Related papers: Bayesian error regions in quantum estimation II: r…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
Quantum error mitigation (QEM) has been proposed as a class of hardware-friendly error suppression techniques. While QEM has been primarily studied for mitigating errors in the estimation of expectation values of observables, recent works…
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
Bayesian methods lie at the heart of modern data science and provide a powerful scaffolding for estimation in data-constrained settings and principled quantification and propagation of uncertainty. Yet in many real-world use cases where…
An analytical method was developed to estimate errors in quantities depended on full one-port vector network analyser (VNA) measurements using differentials and a complex differential error region (DER) was defined. To evaluate the method,…
Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…
We present a general approach to error detection of bosonic quantum error-correction codes via an adaptive quantum phase estimation algorithm assisted by a single ancilla qubit. The approach is applicable to a broad class of bosonic codes…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
Scientific experimentation is largely driven by statistical hypothesis testing to determine significant differences in interventions. Traditionally, experimenters allocate samples uniformly between each intervention. However, such an…
This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…
Online averaged stochastic gradient algorithms are more and more studied since (i) they can deal quickly with large sample taking values in high dimensional spaces, (ii) they enable to treat data sequentially, (iii) they are known to be…
We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…
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…
Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
Fitting models to data using Bayesian inference is quite common, but when each point in parameter space gives a curve, fitting the curve to a data set requires new nuisance parameters, which specify the metric embedding the one-dimensional…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…