Related papers: Bayesian parameter estimation using Gaussian state…
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
Phase estimation with potentially large phase values, i.e., with large dynamic range, has many applications in quantum metrology, for example to atomic clocks. A recently proposed phase estimation scheme approaches the Heisenberg scaling in…
Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of…
We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…
This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…
Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE),…
We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation. In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically…