Related papers: Analytic Solutions for D-optimal Factorial Designs…
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies…
The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. In this paper we focus on gamma models having a linear predictor without intercept. For a specific…
We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space S. The main motivation (and result) is that if S in R^d is…
This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for $t <= p$, are considered. The designs proposed in this paper minimize the log determinant of…
In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
Given two 2-level factors of interest, a 2^2 split-plot design} (a) takes each of the $2^2=4$ possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d)…
For run sizes that are a multiple of four, the literature offers many two-level designs that are D- and A-optimal for the main-effects model and minimize the aliasing between main effects and interaction effects and among interaction…
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…
Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each…
A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine…
We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a…
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…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we…
Estimating how individual input variables affect the output of a black-box model is a central task in explainable machine learning. However, existing methods suffer from two key limitations: sensitivity to out-of-distribution (OOD)…
The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…