Related papers: The posterior probability of a null hypothesis giv…
A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…
A non parametric method based on the empirical likelihood is proposed for detecting the change in the coefficients of high-dimensional linear model where the number of model variables may increase as the sample size increases. This amounts…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
Global hypothesis tests are a useful tool in the context of, e.g, clinical trials, genetic studies or meta analyses, when researchers are not interested in testing individual hypotheses, but in testing whether none of the hypotheses is…
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a…
Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…
Recent research has generated hope that inference scaling, such as resampling solutions until they pass verifiers like unit tests, could allow weaker models to match stronger ones. Beyond inference, this approach also enables training…
Statistical significance testing is used in natural language processing (NLP) to determine whether the results of a study or experiment are likely to be due to chance or if they reflect a genuine relationship. A key step in significance…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
False positives are equally dangerous as false negatives. Ideally the false positive rate should remain 0 or very close to 0. Even a slightest increase in false positive rate is considered as undesirable. Although the specific methods…
It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
This paper is concerned with Bayesian inference when the likelihood is analytically intractable but can be unbiasedly estimated. We propose an annealed importance sampling procedure for estimating expectations with respect to the posterior.…
When interpreting A/B tests, we typically focus only on the statistically significant results and take them by face value. This practice, termed post-selection inference in the statistical literature, may negatively affect both point…
Large-scale replication studies like the Reproducibility Project: Psychology (RP:P) provide invaluable systematic data on scientific replicability, but most analyses and interpretations of the data fail to agree on the definition of…
Particularly in genomics, but also in other fields, it has become commonplace to undertake highly multiple Student's $t$-tests based on relatively small sample sizes. The literature on this topic is continually expanding, but the main…
Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…
A definition for the statistical significance of a signal in an experiment is proposed by establishing a correlation between the observed p-value and the normal distribution integral probability, which is suitable for both counting…
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…