Related papers: Optimal Designs for Two-Stage Inference
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Evaluating blocked randomized experiments from a potential outcomes perspective has two primary branches of work. The first focuses on larger blocks, with multiple treatment and control units in each block. The second focuses on matched…
We improve the existing results of optimal partial profile paired choice designs and provide new designs for situations where the choice set sizes are greater than two. The optimal designs are obtained under the main effects models and the…
In oncology, phase II studies are crucial for clinical development plans as such studies identify potent agents with sufficient activity to continue development in the subsequent phase III trials. Traditionally, phase II studies are…
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…
Forensic scientists are often criticised for the lack of quantitative support for the conclusions of their examinations. While scholars advocate for the use of a Bayes factor to quantify the weight of forensic evidence, it is often…
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…
Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional factorial designs can have better properties than regular designs, but their construction is challenging. Current research on the…
Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. Here we present prediction deviation, a new metric of uncertainty that…
Developing large language models is expensive and involves making decisions with small experiments, typically by evaluating on large, multi-task evaluation suites. In this work, we analyze specific properties which make a benchmark more…
The process of discovery in the physical, biological and medical sciences can be painstakingly slow. Most experiments fail, and the time from initiation of research until a new advance reaches commercial production can span 20 years. This…
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
Noisy training labels can hurt model performance. Most approaches that aim to address label noise assume label noise is independent from the input features. In practice, however, label noise is often feature or \textit{instance-dependent},…
We describe here the general mathematical approach to constructing likelihoods for fitting observed spectra in one or more dimensions with multiple sources, including the effects of systematic uncertainties represented as nuisance…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…
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…
The determination of the sample size required by a crossover trial typically depends on the specification of one or more variance components. Uncertainty about the value of these parameters at the design stage means that there is often a…
A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…
This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator…