Related papers: Test statistics and p-values
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
Statistical hypothesis testing is the central method to demarcate scientific theories in both exploratory and inferential analyses. However, whether this method befits such purpose remains a matter of debate. Established approaches to…
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…
Cluster analysis is a fundamental research issue in statistics and machine learning. In many modern clustering methods, we need to determine whether two subsets of samples come from the same cluster. Since these subsets are usually…
The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…
Applied statistical problems often come with pre-specified groupings to predictors. It is natural to test for the presence of simultaneous group-wide signal for groups in isolation, or for multiple groups together. Classical tests for the…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models…
The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
Significance testing based on p-values has been implicated in the reproducibility crisis in scientific research, with one of the proposals being to eliminate them in favor of Bayesian analyses. Defenders of the p-values have countered that…
For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional…
Null hypothesis statistical significance testing (NHST) is the dominant approach for evaluating results from randomized controlled trials. Whereas NHST comes with long-run error rate guarantees, its main inferential tool -- the $p$-value --…
While P-values are widely abused, they are a useful tool for many purposes; banning them is analogous to banning scalpels because most people do not know how to perform surgery. Many reported P-values are not genuine P-values, for a variety…
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…
We examine the role of trustworthiness and trust in statistical inference, arguing that it is the extent of trustworthiness in inferential statistical tools which enables trust in the conclusions. Certain tools, such as the p-value and…
The paper is focused on the problem of estimating the probability $p$ of individual contaminated sample, under group testing. The precision of the estimator is given by the probability of proportional closeness, a concept defined in the…
The customary use of P-values in scientific research has been attacked as being ill-conceived, and the utility of P-values has been derided. This paper reviews common misconceptions about P-values and their alleged deficits as indices of…