Related papers: Efficient Bayesian phase estimation using mixed pr…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…
Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…
Implementing state estimation in low and medium voltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault…
Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint…
In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…
This paper presents a Bayesian approach to symbol and phase inference in a phase-unsynchronized digital receiver. It primarily extends [Quinn 2011] to the multi-symbol case, using the variational Bayes (VB) approximation to deal with the…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…
Quantum metrology and sensing seek advantage in estimating an unknown parameter of some quantum state or channel, using entanglement such as spin squeezing produced by one-axis twists or other quantum resources. In particular, qubit phase…
We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is…
Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference-based adaptive algorithm that can learn and mitigate quantum…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…