Related papers: Statistical testing in a Linear Probability Space
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set…
This paper investigates the performance of a likelihood ratio test in combination with a polynomial subspace projection approach to detect weak transient signals in broadband array data. Based on previous empirical evidence that a…
Simulation schemes for probabilistic inference in Bayesian belief networks offer many advantages over exact algorithms; for example, these schemes have a linear and thus predictable runtime while exact algorithms have exponential runtime.…
Likelihood methods for measuring statistical evidence obey the likelihood principle while maintaining bounded and well-controlled frequency properties. These methods lend themselves to sequential study designs because they measure the…
Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an…
In multigroup data settings with small within-group sample sizes, standard $F$-tests of group-specific linear hypotheses can have low power, particularly if the within-group sample sizes are not large relative to the number of explanatory…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
In Bayesian statistics, the marginal likelihood, also known as the evidence, is used to evaluate model fit as it quantifies the joint probability of the data under the prior. In contrast, non-Bayesian models are typically compared using…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…
Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in…
The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…
A new test statistic based on success runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic $\chi^{2}$ test which ignores the…
Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
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…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…