Radio Networks
Knowledge about the location of licensed primary-users (PU) could enable
several key features in cognitive radio (CR) networks including improved
spatio-temporal sensing, intelligent location-aware routing, as well as aiding
spectrum policy enforcement. In this paper we consider the achievable accuracy
of PU localization algorithms that jointly utilize received-signal-strength
(RSS) and direction-of-arrival (DoA) measurements by evaluating the Cramer-Rao
Bound (CRB). Previous works evaluate the CRB for RSS-only and DoA-only
localization algorithms separately and assume DoA estimation error variance is
a fixed constant or rather independent of RSS. We derive the CRB for joint
RSS/DoA-based PU localization algorithms based on the mathematical model of DoA
estimation error variance as a function of RSS, for a given CR placement. The
bound is compared with practical localization algorithms and the impact of
several key parameters, such as number of nodes, number of antennas and
samples, channel shadowing variance and correlation distance, on the achievable
accuracy are thoroughly analyzed and discussed. We also derive the closed-form
asymptotic CRB for uniform random CR placement, and perform theoretical and
numerical studies on the required number of CRs such that the asymptotic CRB
tightly approximates the numerical integration of the CRB for a given
placement.Comment: 20 pages, 11 figures, 1 table, submitted to IEEE Transactions on
Wireless Communication
Linear theory for filtering nonlinear multiscale systems with model error
We study filtering of multiscale dynamical systems with model error arising
from unresolved smaller scale processes. The analysis assumes continuous-time
noisy observations of all components of the slow variables alone. For a linear
model with Gaussian noise, we prove existence of a unique choice of parameters
in a linear reduced model for the slow variables. The linear theory extends to
to a non-Gaussian, nonlinear test problem, where we assume we know the optimal
stochastic parameterization and the correct observation model. We show that
when the parameterization is inappropriate, parameters chosen for good filter
performance may give poor equilibrium statistical estimates and vice versa.
Given the correct parameterization, it is imperative to estimate the parameters
simultaneously and to account for the nonlinear feedback of the stochastic
parameters into the reduced filter estimates. In numerical experiments on the
two-layer Lorenz-96 model, we find that parameters estimated online, as part of
a filtering procedure, produce accurate filtering and equilibrium statistical
prediction. In contrast, a linear regression based offline method, which fits
the parameters to a given training data set independently from the filter,
yields filter estimates which are worse than the observations or even divergent
when the slow variables are not fully observed
Gap bootstrap methods for massive data sets with an application to transportation engineering
In this paper we describe two bootstrap methods for massive data sets. Naive
applications of common resampling methodology are often impractical for massive
data sets due to computational burden and due to complex patterns of
inhomogeneity. In contrast, the proposed methods exploit certain structural
properties of a large class of massive data sets to break up the original
problem into a set of simpler subproblems, solve each subproblem separately
where the data exhibit approximate uniformity and where computational
complexity can be reduced to a manageable level, and then combine the results
through certain analytical considerations. The validity of the proposed methods
is proved and their finite sample properties are studied through a moderately
large simulation study. The methodology is illustrated with a real data example
from Transportation Engineering, which motivated the development of the
proposed methods.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS587 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Parameter Estimation and Uncertainty Quantication for an Epidemic Model
We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )—an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used to investigate how the frequency at which data is sampled affects the estimation process and how the accuracy and uncertainty of estimates improves as data is collected over the course of an outbreak. We assess the informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. This technique can be used to design data sampling schemes in more general contexts
Advances in forecast evaluation
This paper surveys recent developments in the evaluation of point forecasts. Taking West’s (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West’s writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multistep forecasts can be improved with the judicious choice of HAC estimator (it can); and the extension of West’s (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting ; Time-series analysis
Real-time flutter analysis
The important algorithm issues necessary to achieve a real time flutter monitoring system; namely, the guidelines for choosing appropriate model forms, reduction of the parameter convergence transient, handling multiple modes, the effect of over parameterization, and estimate accuracy predictions, both online and for experiment design are addressed. An approach for efficiently computing continuous-time flutter parameter Cramer-Rao estimate error bounds were developed. This enables a convincing comparison of theoretical and simulation results, as well as offline studies in preparation for a flight test. Theoretical predictions, simulation and flight test results from the NASA Drones for Aerodynamic and Structural Test (DAST) Program are compared
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