The authors present a comprehensive consideration of the process characteristics of visual search in contexts that vary in their meaningfulness. The authors frame hypotheses regarding process architecture, stopping rule, capacity, and channel independence, using analytic results and a rigorously specified dynamic system to characterize a set of alternative hypotheses that vary along all of thes...

Many machine learning problems, such as K-means, are non-convex optimization problems. Usually they are solved by performing several local searches with random initializations. How many searches should be done? Typically a fixed number is performed, but how do we know it was enough? We present a new stopping rule with non-asymptotic frequentist guarantees, which, to our knowledge, no existing r...

The regularizing properties of the conjugate gradient iteration, applied to the normal equation of a linear ill-posed problem, were established by Nemirovskii in 1986. A seemingly more attractive variant of this algorithm is the minimal error method suggested by King. The present paper analyzes the regularizing properties of the minimal error method. It is shown that the discrepancy principle i...

In the papers (Kaminskas, 1973; Kaminskas and Nemura, 1975) the stopping rule of recursive least squares (RLS) is worked out using the length of the confidence interval for the respective current meaning of the true output signal of a linear dynamic system. The aim of the given paper is the development of techniques for calculating threshold intervals of respective criteria, used in such a stop...

Null hypothesis significance testing (NHST) is the most commonly used statistical methodology in psychology. The probability of achieving a value as extreme or more extreme than the statistic obtained from the data is evaluated, and if it is low enough, the null hypothesis is rejected. However, because common experimental practice often clashes with the assumptions underlying NHST, these calcul...

A process X is observed continuously in time; it behaves like Brownian motion with drift, which changes from zero to a known constant θ > 0 at some time τ that is not directly observable. It is important to detect this change when it happens, and we attempt to do so by selecting a stopping rule T∗ that minimizes the “expected miss” E |T − τ | over all stopping rules T . Assuming that τ has an e...

The expectation maximization algorithm is commonly used to reconstruct images obtained from positron emission tomography sinograms. For images with acceptable signal to noise ratios, iterations are terminated prior to convergence. A new quantitative and reproducible stopping rule is designed and validated on simulations using a Monte-Carlo generated transition matrix with a Poisson noise distri...

This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to ∞. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity o...

We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases—either a discrete alternative or a continuous alternative that can be embedded into an exponential family. For each case, we find a mixture-based stopping rule that is nearly minimax in the sense of minimizing t...

The iteratively regularized Gauss-Newton method is applied to compute the stable solutions to nonlinear ill-posed problems F (x) = y when the data y is given approximately by yδ with ‖yδ − y‖ ≤ δ. In this method, the iterative sequence {xk} is defined successively by xk+1 = x δ k − (αkI +F (xk)F (xk)) ( F (xk) ∗(F (xk)− y) +αk(xk − x0) ) , where x0 := x0 is an initial guess of the exact solutio...