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

Volcanic air pollution and mortality in France 1783?1784

Grattan J.P., Rabartin, R., Self, S. & Thordarson, Th. 2005. Volcanic air pollution and mortality in France 1783-84. Comptes Rendu Geosciences. 641-651 This item is available in both English and French in the PDF file.

Invertebrates of ancient heavy metal spoil and smelting tip sites in southern Jordan: Thier distribution and use as bioindicators of metalliferous pollution derived from ancient sources

Pyatt, B. Amos, D. Grattan, J. Pyatt, A. Terrell-Nield, C. Invertebrates of ancient heavy metal spoil and smelting tip sites in southern Jordan: Thier distribution and use as bioindicators of metalliferous pollution derived from ancient sources. Journal of Arid Environments. 2002. 52 pp 53-62

Pollution and paradigms: lessons from Icelandic volcanism for continental flood basalt studies

Grattan, J. Pollution and paradigms: Lessons from Icelandic volcanism for continental flood basalt studies. Lithos. 2005. 79 pp 343-353

Geochemical evidence for atmospheric pollution derived from prehistoric copper mining at Copa hill, Cwmystwyth, mid-Wales. UK

Mighall, T. Abrahams, P. Grattan, J. Hayes, D. Timberlake, S. Forsyth, S. Geochemical evidence for atmospheric pollution derived from prehistoric copper mining at Copa Hill, Cwmystwyth, mid-Wales, UK. The Science of the Total Environment. 2002. 292 pp 69-80

The local and global dimensions of metalliferous pollution derived from a reconstruction of an eight thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan

Grattan, J.P., Gilbertson, D.D., Hunt, C.O. (2007). The local and global dimensions of metaliferrous air pollution derived from a reconstruction of an 8 thousand year record of copper smelting and mining at a desert-mountain frontier in southern Jordan. Journal of Archaeological Science 34, 83-110

Littered with meaning: The problem of sign pollution in postmodern, post-structuralist, and ecocritical thought

Slocombe, W. (2005). Littered with meaning: The problem of sign pollution in postmodern, post-structuralist, and ecocritical thought. Textual Practice. 19 (4), 493-508. RAE2008

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.

Agglomeration effects in foreign direct investment and the pollution haven hypothesis

Does environmental regulation impair international competitiveness of pollution-intensive industries to the extent that they relocate to countries with less stringent regulation, turning those countries into "pollution havens"? We test this hypothesis using panel data on outward foreign direct investment (FDI) flows of various industries in the German manufacturing sector and account for several econometric issues that have been ignored in previous studies. Most importantly, we demonstrate that externalities associated with FDI agglomeration can bias estimates away from finding a pollution haven effect if omitted from the analysis. We include the stock of inward FDI as a proxy for agglomeration and employ a GMM estimator to control for endogenous time-varying determinants of FDI flows. Furthermore, we propose a difference estimator based on the least polluting industry to break the possible correlation between environmental regulatory stringency and unobservable attributes of FDI recipients in the cross-section. When accounting for these issues we find robust evidence of a pollution haven effect for the chemical industry. © 2008 Springer Science+Business Media B.V.