SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

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Regression Shrinkage and Selection via the Lasso

Size-Distribution Analysis of Macromolecules by Sedimentation Velocity Ultracentrifugation and Lamm Equation Modeling

We present a comprehensive study of the physical properties of ∼ 10 5 galaxies with measurable star formation in the Sloan Digital Sky Survey (SDSS). By comparing physical information extracted from the emission lines with continuum properties, we build up a picture of the nature of star-forming galaxies at z < 0.2. We develop a method for aperture correction using resolved imaging and show that our method takes out essentially all aperture bias in the star formation rate (SFR) estimates, allowing an accurate estimate of the total SFRs in galaxies. We determine the SFR density to be 1.915 +0.02 −0.01 (random) +0.14

The physical properties of star-forming galaxies in the low-redshift universe

We have developed an efficient method to determine high-resolution hypocenter locations over large distances. The location method incorporates ordinary absolute travel-time measurements and/or cross-correlation P-and S-wave differential travel-time measurements. Residuals between observed and theoretical travel-time differences (or double-differences) are minimized for pairs of earthquakes at each station while linking together all observed event-station pairs. A least-squares solu- tion is found by iteratively adjusting the vector difference between hypocentral pairs. The double-difference algorithm minimizes errors due to unmodeled velocity struc- ture without the use of station corrections. Because catalog and cross-correlation data are combined into one system of equations, interevent distances within multiplets are determined to the accuracy of the cross-correlation data, while the relative lo- cations between multiplets and uncorrelated events are simultaneously determined to the accuracy of the absolute travel-time data. Statistical resampling methods are used to estimate data accuracy and location errors. Uncertainties in double-difference locations are improved by more than an order of magnitude compared to catalog locations. The algorithm is tested, and its performance is demonstrated on two clus- ters of earthquakes located on the northern Hayward fault, California. There it col- lapses the diffuse catalog locations into sharp images of seismicity and reveals hor- izontal lineations of hypocenters that define the narrow regions on the fault where stress is released by brittle failure.

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A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California

A revised regular solution-type thermodynamic model for twelve-component silicate liquids in the system SiO2-TiO2-Al2O3-Fe2O3-Cr2O3-FeO-MgO-CaO-Na2O-K2O-P2O5-H2O is calibrated. The model is referenced to previously published standard state thermodynamic properties and is derived from a set of internally consistent thermodynamic models for solid solutions of the igneous rock forming minerals, including: (Mg,Fe2+,Ca)-olivines, (Na,Mg,Fe2+,Ca)M2 (Mg,Fe2+, Ti, Fe3+, Al)M1 (Fe3+, Al,Si)2TETO6-pyroxenes, (Na,Ca,K)-feldspars, (Mg,Fe2+) (Fe3+, Al, Cr)2O4-(Mg,Fe2+)2 TiO4 spinels and (Fe2+, Mg, Mn2+)TiO3-Fe2O3 rhombohedral oxides. The calibration utilizes over 2,500 experimentally determined compositions of silicate liquids coexisting at known temperatures, pressures and oxygen fugacities with apatite ±feldspar ±leucite ±olivine ±pyroxene ±quartz ±rhombohedral oxides ±spinel ±whitlockite ±water. The model is applicable to natural magmatic compositions (both hydrous and anhydrous), ranging from potash ankaratrites to rhyolites, over the temperature (T) range 900°–1700°C and pressures (P) up to 4 GPa. The model is implemented as a software package (MELTS) which may be used to simulate igneous processes such as (1) equilibrium or fractional crystallization, (2) isothermal, isenthalpic or isochoric assimilation, and (3) degassing of volatiles. Phase equilibria are predicted using the MELTS package by specifying bulk composition of the system and either (1) T and P, (2) enthalpy (H) and P, (3) entropy (S) and P, or (4) T and volume (V). Phase relations in systems open to oxygen are determined by directly specifying the fo2 or the T-P-fo2 (or equivalently H-P-fo2, S-P-fo2, T-V-fo2) evolution path. Calculations are performed by constrained minimization of the appropriate thermodynamic potential. Compositions and proportions of solids and liquids in the equilibrium assemblage are computed.

Chemical mass transfer in magmatic processes IV. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated temperatures and pressures

Ake Bjork

Papers

Solving Least Squares Problems