Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

Towards a Continuous Record of the Sky

It is currently feasible to start a continuous digital record of the entire sky sensitive to any visual magnitude brighter than 15 each night. Such a record could be created with a modest array of small telescopes, which collectively generate no more than a few Gigabytes of data daily. Alternatively, a few small telescopes could continually re-point to scan and reco rd the entire sky down to any visual magnitude brighter than 15 with a recurrence epoch of at most a few weeks, again always generating less than one Gigabyte of data each night. These estimates derive from CCD ability and budgets typical of university research projects. As a prototype, we have developed and are utilizing an inexpensive single-telescope system that obtains optical data from about 1500 square degrees. We discuss the general case of creating and storing data from a both an epochal survey, where a small number of telescopes continually scan the sky, and a continuous survey, composed of a constellation of telescopes dedicated each continually inspect a designated section of the sky. We compute specific limitations of canonical surveys in visible light, and estimate that all-sky continuous visual light surveys could be sensitive to magnitude 20 in a single night by about 2010. Possible scientific returns of continuous and epochal sky surveys include continued monitoring of most known variable stars, establishing case histories for variables of future interest, uncovering new forms of stellar variability, discovering the brightest cases of microlensing, discovering new novae and supernovae, discovering new counterparts to gamma-ray bursts, monitoring known Solar System objects, discovering new Solar System objects, and discovering objects that might strike the Earth.Comment: 38 pages, 9 postscript figures, 2 gif images. Revised and new section added. Accepted to PASP. Source code submitted to ASCL.ne

SN 1997bs in M66: Another Extragalactic Eta Carinae Analog?

We report on SN 1997bs in NGC 3627 (M66), the first supernova discovered by the Lick Observatory Supernova Search using the 0.75-m Katzman Automatic Imaging Telescope (KAIT). Based on its early-time optical spectrum, SN 1997bs was classified as Type IIn. However, from the BVRI light curves obtained by KAIT early in the supernova's evolution, and F555W and F814W light curves obtained from Hubble Space Telescope archival WFPC2 images at late times, we question the identification of SN 1997bs as a bona fide supernova. We believe that it is more likely a super-outburst of a very massive luminous blue variable star, analogous to Eta Carinae, and similar to SN 1961V in NGC 1058 (Filippenko et al. 1995 [AJ, 110, 2261]) and SN 1954J (``Variable 12'') in NGC 2403 (Humphreys & Davidson 1994 [PASP, 106, 1025]). The progenitor may have survived the outburst, since the SN is seen in early 1998 at m_F555W=23.4, about 0.5 mag fainter than the progenitor identified by Van Dyk et al. (1999, [AJ, 118, 2331]) in a pre-discovery image. Based on analysis of its environment in the Hubble Space Telescope images, the progenitor was not in an H II region or association of massive stars. The recent discovery of additional objects with properties similar to those of SN 1997bs suggests that the heterogeneous class of Type IIn supernovae consists in part of ``impostors.''Comment: 15 pages, 8 figures, to appear in the PASP (2000 Dec issue

The Economic Impact of Wildlife Damage on Hudson Valley Orchards

The impact of wildlife damage on the profitability of apple farming in New York\u27s Hudson Valley was determined by use of a Standard Net Present Value (NPV) analysis as a means to measure long-term impact. Data were gathered through questionnaire and interview of a stratified random sample of 39 growers that represented 17% of the regional growers. Data concerning species causing damage, extent of wildlife damage and types of controls used were combined with current and long-range costs including revenue lost through damage and control costs. Limitations of the analysis are discussed along with results that indicate an annual equivalent cost flow for all wildlife damage between $3.8 and$3.85 million or $184 to$188 per acre. This study shows that a typical grower experienced combined revenue losses and control costs of $12,500 during 1986. Fifty-two percent of this was associated with wildlife controls, 40$53 and $62 million depending upon whether a 3.5% or 5.0% discount rate is used

Distinguishing cancerous from non-cancerous cells through analysis of electrical noise

Since 1984, electric cell-substrate impedance sensing (ECIS) has been used to monitor cell behavior in tissue culture and has proven sensitive to cell morphological changes and cell motility. We have taken ECIS measurements on several cultures of non-cancerous (HOSE) and cancerous (SKOV) human ovarian surface epithelial cells. By analyzing the noise in real and imaginary electrical impedance, we demonstrate that it is possible to distinguish the two cell types purely from signatures of their electrical noise. Our measures include power-spectral exponents, Hurst and detrended fluctuation analysis, and estimates of correlation time; principal-component analysis combines all the measures. The noise from both cancerous and non-cancerous cultures shows correlations on many time scales, but these correlations are stronger for the non-cancerous cells.Comment: 8 pages, 4 figures; submitted to PR

An attempt to observe economy globalization: the cross correlation distance evolution of the top 19 GDP's

Economy correlations between the 19 richest countries are investigated through their Gross Domestic Product increments. A distance is defined between increment correlation matrix elements and their evolution studied as a function of time and time window size. Unidirectional and Bidirectional Minimal Length Paths are generated and analyzed for different time windows. A sort of critical correlation time window is found indicating a transition for best observations. The mean length path decreases with time, indicating stronger correlations. A new method for estimating a realistic minimal time window to observe correlations and deduce macroeconomy conclusions from such features is thus suggested.Comment: to be published in the Dyses05 proceedings, in Int. J. Mod Phys C 15 pages, 5 figures, 1 tabl

Toward a Symphony of Reactivity: Cascades Involving Catalysis and Sigmatropic Rearrangements

Catalysis and synthesis are intimately linked in modern organic chemistry. The synthesis of complex molecules is an ever evolving area of science. In many regards, the inherent beauty associated with a synthetic sequence can be linked to a certain combination of the creativity with which a sequence is designed and the overall efficiency with which the ultimate process is performed. In synthesis, as in other endeavors, beauty is very much in the eyes of the beholder.† It is with this in mind that we will attempt to review an area of synthesis that has fascinated us and that we find extraordinarily beautiful, namely the combination of catalysis and sigmatropic rearrangements in consecutive and cascade sequences