133,036 research outputs found
Response-adaptive dose-finding under model uncertainty
Dose-finding studies are frequently conducted to evaluate the effect of
different doses or concentration levels of a compound on a response of
interest. Applications include the investigation of a new medicinal drug, a
herbicide or fertilizer, a molecular entity, an environmental toxin, or an
industrial chemical. In pharmaceutical drug development, dose-finding studies
are of critical importance because of regulatory requirements that marketed
doses are safe and provide clinically relevant efficacy. Motivated by a
dose-finding study in moderate persistent asthma, we propose response-adaptive
designs addressing two major challenges in dose-finding studies: uncertainty
about the dose-response models and large variability in parameter estimates. To
allocate new cohorts of patients in an ongoing study, we use optimal designs
that are robust under model uncertainty. In addition, we use a Bayesian
shrinkage approach to stabilize the parameter estimates over the successive
interim analyses used in the adaptations. This approach allows us to calculate
updated parameter estimates and model probabilities that can then be used to
calculate the optimal design for subsequent cohorts. The resulting designs are
hence robust with respect to model misspecification and additionally can
efficiently adapt to the information accrued in an ongoing study. We focus on
adaptive designs for estimating the minimum effective dose, although
alternative optimality criteria or mixtures thereof could be used, enabling the
design to address multiple objectives.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS445 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Asymptotic properties of robust complex covariance matrix estimates
In many statistical signal processing applications, the estimation of
nuisance parameters and parameters of interest is strongly linked to the
resulting performance. Generally, these applications deal with complex data.
This paper focuses on covariance matrix estimation problems in non-Gaussian
environments and particularly, the M-estimators in the context of elliptical
distributions. Firstly, this paper extends to the complex case the results of
Tyler in [1]. More precisely, the asymptotic distribution of these estimators
as well as the asymptotic distribution of any homogeneous function of degree 0
of the M-estimates are derived. On the other hand, we show the improvement of
such results on two applications: DOA (directions of arrival) estimation using
the MUSIC (MUltiple SIgnal Classification) algorithm and adaptive radar
detection based on the ANMF (Adaptive Normalized Matched Filter) test
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression provides a general framework for complex
Gaussian and non-Gaussian regression models, with predictors comprising
arbitrary combinations of nonlinear functions and surfaces, spatial effects,
varying coefficients, random effects and further regression terms. The large
flexibility of structured additive regression makes function selection a
challenging and important task, aiming at (1) selecting the relevant
covariates, (2) choosing an appropriate and parsimonious representation of the
impact of covariates on the predictor and (3) determining the required
interactions. We propose a spike-and-slab prior structure for function
selection that allows to include or exclude single coefficients as well as
blocks of coefficients representing specific model terms. A novel
multiplicative parameter expansion is required to obtain good mixing and
convergence properties in a Markov chain Monte Carlo simulation approach and is
shown to induce desirable shrinkage properties. In simulation studies and with
(real) benchmark classification data, we investigate sensitivity to
hyperparameter settings and compare performance to competitors. The flexibility
and applicability of our approach are demonstrated in an additive piecewise
exponential model with time-varying effects for right-censored survival times
of intensive care patients with sepsis. Geoadditive and additive mixed logit
model applications are discussed in an extensive appendix
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations
We derive a posteriori error estimates for the hybridizable discontinuous
Galerkin (HDG) methods, including both the primal and mixed formulations, for
the approximation of a linear second-order elliptic problem on conforming
simplicial meshes in two and three dimensions.
We obtain fully computable, constant free, a posteriori error bounds on the
broken energy seminorm and the HDG energy (semi)norm of the error. The
estimators are also shown to provide local lower bounds for the HDG energy
(semi)norm of the error up to a constant and a higher-order data oscillation
term. For the primal HDG methods and mixed HDG methods with an appropriate
choice of stabilization parameter, the estimators are also shown to provide a
lower bound for the broken energy seminorm of the error up to a constant and a
higher-order data oscillation term. Numerical examples are given illustrating
the theoretical results
Dense and accurate motion and strain estimation in high resolution speckle images using an image-adaptive approach
Digital image processing methods represent a viable and well acknowledged alternative to strain gauges and interferometric techniques for determining full-field displacements and strains in materials under stress. This paper presents an image adaptive technique for dense motion and strain estimation using high-resolution speckle images that show the analyzed material in its original and deformed states. The algorithm starts by dividing the speckle image showing the original state into irregular cells taking into consideration both spatial and gradient image information present. Subsequently the Newton-Raphson digital image correlation technique is applied to calculate the corresponding motion for each cell. Adaptive spatial regularization in the form of the Geman-McClure robust spatial estimator is employed to increase the spatial consistency of the motion components of a cell with respect to the components of neighbouring cells. To obtain the final strain information, local least-squares fitting using a linear displacement model is performed on the horizontal and vertical displacement fields. To evaluate the presented image partitioning and strain estimation techniques two numerical and two real experiments are employed. The numerical experiments simulate the deformation of a specimen with constant strain across the surface as well as small rigid-body rotations present while real experiments consist specimens that undergo uniaxial stress. The results indicate very good accuracy of the recovered strains as well as better rotation insensitivity compared to classical techniques
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