Related papers: The posterior probability of a null hypothesis giv…
In an observational study, it is common to leverage known null effect to detect bias. One such strategy is to set aside a placebo sample -- a subset of data immune from the hypothesized cause-and-effect relationship. Existence of an effect…
Positivity is one of the three conditions for causal inference from observational data. The standard way to validate positivity is to analyze the distribution of propensity. However, to democratize the ability to do causal inference by…
Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis, as in Pericchi et al. (2017). In this article, we show posterior probabilities of hypothesis by…
A simple and common type of medical research involves the comparison of one treatment against another. The logical aim should be both to establish which treatment is superior and the strength of evidence supporting this conclusion, a task…
In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable,…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
It is demonstrated that the statistical method of the famous Aspect - Bell experiment requires negative probability densities and negative probabilities from "the thing" researched, else that thing doesn't exist. The thing refers here to…
In most circumstances, probability sampling is the only way to ensure unbiased inference about population quantities where a complete census is not possible. As we enter the era of 'big data', however, nonprobability samples, whose sampling…
We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…
In hypothesis testing, the phenomenon of label noise, in which hypothesis labels are switched at random, contaminates the likelihood functions. In this paper, we develop a new method to determine the decision rule when we do not have…
This work explores the effects of relevant and irrelevant boolean variables on the accuracy of classifiers. The analysis uses the assumption that the variables are conditionally independent given the class, and focuses on a natural family…
Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…
The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…
Despite its importance to experimental design, statistical power (the probability that, given a real effect, an experiment will reject the null hypothesis) has largely been ignored by the NLP community. Underpowered experiments make it more…
We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…
Positive predictive value and negative predictive value are two widely used parameters to assess the clinical usefulness of a medical diagnostic test. When there are two diagnostic tests, it is recommendable to make a comparative assessment…
Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…
Much research on Machine Learning testing relies on empirical studies that evaluate and show their potential. However, in this context empirical results are sensitive to a number of parameters that can adversely impact the results of the…
Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth…
Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function,…