Related papers: Efficient Bayesian phase estimation using mixed pr…
Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose…
Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are…
The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation…
For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model in which portfolio optimization is usually done through dynamic programming.…
We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and…
Measurements on near-term quantum processors are inevitably subject to hardware imperfections that lead to readout errors. Mitigation of such unavoidable errors is crucial to better explore and extend the power of near-term quantum…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. In previous work, a Bayesian…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…
We consider the problem of aggregating predictions or measurements from a set of human forecasters, models, sensors or other instruments which may be subject to bias or miscalibration and random heteroscedastic noise. We propose a Bayesian…
The problem of estimating a high-dimensional sparse vector $\boldsymbol{\theta} \in \mathbb{R}^n$ from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…