Models of Noise and Robust Estimates

Given n noisy observations g; of the same quantity f, it is common use to give an estimate of f by minimizing the function Eni=1(gi-f)2. From a statistical point of view this corresponds to computing the Maximum likelihood estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the data. For this reason it has been proposed to minimize the functions of the form Eni=1V(gi-f), where V is a function that increases less rapidly than the square. Several choices for V have been proposed and successfully used to obtain "robust" estimates. In this paper we show that, for a class of functions V, using these robust estimators corresponds to assuming that data are corrupted by Gaussian noise whose variance fluctuates according to some given probability distribution, that uniquely determines the shape of V.

Learning Qualitative Models in the Presence of Noise

G. M. Coghill, S. M. Garrett and R. D. King (2002), Learning Qualitative Models in the Presence of Noise, QR'02 Workshop on Qualitative Reasoning

Exponential sensitivity of noise-driven switching in genetic networks

Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. However, provided mRNA lifetimes are short, switching can still be accurately simulated using protein-only models of gene expression. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably.

Statistical Properties of Single and Competing Non-Linear Fast-Slow Oscillators in Noise

Statistical properties offast-slow Ellias-Grossberg oscillators are studied in response to deterministic and noisy inputs. Oscillatory responses remain stable in noise due to the slow inhibitory variable, which establishes an adaptation level that centers the oscillatory responses of the fast excitatory variable to deterministic and noisy inputs. Competitive interactions between oscillators improve the stability in noise. Although individual oscillation amplitudes decrease with input amplitude, the average to'tal activity increases with input amplitude, thereby suggesting that oscillator output is evaluated by a slow process at downstream network sites.

Sequential anomaly detection in the presence of noise and limited feedback

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: 1) filtering, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations and 2) hedging, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset. © 1963-2012 IEEE.

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation.

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noisemodulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.

Invariant measure selection by noise. An example

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.

Comparing the model-simulated global warming signal to observations using empirical estimates of unforced noise.

The comparison of observed global mean surface air temperature (GMT) change to the mean change simulated by climate models has received much public and scientific attention. For a given global warming signal produced by a climate model ensemble, there exists an envelope of GMT values representing the range of possible unforced states of the climate system (the Envelope of Unforced Noise; EUN). Typically, the EUN is derived from climate models themselves, but climate models might not accurately simulate the correct characteristics of unforced GMT variability. Here, we simulate a new, empirical, EUN that is based on instrumental and reconstructed surface temperature records. We compare the forced GMT signal produced by climate models to observations while noting the range of GMT values provided by the empirical EUN. We find that the empirical EUN is wide enough so that the interdecadal variability in the rate of global warming over the 20(th) century does not necessarily require corresponding variability in the rate-of-increase of the forced signal. The empirical EUN also indicates that the reduced GMT warming over the past decade or so is still consistent with a middle emission scenario's forced signal, but is likely inconsistent with the steepest emission scenario's forced signal.

Ambient Noise in the Kitimat Fjord System

Sound is an important medium for communication and marine organisms have evolved to capitalize on the efficiency with which sound energy travels through water. Anthropogenic and natural sound sources contribute to ocean ambient noise, which can interfere with the use of this sensory modality by marine animals. Anthropogenic noise sources have been increasing steadily over recent decades largely due to coastal population growth, increased global transportation, and offshore industrialization. Understanding the potential impacts of anthropogenic noise requires the establishment of ambient acoustic baselines from which to measure change. Establishing baselines, especially in quiet areas still largely unaffected by anthropogenic stressors, is particularly crucial in the face of the expansion of offshore industries, increasing coastal population and growing reliance on the ocean for global transportation. Global demand for liquid natural gas (LNG), catalyzed primarily by a growing Asian market, is expected to increase significantly in the next 20 years. The geographic position of British Columbia relative to these markets, a growing supply of LNG and new technology for extraction and shipping situate British Columbia as a strong competitor in the lucrative market. The LNG industry could have many adverse impacts on these territories and ecosystems. The Kitimat Fjord System is slated for the development of these LNG export facilities increasing shipping traffic for the port and thus increasing ambient noise in the fjord system. The purpose of this study is to 1) quantify the existing sound levels in the area surrounding Gil Island and 2) identify potential source mechanisms in order to provide a baseline study of the acoustic environment in the Kitimat Fjord system prior to potential increases from LNG shipping.

Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.

Object Restoration Beyond the Rayleigh Limit in the Presence of Noise

info:eu-repo/semantics/published

Measurements and simulations of noise imposed on supercontinuum generated in microstructure fiber

We present experimental and theoretical investigations of the highly nonlinear and broadband noise that exists on supercontinuum spectra generated from launching femtosecond Ti:Sapphire pulses into microstructure fiber.

Amplitude noise on supercontinuum generated in microstructure fiber: Measurements and simulations

Supercontinua generated in microstructure fiber can exhibit significant excess amplitude noise. We present experimental and numerical studies of the origins of this excess noise and its dependence on the input laser pulse parameters.