Related papers: Large deviations of continuous regular conditional…

Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…

We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…

We show some level-2 large deviation principles for real and complex one-dimensional maps satisfying a weak form of hyperbolicity. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic…

We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…

We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…

In this paper we derive variability measures for the conditional probability distributions of a pair of random variables, and we study its application in the inference of causal-effect relationships. We also study the combination of the…

In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…

In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…

Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…

For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number…

Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…

We give sufficient conditions for the expected excess and the upper semideviation of recourse functions to be strongly convex. This is done in the setting of two-stage stochastic programs with complete linear recourse and random right-hand…

We prove an energy estimate for the polar empirical measure of the two-dimensional symmetric simple exclusion process. We deduce from this estimate and from results in reference [2] large deviations principles for the polar empirical…

Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic…