Related papers: Statistical Significance Revisited
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…
Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power…
Most of the statistical tests currently used to detect differentially expressed genes are based on asymptotic results, and perform poorly for low expression tags. Another problem is the common use of a single canonical cutoff for the…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…
Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification without priors -- was more ambitious than Neyman's, and…
Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical…
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues I revisit the posterior Bayes factor,…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively…
We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…
We develop our previous works concerning the identification of the collection of significant factors determining some, in general, non-binary random response variable. Such identification is important, e.g., in biological and medical…
We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over…
Frank Porter has recently posted a review of "Confidence intervals for the Poisson distribution" (arXiv:2509.02852). The long, diverse history of such intervals is closely related to that of confidence intervals for the parameter of the…
A common problem in machine learning is determining if a variable significantly contributes to a model's prediction performance. This problem is aggravated for datasets, such as gene expression datasets, that suffer the worst case of…
This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related…
In a recent presentation at the 17th International Conference on Science and Technology Indicators, Schneider (2012) criticised the proposal of Bornmann, de Moya Anegon, and Leydesdorff (2012) and Leydesdorff and Bornmann (2012) to use…
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…