Estimating stellar oscillation-related parameters and their uncertainties with the moment method

The moment method is a well known mode identification technique in asteroseismology (where `mode' is to be understood in an astronomical rather than in a statistical sense), which uses a time series of the first 3 moments of a spectral line to estimate the discrete oscillation mode parameters l and m. The method, contrary to many other mode identification techniques, also provides estimates of other important continuous parameters such as the inclination angle alpha, and the rotational velocity v_e. We developed a statistical formalism for the moment method based on so-called generalized estimating equations (GEE). This formalism allows the estimation of the uncertainty of the continuous parameters taking into account that the different moments of a line profile are correlated and that the uncertainty of the observed moments also depends on the model parameters. Furthermore, we set up a procedure to take into account the mode uncertainty, i.e., the fact that often several modes (l,m) can adequately describe the data. We also introduce a new lack of fit function which works at least as well as a previous discriminant function, and which in addition allows us to identify the sign of the azimuthal order m. We applied our method to the star HD181558, using several numerical methods, from which we learned that numerically solving the estimating equations is an intensive task. We report on the numerical results, from which we gain insight in the statistical uncertainties of the physical parameters involved in the moment method.Comment: The electronic online version from the publisher can be found at http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2005.00487.

Graphics for uncertainty

Graphical methods such as colour shading and animation, which are widely available, can be very effective in communicating uncertainty. In particular, the idea of a ‘density strip’ provides a conceptually simple representation of a distribution and this is explored in a variety of settings, including a comparison of means, regression and models for contingency tables. Animation is also a very useful device for exploring uncertainty and this is explored particularly in the context of flexible models, expressed in curves and surfaces whose structure is of particular interest. Animation can further provide a helpful mechanism for exploring data in several dimensions. This is explored in the simple but very important setting of spatiotemporal data

Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

Geodynamic evolution of the lithosphere and upper mantle beneath the Alboran region of the western Mediterranean: Constraints from travel time tomography

An edited version of this paper was published by the American Geophysical Union. Copyright 2000, AGU. See also: http://www.agu.org/pubs/crossref/2000/2000JB900024.shtml; http://atlas.geo.cornell.edu/morocco/publications/calvert2000.htmA number of different geodynamic models have been proposed to explain the extension that occurred during the Miocene in the Alboran Sea region of the western Mediterranean despite the continued convergence and shortening of northern Africa and southern Iberia. In an effort to provide additional geophysical constraints on these models, we performed a local, regional, and teleseismic tomographic travel time inversion for the lithospheric and upper mantle velocity structure and earthquake locations beneath the Alboran region in an area of 800 x 800 km^2. We picked P and S arrival times from digital and analog seismograms recorded by 96 seismic stations in Morocco and Spain between 1989 and 1996 and combined them with arrivals carefully selected from local and global catalogs (1964-1998) to generate a starting data set containing over 100,000 arrival times. Our results indicate that a N-S line of intermediate depth earthquakes extending from crustal depths significantly inland from the southern Iberian coat to depths of over 100 km beneath the center of the Alboran Sea coincided with a W to E transition from high to low velocities imaged in the uppermost mantle. A high-velocity body, striking approximately NE-SW, is imaged to dip southeastwards from lithospheric depths beneath the low-velocity region to depths of ~350 km. Between 350 and 500 km the imaged velocity anomalies become more diffuse. However, pronounced high-velocity anomalies are again imaged at 600 km near an isolated cluster of deep earthquakes. In addition to standard tomographic methods of error assessment, the effects of systematic and random errors were assessed using block shifting and bootstrap resampling techniques, respectively. We interpret the upper mantle high-velocity anomalies as regions of colder mantle that originate from lithospheric depths. These observations, when combined with results from other studies, suggest that delamination of a continental lithosphere played an important role in the Neogene and Quaternary evolution of the region

Propagation of regional seismic phases (Lg and Sn) and Pn velocity structure along the Africa-Iberia plate boundary zone

An edited version of this paper was published by Blackwell Publishing. Copyright 2000, Blackwell Publishing. See also: http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-246x.2000.00160.x; http://atlas.geo.cornell.edu/morocco/publications/calvert2000GJI.htmWe used over 1000 regional waveforms recorded by 60 seismic stations located in northwest Africa and Iberia to map the efficiency of L g and Sn wave propagation beneath the Gulf of Cadiz, Alboran Sea and bounding Betic, Rif and Atlas mountain belts. Crustal attenuation is inferred from the tomographic inversion of L g/Pg amplitude ratios. Upper mantle attenuation is inferred from maps of Sn propagation efficiency derived by inversion of well-defined qualitative efficiency assignments based on waveform characteristics. Regions of L g attenuation correlate well with areas of thinned continental or oceanic crust, significant sedimentary basins, and lateral crustal variations. Comparison of the Sn efficiency results with velocities obtained from an anisotropic Pn traveltime inversion shows a fairly good correlation between regions of poor Sn efficiency and low Pn velocity. A low Pn velocity (7.6?7.8 km s-1) and significant Sn attenuation in the uppermost mantle is imaged beneath the Betics in southern Spain, in sharp contrast to the relatively normal Pn velocity (8.0?8.1 km s-1) and efficient Sn imaged beneath the Alboran Sea. Slow Pn velocity anomalies are also imaged beneath the Rif and Middle Atlas in Morocco. We do not identify any conclusive evidence of lithospheric-scale upper mantle attenuation beneath the Rif, although the crust in the Gibraltar region appears highly attenuating, making observations at stations in this region ambiguous. Paths crossing the Gulf of Cadiz, eastern Atlantic and the Moroccan and Iberian mesetas show very efficient Sn propagation and are imaged with high Pn velocities (8.1?8.2 km s-1). The spatial distribution of attenuation and velocity anomalies lead us to conclude that some recovery of the mantle lid beneath the Alboran Sea must have occurred since the early Miocene episode of extension and volcanism. We interpret the low velocity and attenuating regions beneath the Betics and possibly the Rif as indicating the presence of partial melt in the uppermost mantle which may be underlain by faster less attenuating mantle. In the light of observations from other geophysical and geological studies, the presence of melt at the base of the Betic crust may be an indication that delamination of continental lithosphere has played a role in the Neogene evolution of the Alboran Sea region

Long-Term PIT and T-Bar Anchor Tag Retention Rates in Adult Muskellunge

Mark-recapture studies require knowledge of tag retention rates specific to tag types, fish species and size, and study duration. We determined the probability of tag loss for passive integrated transponder (PIT) tags implanted into dorsal musculature, T-bar anchor tags attached to dorsal pterygiophores, and loss of both tags in relation to years post-tagging for double-marked adult muskellunge Esox masquinongy over a 10 year period. We also used PIT tags as a benchmark to assess the interactive effects of fish length at tagging, sex, and years post-tagging on T-bar anchor tag loss rates. Only five instances of PIT tag loss were identified; the calculated probability of a fish losing its PIT tag was consistently \u3c 1.0% for up to 10 years post-tagging. The probability of T-bar anchor tag loss by muskellunge was related to the number of years post-tagging and total length of fish at tagging. T-bar anchor tag loss rate one year after tagging was 6.5%. Individuals \u3c 750 mm total length at tagging had anchor tag loss rates \u3c 10% for up to 6 years after tagging. However, the proportion of fish losing T-bar anchor tags steadily increased with increasing years post-tagging (~30% after 6 years) for larger muskellunge. Fish gender did not influence probability of T-bar anchor tag loss. Our results indicate that T-bar anchor tags are best suited for short-term applications (≤ 1 year duration) involving adult muskellunge. We recommend use of PIT tags for longer-term tagging studies, particularly for muskellunge \u3e 750 mm total length

Estimating Nuisance Parameters in Inverse Problems

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.Comment: 16 pages, 5 figure

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture-recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture-recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi-likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture-recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods

Estimating Omissions from Searches

The mark-recapture method was devised by Petersen in 1896 to estimate the number of fish migrating into the Limfjord, and independently by Lincoln in 1930 to estimate waterfowl abundance. The technique applies to any search for a finite number of items by two or more people or agents, allowing the number of searched-for items to be estimated. This ubiquitous problem appears in fields from ecology and epidemiology, through to mathematics, social sciences, and computing. Here we exactly calculate the moments of the hypergeometric distribution associated with this long-standing problem, confirming that widely used estimates conjectured in 1951 are often too small. Our Bayesian approach highlights how different search strategies will modify the estimates. As an example, we assess the accuracy of a systematic literature review, an application we recommend.Comment: One figure. Supplementary Material included as an Appendi