Samuel Rosa

Comenius University Bratislava · Department of Applied Mathematics and Statistics

Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution. Often, however, there exists a rich set of optimal designs, and the knowledge of this set can lead to substantiall...

Despite the increasing prevalence of vector observations, computation of optimal experimental design for multi-response models has received limited attention. To address this problem within the framework of approximate designs, we introduce mREX, an algorithm that generalizes the randomized exchange algorithm REX (J Am Stat Assoc 115:529, 2020), or...

For many statistical experiments, there exists a multitude of optimal designs. If we consider models with uncorrelated observations and adopt the approach of approximate experimental design, the set of all optimal designs typically forms a multivariate polytope. In this paper, we mathematically characterize the polytope of optimal designs. In parti...

An algorithm is provided for calculating the minimum-volume enclosing ellipsoid (MVEE) for a large dataset stored in a separate database, for which the existing algorithms run out of memory or become prohibitively slow. The focus is on tall datasets, i.e., those consisting of huge numbers of data points of moderate dimensionality. The proposed Big...

We propose an algorithm for computing efficient approximate experimental designs that can be applied in the case of very large grid-like design spaces. Such a design space typically corresponds to the set of all combinations of multiple genuinely discrete factors or densely discretized continuous factors. The proposed algorithm alternates between t...

For computing efficient approximate designs of multifactor experiments, we propose a simple algorithm based on adaptive exploration of the grid of all combinations of factor levels. We demonstrate that the algorithm significantly outperforms several state-of-the-art competitors for problems with discrete, continuous, as well as mixed factors. Impor...

In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for the variances of the responses to depend on the chosen treatments, which introduces heteroscedasticity into th...

D-efficient saturated subsets are natural initial solutions of various algorithms applied in statistics and computational geometry. We propose two greedy heuristics for the construction of D-efficient saturated subsets: an improvement of the method suggested by Galil and Kiefer in the context of D-optimal experimental designs and a modification of...

Fungal spores are an important cause of allergic respiratory diseases worldwide. However, little is known about the intradiurnal pattern of spore concentrations of different fungal spore types in the air of the urban area. In this study, we evaluated bihourly variation in spore concentration of eight predominant fungal spore types in the atmosphere...

The recently introduced weighted optimality criteria for experimental designs allow one to place various emphasis on different parameters or functions of parameters of interest. However, various emphasis on parameter functions can also be expressed by considering the well-developed optimality criteria for estimating a parameter system of interest (...

In clinical trials, the response of a given subject often depends on the selected treatment as well as on some covariates. We study optimal approximate designs of experiments in the models with treatment and covariate effects. We allow for the variances of the responses to depend on the chosen treatments, which introduces heteroscedasticity into th...

Let $\mathcal{F}$ be a set consisting of $n$ real vectors of dimension $m \leq n$. For any saturated, i.e., $m$-element, subset $\mathcal{S}$ of $\mathcal{F}$, let $\mathrm{vol}(\mathcal{S})$ be the volume of the parallelotope formed by the vectors of $\mathcal{S}$. A set $\mathcal{S}^*$ is called a $D$-optimal saturated subset of $\mathcal{F}$, if...

We propose a method of removal of design points that cannot support any E-optimal experimental design of a linear regression model with uncorrelated observations. The proposed method can be used to reduce the size of some large E-optimal design problems such that they can be efficiently solved by semidefinite programming. This paper complements the...

We propose a method for removing design points that cannot support any E-optimal experimental design of a linear regression model with uncorrelated observations. The proposed method can be used to reduce the size of some large -optimal design problems such that they can be efficiently solved by semidefinite programming. This paper complements the r...

We study optimal block designs for comparing a set of test treatments with a control treatment. We provide the class of all E-optimal approximate block designs characterized by simple linear constraints. Employing this characterization, we obtain a class of E-optimal exact designs for treatment-control comparisons for unequal block sizes. In the st...

Consider an experiment consisting of a set of independent trials for comparing a set of treatments. In each trial, one treatment is chosen and the mean response of the trial is equal to the effect of the chosen treatment. We examine the optimal approximate designs for the estimation of a system of treatment contrasts under such model. These approxi...

Suppose that we intend to perform an experiment consisting of a set of independent trials. The mean value of the response of each trial is assumed to be equal to the sum of the effect of the treatment selected for the trial, and some nuisance effects, e.g., the effect of a time trend, or blocking. In this model, we examine optimal approximate desig...

When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for estimating this set of functions of interest. Also, given a weighted eigenvalue-based criterion, w...

Consider an experiment, where a new drug is tested for the first time on human subjects - healthy volunteers. Such experiments are often performed as dose-escalation studies, where a set of increasing doses is pre-selected, individuals are grouped into cohorts and a dose is given to subjects in a cohort only if the preceding dose was already given...