Related papers: Statistical hypothesis testing by weak-value ampli…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
The weak value amplification technique has been proved useful for precision metrology in both theory and experiment. To explore the ultimate performance of weak value amplification for multi-parameter estimation, we investigate a general…
A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the…
We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly…
For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values…
Weak measurement with a coherent state pointer and in combination with an orthogonal postselection can lead to a surprising amplification effect, and we give a fire-new physical mechanism about the weak measurement in order to understand…
We show that weak measurement can be used to "amplify" optical nonlinearities at the single- photon level, such that the effect of one properly post-selected photon on a classical beam may be as large as that of many un-post-selected…
This paper presents a hypothesis testing method given independent samples from a number of connected populations. The method is motivated by a forestry project for monitoring change in the strength of lumber. Traditional practice has been…
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed…
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and…
Current quantum computer technology is sufficient to realize weak measurements and the corresponding concept of weak values. We demonstrate how the weak value anomaly can be tested, along with consistency and simultaneity of weak values,…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
In traditional hypothesis testing one must pre-specify the significance level $\alpha$ to bound the `size' of the test: its probability to falsely reject the hypothesis. Indeed, a data-dependent selection of $\alpha$ would generally distort…
Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional…
The large-scale multiple testing inherent to high throughput biological data necessitates very high statistical stringency and thus true effects in data are difficult to detect unless they have high effect sizes. One solution to this…
Genome-wide association analysis has generated much discussion about how to preserve power to detect signals despite the detrimental effect of multiple testing on power. We develop a weighted multiple testing procedure that facilitates the…
P-hacking is prevalent in reality but absent from classical hypothesis testing theory. As a consequence, significant results are much more common than they are supposed to be when the null hypothesis is in fact true. In this paper, we build…