A comparative geochemical study of Mars and Earth basalt petrogenesis

2013 ◽  
Vol 50 (1) ◽  
pp. 78-93 ◽  
Author(s):  
John D. Greenough ◽  
Avee Ya’acoby
Keyword(s):  
Incompatible Element ◽  
A Priori ◽  
Correlation Coefficients ◽  
Small Sample ◽  
Geochemical Data ◽  
Data Set ◽  
Element Ratios ◽  
Highly Correlated ◽  
Small Sample Sizes ◽  
Priori Information

Geochemical data, from the Mars Meteorite Compendium web site, for 13 basaltic meteorites, possibly from only four localities on Mars, are used to study Martian petrogenetic processes. To achieve this goal, an exploratory data analysis technique, multidimensional scaling (MDS), is used to quantitatively assess the relative behavior (measured with correlation coefficients) of 160 incompatible element ratios involving 25 “trace” elements. The ratios behave as in Earth basalts, suggesting that relative element incompatibility is similar in both planets. Because mineralogy controls incompatibility, the mineralogy of Earth and Mars mantles appears similar. In addition, results suggest that ratios involving elements with highly different incompatibility (e.g., La/Yb) are dominantly controlled by % melting. Plots of SiO2 (pressure proxy; decreases with increasing pressure) versus La/Yb and Nb/Y (decrease as melting increases) imply that Mars basalts, like Earth tholeiites, reflect high percentages of melting, but opposite to Earth, % melting appears to increase with increasing pressure. The moderately correlated, positive, SiO2–La/Yb Mars relationship parallels highly correlated Lunar KREEP data and contrasts with Earth’s negative correlation. The positive relationships may reflect restricted mantle convection in some (Mars and the Moon are smaller) planetary bodies. Using similarly incompatible element ratios that are sensitive to source composition, to compare Mars and Earth with MDS, Mars sources most resemble depleted Earth mantle. Additionally, these ratios group Mars sources into enriched, depleted, and intermediate types. The groupings are the same as those suggested by isotopes, and we conclude that trace element data support the hypothesis that chemical variation in Mars may reflect crystallization of a Mars magma ocean. The natural patterns in ratios and samples revealed using MDS, which has no a priori information about relationships, support integrity of the geochemical data set, despite potential shortcomings such as small sample sizes, alteration, and weathering. However, whether the meteorites are representative of Mars as a whole is unknown.

Penalized Binary Regression for Gene Expression Profiling

2004 ◽  
Vol 43 (05) ◽  
pp. 439-444 ◽  
Author(s):  
Michae Schimek
Keyword(s):  
Microarray Analysis ◽  
Predictive Performance ◽  
Small Sample ◽  
Probit Regression ◽  
Binary Regression ◽  
Data Set ◽  
Small Sample Sizes ◽  
Bayesian Probit Regression

Summary Objectives: A typical bioinformatics task in microarray analysis is the classification of biological samples into two alternative categories. A procedure is needed which, based on the expression levels measured, allows us to compute the probability that a new sample belongs to a certain class. Methods: For the purpose of classification the statistical approach of binary regression is considered. High-dimensionality and at the same time small sample sizes make it a challenging task. Standard logit or probit regression fails because of condition problems and poor predictive performance. The concepts of frequentist and of Bayesian penalization for binary regression are introduced. A Bayesian interpretation of the penalized log-likelihood is given. Finally the role of cross-validation for regularization and feature selection is discussed. Results: Penalization makes classical binary regression a suitable tool for microarray analysis. We illustrate penalized logit and Bayesian probit regression on a well-known data set and compare the obtained results, also with respect to published results from decision trees. Conclusions: The frequentist and the Bayesian penalization concept work equally well on the example data, however some method-specific differences can be made out. Moreover the Bayesian approach yields a quantification (posterior probabilities) of the bias due to the constraining assumptions.

scholarly journals Coupling of Functional Gene Diversity and Geochemical Data from Environmental Samples

2004 ◽  
Vol 70 (11) ◽  
pp. 6525-6534 ◽  
Author(s):  
A. V. Palumbo ◽  
J. C. Schryver ◽  
M. W. Fields ◽  
C. E. Bagwell ◽  
J.-Z. Zhou ◽  
...  
Keyword(s):  
Organic Carbon ◽  
Small Sample ◽  
Geochemical Data ◽  
Sulfite Reductase ◽  
Model Parameters ◽  
Generalization Error ◽  
Sample Sizes ◽  
Dissimilatory Sulfite Reductase ◽  
Small Sample Sizes ◽  
Error Weight

ABSTRACT Genomic techniques commonly used for assessing distributions of microorganisms in the environment often produce small sample sizes. We investigated artificial neural networks for analyzing the distributions of nitrite reductase genes (nirS and nirK) and two sets of dissimilatory sulfite reductase genes (dsrAB 1 and dsrAB 2) in small sample sets. Data reduction (to reduce the number of input parameters), cross-validation (to measure the generalization error), weight decay (to adjust model parameters to reduce generalization error), and importance analysis (to determine which variables had the most influence) were useful in developing and interpreting neural network models that could be used to infer relationships between geochemistry and gene distributions. A robust relationship was observed between geochemistry and the frequencies of genes that were not closely related to known dissimilatory sulfite reductase genes (dsrAB 2). Uranium and sulfate appeared to be the most related to distribution of two groups of these unusual dsrAB-related genes. For the other three groups, the distributions appeared to be related to pH, nickel, nonpurgeable organic carbon, and total organic carbon. The models relating the geochemical parameters to the distributions of the nirS, nirK, and dsrAB 1 genes did not generalize as well as the models for dsrAB 2. The data also illustrate the danger (generating a model that has a high generalization error) of not using a validation approach in evaluating the meaningfulness of the fit of linear or nonlinear models to such small sample sizes.

Towards AOD1B RL07

2020 ◽  
Author(s):  
Linus Shihora ◽  
Henryk Dobslaw
Keyword(s):  
General Circulation ◽  
A Priori ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
Temporal Variations ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Ocean Bottom ◽  
Data Set ◽  
Priori Information

<p>The Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) product provides a priori information about temporal variations in the Earth's gravity field caused by global mass variability in the atmosphere and ocean and is routinely used as background model in satellite gravimetry. The current version 06 provides Stokes coefficients expanded up to d/o 180 every 3 hours. It is based on ERA-Interim and the ECMWF operational model for the atmosphere, and simulations with the global ocean general circulation model MPIOM consistently forced with the fields from the same atmospheric data-set.</p> <p>We here present preliminary numerical experiments in the development towards a new release 07 of AOD1B. The experiments are performed with the TP10 configuration of MPIOM and include (I) new hourly atmospheric forcing based on the new ERA-5 reanalysis from ECMWF; (II) an improved bathymetry around Antarctica including cavities under the ice shelves; and (III) an explicit implementation of the feedback effects of self-attraction and loading to ocean dynamics. The simulated ocean bottom pressure variability is discussed with respect to AOD1B version 6 as well as in situ ocean observations. A preliminary timeseries of hourly AOD1B-like coefficients for the year 2019 that incorporate the above mentioned improvements will be made available for testing purposes.</p>

Sample Size and Accuracy of Estimates in Multilevel Models

Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 111-120 ◽  
Author(s):  
Omar Paccagnella
Keyword(s):  
Variance Components ◽  
Multilevel Models ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Estimation Procedure ◽  
Small Sample ◽  
Standard Errors ◽  
Sample Sizes ◽  
Monte Carlo Simulation Study ◽  
Small Sample Sizes

In a multilevel framework several researches have investigated the behavior of estimates in finite samples, particularly for continuous dependent variables. Some findings show poor precise estimates for the variance components. On the other hand, discrete response multilevel models have been investigated less widely. In this paper we analyze the influence of different factors on the accuracy of estimates and standard errors of estimates in a binary response 2-level model, through a Monte Carlo simulation study. We investigate the hypothesis of: (a) small sample sizes; (b) different intraclass correlation coefficients; (c) different numbers of quadrature points in the estimation procedure. Standard errors of estimates are studied through a noncoverage indicator. In all instances we have considered, the point estimates are unbiased (even with very small sample sizes), while the variance components are underestimated. The accuracy of the standard errors of variance estimates needs a very large number of groups.

scholarly journals Multi-constellation GNSS interferometric reflectometry with mass-market sensors as a solution for soil moisture monitoring

2019 ◽  
Author(s):  
Angel Martín ◽  
Sara Ibáñez ◽  
Carlos Baixauli ◽  
Sara Blanc ◽  
Ana B. Anquela
Keyword(s):  
Soil Moisture ◽  
Arable Land ◽  
Correlation Coefficients ◽  
Moisture Determination ◽  
Data Set ◽  
Mass Market ◽  
Innovative Solutions ◽  
Highly Correlated ◽  
Gnss Observations

Abstract. Per capita arable land is decreasing due to rapidly increasing population, and fresh water is becoming scarce and more expensive. Therefore, farmers should continue to use technology and innovative solutions to improve efficiency, save input costs, and optimise environmental resources (such as water). In the case study presented in this manuscript, the GNSS-IR technique was used to monitor soil moisture during 66 days, from December 3, 2018, to February 6, 2019, in the installations of the Cajamar Centre of Experiences, Paiporta, Valencia, Spain. Two main objectives were pursued. The first was the extension of the technique to a multi-constellation solution using GPS, GLONASS, and GALILEO satellites, and the second was to test whether mass-market sensors could be used for this technique. Both objectives were achieved. At the same time the GNSS observations were made, soil samples taken at 5 cm depth were used for soil moisture determination to establish a reference dataset. Based on a comparison with that reference data set, all GNSS solutions, including the three constellations and the two sensors (geodetic and mass-market), were highly correlated, with a correlation coefficients between 70 % and 85 %.

scholarly journals Numerical evaluation of magnetic absolute measurements with arbitrarily distributed DI-fluxgate theodolite orientations

2018 ◽  
Vol 7 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Heinz-Peter Brunke ◽  
Jürgen Matzka
Keyword(s):  
Evaluation Method ◽  
A Priori ◽  
Fixed Number ◽  
Data Set ◽  
Alternative Evaluation ◽  
Vector Magnetometer ◽  
Flux Measurements ◽  
Priori Information ◽  
Absolute Measurements ◽  
Magnetic Meridian

Abstract. At geomagnetic observatories the absolute measurements are needed to determine the calibration parameters of the continuously recording vector magnetometer (variometer). Absolute measurements are indispensable for determining the vector of the geomagnetic field over long periods of time. A standard DI (declination, inclination) measuring scheme for absolute measurements establishes routines in magnetic observatories. The traditional measuring schema uses a fixed number of eight orientations (Jankowski et al., 1996). We present a numerical method, allowing for the evaluation of an arbitrary number (minimum of five as there are five independent parameters) of telescope orientations. Our method provides D, I and Z base values and calculated error bars of them. A general approach has significant advantages. Additional measurements may be seamlessly incorporated for higher accuracy. Individual erroneous readings are identified and can be discarded without invalidating the entire data set. A priori information can be incorporated. We expect the general method to also ease requirements for automated DI-flux measurements. The method can reveal certain properties of the DI theodolite which are not captured by the conventional method. Based on the alternative evaluation method, a new faster and less error-prone measuring schema is presented. It avoids needing to calculate the magnetic meridian prior to the inclination measurements. Measurements in the vicinity of the magnetic equator are possible with theodolites and without a zenith ocular. The implementation of the method in MATLAB is available as source code at the GFZ Data Center (Brunke, 2017).

scholarly journals A penalized likelihood approach to model the annual maximum flow with small sample sizes

2017 ◽  
Vol 13 (4) ◽  
pp. 563-566
Author(s):  
Nur Farhanah Kahal Musakkal ◽  
Su Na Chin ◽  
Khadizah Ghazali ◽  
Darmesah Gabda
Keyword(s):  
Standard Method ◽  
Penalized Likelihood ◽  
Maximum Flow ◽  
Small Sample ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Annual Maximum ◽  
Sample Sizes ◽  
Data Set ◽  
Small Sample Sizes

The aim of this study is to model the annual maximum flow of several sites in Sabah with small sample sizes using the generalized extreme value (GEV) distribution. Previous studies have shown that the standard method of maximum likelihood estimates would give a poor estimation of the GEV parameters and quantiles for small data set. This study will consider the penalized likelihood estimates as an alternative method to improve the inference over the standard method and retains the modeling flexibility. As comparisons, we will illustrate the results of both methods to model the annual maximum flow in Sabah. The results show the implementation of the penalty function had the same effect to the GEV parameter estimates as suggested by previous studies.

scholarly journals Envisat MIPAS measurements of CFC-11: retrieval, validation, and climatology

2008 ◽  
Vol 8 (2) ◽  
pp. 4561-4602 ◽  
Author(s):  
L. Hoffmann ◽  
M. Kaufmann ◽  
R. Spang ◽  
R. Müller ◽  
J. J. Remedios ◽  
...  
Keyword(s):  
Large Scale ◽  
Lower Stratosphere ◽  
A Priori ◽  
Michelson Interferometer ◽  
Optimal Estimation ◽  
Atmospheric Conditions ◽  
Data Set ◽  
Mixing Ratios ◽  
Priori Information ◽  
The Individual

Abstract. From July 2002 to March 2004 the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) aboard the European Space Agency's Environmental Satellite (Envisat) measured nearly continuously mid infrared limb radiance spectra. These measurements are utilised to retrieve the global distribution of the chlorofluorocarbon CFC-11 by applying a new fast forward model for Envisat MIPAS and an accompanying optimal estimation retrieval processor. A detailed analysis shows that the total retrieval errors of the individual CFC-11 volume mixing ratios are typically below 10% and that the systematic components are dominating. Contribution of a priori information to the retrieval results are less than 5 to 10%. The vertical resolution of the observations is about 3 to 4 km. The data are successfully validated by comparison with several other space experiments, an air-borne in-situ instrument, measurements from ground-based networks, and independent Envisat MIPAS analyses. The retrieval results from 425 000 Envisat MIPAS limb scans are compiled to provide a new climatological data set of CFC-11. The climatology shows significantly lower CFC-11 abundances in the lower stratosphere compared with the Reference Atmospheres for MIPAS (RAMstan V3.1) climatology. Depending on the atmospheric conditions the differences between the climatologies are up to 30 to 110 ppt (45 to 150%) at 19 to 27 km altitude. Additionally, time series of CFC-11 mean abundance and variability for five latitudinal bands are presented. The observed CFC-11 distributions can be explained by the residual mean circulation and large-scale eddy-transports in the upper troposphere and lower stratosphere. The new CFC-11 data set is well suited for further scientific studies.

scholarly journals Removing Noise During the Filtering Images

2020 ◽  
Vol 9 (1) ◽  
pp. 2584-2587
Keyword(s):  
Image Processing ◽  
Statistical Models ◽  
Additive Noise ◽  
A Priori ◽  
Small Sample ◽  
Noise Filtering ◽  
Gaussian Filter ◽  
A Priori Information ◽  
Modified Kalman Filter ◽  
Priori Information

In the problems of image recognition, various approaches used when the image is noisy and there is a small sample of observations. The article discusses the issue of noise filtering in image processing. The lack of a priori information complicates the processing of data, as a result of which it is necessary to rely on some statistical models of signals and noise. The use of known filters does not always give the desired result. A Gaussian filter can be used for additive noise, a modified Kalman filter eliminates a wider range of noise

Petrological and geochemical constraints on the genesis of Mesozoic–Cenozoic magmatism of King George Island, South Shetland Islands, Antarctica

1991 ◽  
Vol 3 (3) ◽  
pp. 293-308 ◽  
Author(s):  
K. Birkenmajer ◽  
L. Francalanci ◽  
A. Peccerillo
Keyword(s):  
Incompatible Element ◽  
South Shetland Islands ◽  
Geochemical Data ◽  
King George Island ◽  
Island Arcs ◽  
Calc Alkaline ◽  
Constant Composition ◽  
Shetland Islands ◽  
Element Ratios ◽  
Incompatible Trace Elements

Petrological and geochemical data are reported for a series of Late Cretaceous-Middle Miocene volcanic, hypabyssal and intrusive rocks from King George Island (KGI) and from nearby Ridley Island, South Shetland Islands. Major element data indicate a calc-alkaline, basic to intermediate composition for the analysed samples. Although emplaced on a continental margin, the KGI rocks generally display low abundances of incompatible trace elements, close to those typically observed in calc-alkaline suites erupted in intraoceanic island arcs. A few samples have a significant negative Ce anomaly. Many incompatible elements define smooth positive trends on interelemental variation diagrams which suggests that magmas erupted at different times on KGI maintained a rather constant composition in terms of incompatible element ratios. Geochemical modelling, based on Sr isotope ratios and incompatible element ratios, suggests that the primary calc-alkaline magmas of KGI were all generated in an upper mantle modified by addition of small amounts of pelagic sediments dragged down by subduction processes.

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