Related papers: Group sequential hypothesis tests with variable gr…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…
We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential…
We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at…
Modern machine learning models may be susceptible to learning spurious correlations that hold on average but not for the atypical group of samples. To address the problem, previous approaches minimize the empirical worst-group risk. Despite…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
In simulation-based optimization, the optimal setting of the input parameters of the objective function can be determined by heuristic optimization techniques. However, when simulators model the stochasticity of real-world problems, their…
We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under…
We consider the problem of collaborative distributed estimation in a large scale sensor network with statistically dependent sensor observations. In collaborative setup, the aim is to maximize the overall estimation performance by modeling…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…
We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the design of experiments in such studies to assume uncorrelated errors for each subject. In…
We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Detection of defective members of large populations has been widely studied in the statistics community under the name "group testing", a problem which dates back to World War II when it was suggested for syphilis screening. There the main…
Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date,…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
Stochastic Gradient Descent (SGD) and its variants are almost universally used to train neural networks and to fit a variety of other parametric models. An important hyperparameter in this context is the batch size, which determines how…