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We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal…
This paper studies choice situations in which a decision maker can choose multiple alternatives. Given a menu of available options, the decision maker selects a subset of the menu with certain probabilities. We employ an axiomatic approach…
A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive,…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the…
A recent physics challenge shows a circuit, where a voltmeter is connected in series. Indeed, real voltmeters have finite input resistance, therefore one may think that they can be used as resistors. In addition, voltmeters measure the…
Fast robust methods for calculating likelihoods from CMB observations on small scales generally rely on approximations based on a set of power spectrum estimators and their covariances. We investigate the optimality of these approximation,…
We consider the problem of generating randomized control sequences for complex networked systems typically actuated by human agents. Our approach leverages a concept known as control improvisation, which is based on a combination of…
Selective reflection is a high-resolution spectroscopic method that allows the probing of atomic and molecular gases in the near field of dielectric cell windows. It is a sensitive technique for measuring interactions between excited atoms…
In atomic magnetometers, the vector AC-Stark shift associated with circularly polarized light generates spatially varying effective magnetic fields which limit the magnetometer response and serve as sources of noise. We describe a scheme…
In this paper, one of the major shortcomings of the conventional numerical approaches is alleviated by introducing the probabilistic nature of molecular transitions into the framework of classical computational electrodynamics. The main aim…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
A method for measuring the transmittivity of optical samples by using squeezed--vacuum radiation is illustrated. A squeezed vacuum field generated by a below--threshold optical parametric oscillator is propagated through a nondispersive…
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains…
In general, real world signals are analog in nature. To capture these signals for further processing, or transmission, signals are converted into digital bits using analog-to-digital converter (ADC). In this conversion, a good amount of…
Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $\theta \in…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
The experimental technique of a.c. susceptibility can be used as a probe of magnetic dynamics in a wide variety of systems. Its use is restricted to the low-frequency regime and thus is sensitive to relatively slow processes. Rather than…
The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…
Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…