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Trace distance and infidelity (induced by square root fidelity), as basic measures of the closeness of quantum states, are commonly used in quantum state discrimination, certification, and tomography. However, the sample complexity for…
Benchmarking estimation and its risk evaluation is a practically important issue in small area estimation. While Bayesian methods have been widely adopted in small area estimation, existing benchmarking approaches are often ad-hoc, such as…
ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC…
Approximate Bayesian Computation (ABC) is a popular sampling method in applications involving intractable likelihood functions. Without evaluating the likelihood function, ABC approximates the posterior distribution by the set of accepted…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we…
Social and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilized by federal statistical agencies are typically constructed to maximize the efficiency of the…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the…
Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering…
Quantum tomography is crucial for characterizing the quantum states of multipartite systems, but its practicality is often limited by the exponentially large dimension of the Hilbert space. Most existing approaches, such as compressed…
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and…
Bayesian inference is a popular and widely-used approach to infer phylogenies (evolutionary trees). However, despite decades of widespread application, it remains difficult to judge how well a given Bayesian Markov chain Monte Carlo (MCMC)…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…