Related papers: The relative efficiency of sequential tests
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
In modern scientific experiments, we frequently encounter data that have large dimensions, and in some experiments, such high dimensional data arrive sequentially rather than full data being available all at a time. We develop multiple…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…
This paper explores an approach to Bayesian sample size determination in clinical trials. The approach falls into the category of what is often called "proper Bayesian", in that it does not mix frequentist concepts with Bayesian ones. A…
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine properties of the classical gamma function.
This paper deals with the issue of testing hypothesis in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These…
We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
Traditional accelerated life test plans are typically based on optimizing the C-optimality for minimizing the variance of an interested quantile of the lifetime distribution. The traditional methods rely on some specified planning values…
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…
The seminal work of Morgan and Rubin (2012) considers rerandomization for all the units at one time. In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be…
Selective classification, in which models can abstain on uncertain predictions, is a natural approach to improving accuracy in settings where errors are costly but abstentions are manageable. In this paper, we find that while selective…
We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
Time-to-event endpoints show an increasing popularity in phase II cancer trials. The standard statistical tool for such one-armed survival trials is the one-sample log-rank test. Its distributional properties are commonly derived in the…
We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…
We consider a Bayesian framework for estimating the sample size of a clinical trial. The new approach, called BESS, is built upon three pillars: Sample size of the trial, Evidence from the observed data, and Confidence of the final decision…