Related papers: Design of Order-of-Addition Experiments
In a mixture experiment, we study the behavior and properties of $m$ mixture components, where the primary focus is on the proportions of the components that make up the mixture rather than the total amount. Mixture-amount experiments are…
We introduce systematic methods to create optimal designs for order-of-addition (OofA) experiments, those that study the order in which $m$ components are applied---for example, the order in which chemicals are added to a reaction or layers…
In an order-of-addition (OofA) experiment, the sequence of m different components can significantly impact the experiment's response. In many OofA experiments, the components are subject to constraints, where certain orders are impossible.…
In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence…
Mixture experiments often involve process variables, such as different chemical reactors in a laboratory or varying mixing speeds in a production line. Organizing the runs in orthogonal blocks allows the mixture model to be fitted…
We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a…
Optimal block designs in small blocks are explored when the treatments have a natural ordering and interest lies in comparing consecutive pairs of treatments. We first develop an approximate theory which leads to a convenient multiplicative…
The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system or treatment. Such experiments may be analysed by various regression models, the most popular ones being based on…
Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which…
Order-of-addition experiments arise when the response depends on the order in which a set of components is added. Since the number of possible orders increases factorially with the number of components, full permutation designs are rarely…
We consider repeated measurement designs when a residual or carry-over effect may be present in at most one later period. Since assuming an additive model may be unrealistic for some applications and leads to biased estimation of treatment…
A combinatorial intervention, consisting of multiple treatments applied to a single unit with potentially interactive effects, has substantial applications in fields such as biomedicine, engineering, and beyond. Given $p$ possible…
Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
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…
The study of combinations of drugs/drug-schedules gained increasing attention in various therapeutic areas recently. In oncology, the aim of phase I combination clinical trial is to find the maximum tolerated combination (MTC). Many…
Well-partial orders, and the ordinal invariants used to measure them, are relevant in set theory, program verification, proof theory and many other areas of computer science and mathematics. In this article we focus on one of the most…
We study the problem of causal structure learning over a set of random variables when the experimenter is allowed to perform at most $M$ experiments in a non-adaptive manner. We consider the optimal learning strategy in terms of minimizing…
The treatment assignment mechanism in a randomized clinical trial can be optimized for statistical efficiency within a specified class of randomization mechanisms. Optimal designs of this type have been characterized in terms of the…