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P values for classification
... of classifying $X$ we propose to construct for each $\theta =1,2,...,L$ a p-value $\pi_{\theta}(X,\mathcal{D})$ for the null hypothesis that $Y=\theta$, treating $Y$ temporarily as a fixed parameter. In other words, the point predictor $\widehat{Y}(X,\mathcal{D})$...
Lutz Duembgen, Bernd-Wolfgang Igl, Axel Munk

Arbitrary p Gradient Values
...For any prime number p and any positive real number {\alpha}, we construct a finitely generated group {\Gamma} with p-gradient equal to {\alpha}. This construction is used to show that there exist uncountably many pairwise non-commensurable groups th...
Nathaniel Pappas

p adic boundary values
...We study in detail certain natural continuous representations of G = GL(n,K) in locally convex vector spaces over a locally compact, non-archimedean field K of characteristic zero. We construct boundary value maps, or integral transforms, between sub...
Peter Schneider, Jeremy Teitelbaum

P values: misunderstood and misused
...P-values are widely used in both the social and natural sciences to quantify the statistical significance of observed results. The recent surge of big data research has made p-value an even more popular tool to test the significance of a study. Howev...
Bertie Vidgen, Taha Yasseri

Fundamentals of p values: Introduction
...We explain the concept of p-values presupposing only rudimentary probability theory. We also use the occasion to introduce the notion of p-function, so that p-values are values of a p-function. The explanation is restricted to the discrete case with ...
Yuri Gurevich, Vladimir Vovk

Test Martingales, Bayes Factors and $p$ Values
...A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering the large...
Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, Vladimir Vovk

Combining p values via averaging
...This note discusses the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. An old result by Rueschendorf shows that the p-values ...
Vladimir Vovk

P values for high dimensional regression
...Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent pro...
Nicolai Meinshausen, Lukas Meier, Peter Bühlmann

Invariant $P$ values for model checking
...$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution, it is not...
Michael Evans, Gun Ho Jang

Exact P values for Network Interference
...We study the calculation of exact p-values for a large class of non-sharp null hypotheses about treatment effects in a setting with data from experiments involving members of a single connected network. The class includes null hypotheses that limit t...
Susan Athey, Dean Eckles, Guido Imbens

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