Related papers: On the connection between probability boxes and po…
Software packages usually report the results of statistical tests using p-values. Users often interpret these by comparing them to standard thresholds, e.g. 0.1%, 1% and 5%, which is sometimes reinforced by a star rating (***, **, *). We…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the $p$-frame energies, i.e. energies with the kernel given by the absolute value of the inner…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
Bayesian supervised predictive classifiers, hypothesis testing, and parametric estimation under Partition Exchangeability are implemented. The two classifiers presented are the marginal classifier (that assumes test data is i.i.d.) next to…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
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…
Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…
Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…
We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the…
In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show…
Roughly speaking, holonomic measures are parametric varifolds without boundary. They provide a setting appropriate for the analysis of many variational problems. In this paper, we characterize the space of variations for these objects, and…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solution in boxes with the side…
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.…
Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of…