Related papers: Support points of locally optimal designs for nonl…
Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…
Consider a logistic partially linear model, in which the logit of the mean of a binary response is related to a linear function of some covariates and a nonparametric function of other covariates. We derive simple, doubly robust estimators…
We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…
Designing efficient experiments under practical constraints is critical in both scientific research and industrial practice. Focusing on minimizing the average variance of the parameter estimates, A-optimal designs show advantages in…
Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…
Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer…
In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary…
Performing a computer experiment can be viewed as observing a mapping between the model parameters and the corresponding model outputs predicted by the computer model. In view of this, experimental design for computer experiments can be…
In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
For frequentist settings in which parameter randomness represents variability rather than uncertainty, the ideal measure of the support for one hypothesis over another is the difference in the posterior and prior log odds. For situations in…
Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that "all models are wrong", but little formal guidance exists on how to…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…