Related papers: Randomness and imprecision: from supermartingales …
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to…
The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of…
The concept of missing at random is central in the literature on statistical analysis with missing data. In general, inference using incomplete data should be based not only on observed data values but should also take account of the…
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so; it…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
(This is the third version of a working paper.) We develop a family of self-normalized concentration inequalities for marginal mean under martingale-difference structure and $\phi/\tilde{\phi}$-mixing conditions, where the latter includes…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
The main purpose of this paper is to establish a noncommutative analogue of the Efron--Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including…
Many quantitative properties of probabilistic programs can be characterized as least fixed points, but verifying their lower bounds remains a challenging problem. We present a new approach to lower-bound verification that exploits and…
Using the game-theoretic framework for probability, Vovk and Shafer. have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests. This…
We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue Space norm estimations for different norms of matrix martingales through these norms for the correspondent martingale differences and through the entropic…
We define a variant of the Miller-Rabin primality test, which is in between Miller-Rabin and Fermat in terms of strength. We show that this test has infinitely many "Carmichael" numbers. We show that the test can also be thought of as a…
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…
Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary…
By Solovay's celebrated completeness result on formal provability we know that the provability logic $\mathrm GL$ describes exactly all provable structural properties for any sound and strong enough arithmetical theory with a decidable…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the…
In this paper we define and examine the power of the {\em conditional-sampling} oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $\mu$ takes as input a subset $S \subset…