相关论文: A classical measure of evidence for general null h…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
It is possible to obtain a large Bayes Factor (BF) favoring the null hypothesis when both the null and alternative hypotheses have low likelihoods, and there are other hypotheses being ignored that are much more strongly supported by the…
In this article we provide a rebuttal against the possible perception that a single number, such as the Likelihood Ratio, can provide an objective, authoritative or definitive weight of evidence. We also illustrate the extent to which…
Importance sampling is a common technique for Monte Carlo approximation, including Monte Carlo approximation of p-values. Here it is shown that a simple correction of the usual importance sampling p-values creates valid p-values, meaning…
Let $(X,Y)$ be a random variable consisting of an observed feature vector $X\in \mathcal{X}$ and an unobserved class label $Y\in \{1,2,...,L\}$ with unknown joint distribution. In addition, let $\mathcal{D}$ be a training data set…
Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…
\citet{Rosenbaum83ps} introduced the notion of the propensity score and discussed its central role in causal inference with observational studies. Their paper, however, caused a fundamental incoherence with an early paper by…
P-values are widely used in both the social and natural sciences to quantify the statistical significance of observed results. The recent surge of big data research has made the p-value an even more popular tool to test the significance of…
We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…
When a scientist performs an experiment they normally acquire a set of measurements and are expected to demonstrate that their results are "statistically significant" thus confirming whatever hypothesis they are testing. The main method for…
In this paper, we focus on testing multivariate normality using the BHEP test with data that are missing completely at random. Our objective is twofold: first, to gain insight into the asymptotic behavior of BHEP test statistics under two…
In this study, we propose a two-stage procedure for hypothesis testing, where the first stage is conventional hypothesis testing and the second is an equivalence testing procedure using an introduced Empirical Equivalence Bound. In 2016,…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
In this note I go through the `proof' of frequentistic confidence intervals and show what it logically implies concerning the value of a physical quantity given an experimental observation (nothing).
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
The randomized $p$-value, (nonrandomized) mid-$p$-value and abstract randomized $p$-value have all been recommended for testing a null hypothesis whenever the test statistic has a discrete distribution. This paper provides a unifying…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…