相关论文: Dynamical hypothesis tests and Decision Theory for…

The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…

This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The…

Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…

Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…

Let $T: X\mapsto X$ be a deterministic dynamical system preserving a probability measure $\mu$. A dynamical Borel-Cantelli lemma asserts that for certain sequences of subsets $A_n\subset X$ and $\mu$-almost every point $x\in X$ the…

Depending on the Higgs-boson and top-quark masses, $M_H$ and $M_t$, the effective potential of the Standard Model at finite (and zero) temperature can have a deep and unphysical stable minimum $\langle \phi(T)\rangle$ at values of the field…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution…

Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…

Maximum likelihood constraint inference is a powerful technique for identifying unmodeled constraints that affect the behavior of a demonstrator acting under a known objective function. However, it was originally formulated only for…

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary system with probability {\it a priori} where thermodynamic infinite-size limit is replaced by multiple-measurement limit. A duality symmetry between Massieu's…

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…

In two-sampling testing, one observes two independent sequences of independent and identically distributed random variables distributed according to the distributions $P_1$ and $P_2$ and wishes to decide whether $P_1=P_2$ (null hypothesis)…

We introduce a general framework for testing statistical hypotheses for probability measures supported on finite spaces, which is based on optimal transport (OT). These tests are inspired by the analysis of variance (ANOVA) and its…

Let $n\ge 2$ and $s\in (n-2,n)$. Assume that $\Omega\subset \mathbb{R}^n$ is a one-sided bounded non-tangentially accessible domain with $s$-Ahlfors regular boundary and $\sigma$ is the surface measure on the boundary of $\Omega$, denoted…

This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…