Bayesian quantum frequency estimation in presence of collective dephasing

We advocate a Bayesian approach to optimal quantum frequency estimation - an important issue for future quantum enhanced atomic clock operation. The approach provides a clear insight into the interplay between decoherence and the extent of the prior knowledge in determining the optimal interrogation times and optimal estimation strategies. We propose a general framework capable of describing local oscillator noise as well as additional collective atomic dephasing effects. For a Gaussian noise the average Bayesian cost can be expressed using the quantum Fisher information and thus we establish a direct link between the two, often competing, approaches to quantum estimation theoryComment: 15 pages, 3 figure

Defining the hundred year flood: a Bayesian approach for using historic data to reduce uncertainty in flood frequency estimates

This paper describes a Bayesian statistical model for estimating flood frequency by combining uncertain annual maximum (AMAX) data from a river gauge with estimates of flood peak discharge from various historic sources that predate the period of instrument records. Such historic flood records promise to expand the time series data needed for reducing the uncertainty in return period estimates for extreme events, but the heterogeneity and uncertainty of historic records make them difficult to use alongside Flood Estimation Handbook and other standard methods for generating flood frequency curves from gauge data. Using the flow of the River Eden in Carlisle, Cumbria, UK as a case study, this paper develops a Bayesian model for combining historic flood estimates since 1800 with gauge data since 1967 to estimate the probability of low frequency flood events for the area taking account of uncertainty in the discharge estimates. Results show a reduction in 95% confidence intervals of roughly 50% for annual exceedance probabilities of less than 0.0133 (return periods over 75 years) compared to standard flood frequency estimation methods using solely systematic data. Sensitivity analysis shows the model is sensitive to 2 model parameters both of which are concerned with the historic (pre-systematic) period of the time series. This highlights the importance of adequate consideration of historic channel and floodplain changes or possible bias in estimates of historic flood discharges. The next steps required to roll out this Bayesian approach for operational flood frequency estimation at other sites is also discussed

Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequencyComment: 6 figures, 13 page

Optical Frequency Comb Noise Characterization Using Machine Learning

A novel tool, based on Bayesian filtering framework and expectation maximization algorithm, is numerically and experimentally demonstrated for accurate frequency comb noise characterization. The tool is statistically optimum in a mean-square-error-sense, works at wide range of SNRs and offers more accurate noise estimation compared to conventional methods

Bayesian modelling of clusters of galaxies from multi-frequency pointed Sunyaev--Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique (Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.Comment: 12 pages, 7 figures, submitted to MNRA

Frequency synchronization for multiuser MIMO-OFDM system using Bayesian approach

This paper addresses the problem of frequency synchronization in multiuser multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. Different from existing work, a Bayesian approach is used in the parameter estimation problem. In this paper, the Bayes estimator for carrier frequency offset (CFO) estimation is proposed and the Bayesian Cramér-Rao bound (BCRB) is also derived in closed form. Direct implementation of the resultant estimation scheme with conventional methods is challenging since a high degree of mathematical sophistication is always required. To solve this problem, the Gibbs sampler is exploited with an efficient sample generation method. Simulation results illustrate the effectiveness of the proposed estimation scheme. ©2010 IEEE.published_or_final_versionThe 2010 IEEE Global Telecommunications Conference (GLOBECOM 2010), Miami, FL., 6-10 December 2010. In Globecom. IEEE Conference and Exhibition, 2010, p. 1-