We apply Bayesian statistics to the estimation of correlation functions. give probability distributions auto- and cross-correlations as functions data. Our procedure uses measured data optimally informs about certainty level estimation. results general stationary processes their essence is a nonparametric spectra. It allows one better understand statistical noise fluctuations, assess correlatio...

We consider the problem of recovering random graph signals from nonlinear measurements. For this setting, closed-form Bayesian estimators are usually intractable and even numerical evaluation may be difficult to compute for large networks. In paper, we propose a signal processing (GSP) framework recovery that utilizes information on structure behind data. First, develop GSP-linear minimum mean-...

Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well a central ingredient in computational chemistry and simulation. While QPE strategies have focused on single phase, applications to simultaneous phases may bring substantial advantages; for instance, presence spatial or temporal constraints. In this work, we study Bayesian algorithm parallel (sim...

Maximum a posteriori estimation (MAP) Point estimates Manually specified Manually specified Modest Classical Bayesian estimation Posterior distributions Manually specified Manually specified Good (1) Nonparametric Bayesian estimation Posterior distributions Posterior distributions ―――― Excellent (2) Hierarchical Posterior distributions ―――― Posterior distributions Excellent Parameters Complexit...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...

This dissertation applies the Bayesian approach as a method to improve the estimation efficiency of existing econometric tools. The first chapter suggests the Continuous Choice Bayesian (CCB) estimator which combines the Bayesian approach with the Continuous Choice (CC) estimator suggested by Imai and Keane (2004). Using simulation study, I provide two important findings. First, the CC estimato...

All mathematical models of real-world phenomena contain parameters that need to be estimated from measurements, either for realistic predictions or simply to understand the characteristics of the model. Bayesian statistics provides a framework for parameter estimation in which uncertainties about models and measurements are translated into uncertainties in estimates of parameters. This paper pr...

Quantum thermometry exploits the high level of control in coherent devices to offer enhanced precision for temperature estimation. This highlights need constructing concrete estimation strategies. Of particular importance is collisional thermometry, where a series ancillae are sent sequentially probe system's temperature. In this paper we put forth complete framework analyzing using Bayesian in...