Related papers: A New Look at $F$-Tests
Inferential models have been proposed for valid and efficient prior-free probabilistic inference. As it gradually gained popularity, this theory is subject to further developments for practically challenging problems. This paper considers…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
We study how to perform tests on samples of pairs of observations and predictions in order to assess whether or not the predictions are prudent. Prudence requires that that the mean of the difference of the observation-prediction pairs can…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…
Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics…
From a variational perspective, many statistical learning criteria involve seeking a distribution that balances empirical risk and regularization. In this paper, we broaden this perspective by introducing a new general class of variational…
Bartholomew's trend test belongs to the broad class of isotonic regression models, specifically with a single qualitative factor, e.g. dose levels. Using the approximation of the ANOVA F-test by the maximum contrast test against grand mean…
In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test…
Although linear classifiers are one of the oldest methods in machine learning, they are still very popular in the machine learning community. This is due to their low computational complexity and robustness to overfitting. Consequently,…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…
Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a…
Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…
Hierarchical inference in (generalized) regression problems is powerful for finding significant groups or even single covariates, especially in high-dimensional settings where identifiability of the entire regression parameter vector may be…