Bayesian estimation applied to multiple species

Observed data are often contaminated by undiscovered interlopers, leading to biased parameter estimation. Here we present BEAMS (Bayesian estimation applied to multiple species) which significantly improves on the standard maximum likelihood approach in the case where the probability for each data point being “pure” is known. We discuss the application of BEAMS to future type-Ia supernovae (SNIa) surveys, such as LSST, which are projected to deliver over a million supernovae light curves without spectra. The multiband light curves for each candidate will provide a probability of being Ia (pure) but the full sample will be significantly contaminated with other types of supernovae and transients. Given a sample of N supernovae with mean probability, ⟨P⟩, of being Ia, BEAMS delivers parameter constraints equal to N⟨P⟩ spectroscopically confirmed SNIa. In addition BEAMS can be simultaneously used to tease apart different families of data and to recover properties of the underlying distributions of those families (e.g. the type-Ibc and II distributions). Hence BEAMS provides a unified classification and parameter estimation methodology which may be useful in a diverse range of problems such as photometric redshift estimation or, indeed, any parameter estimation problem where contamination is an issue

Bayesian single-epoch photometric classification of supernovae

Ongoing supernova (SN) surveys find hundreds of candidates that require confirmation for their various uses. Traditional classification based on follow- up spectroscopy of all candidates is virtually impossible for these large samples. The use of Type Ia SNe as standard candles is at an evolved stage that requires pure, uncontaminated samples. However, other SN survey applications, such as measuring cosmic SN rates, could benefit froma classification of SNe on a statistical basis, rather than case by case. With this objective in mind, we have developed the SN-ABC, an automatic Bayesian classifying algorithm for supernovae. We rely solely on single- epoch multiband photometry and host-galaxy (photometric) redshift information to sort SN candidates into the two major types, Ia and core-collapse supernovae. We test the SN-ABC performance on published samples of SNe from the Supernova Legacy Survey (SNLS) and GOODS projects that have both broadband photometry and spectroscopic classification (so the true type is known). The SN- ABC correctly classifies up to 97% (85%) of the Type Ia (II-P) SNe in SNLS, and similar fractions of the GOODS SNe, depending on photometric redshift quality. Using simulations with large artificial samples, we find similarly high success fractions for Types Ia and II-P, and reasonable (~75%) success rates in classifying Type Ibc SNe as core-collapse. Type IIn SNe, however, are often misclassified as Type Ia. In deep surveys, SNe Ia are best classified at redshifts z ≳ 0.6 or when near maximum. Core-collapse SNe (other than Type IIn) are best recognized several weeks after maximum, or at z ≾ 0.6. Assuming the SNe are young, as would be the case for rolling surveys, the success fractions improve by a degree dependent on the type and redshift. The fractional contamination of a single-epoch photometrically selected sample of SNe la by core-collapse SNe varies between less than 10% and as much as 30%, depending on the intrinsic fraction and redshift distribution of the core-collapse SNe in a given survey. The SN-ABC also allows the rejection of SN "impostors" such as active galactic nuclei (AGNs), with half of the AGNs we simulate rejected by the algorithm. Our algorithm also supplies a good measure of the quality of the classification, which is valuable for error estimation

Statistics for evaluating pre-post change: Relation between change in the distribution center and change in the individual scores

In a number of scientific fields, researchers need to assess whether a variable has changed between two time points. Average-based change statistics (ABC) such as Cohen's d or Hays' ω2 evaluate the change in the distributions' center, whereas Individual-based change statistics (IBC) such as the Standardized Individual Difference or the Reliable Change Index evaluate whether each case in the sample experienced a reliable change. Through an extensive simulation study we show that, contrary to what previous studies have speculated, ABC and IBC statistics are closely related. The relation can be assumed to be linear, and was found regardless of sample size, pre-post correlation, and shape of the scores' distribution, both in single group designs and in experimental designs with a control group. We encourage other researchers to use IBC statistics to evaluate their effect sizes because: (a) they allow the identification of cases that changed reliably; (b) they facilitate the interpretation and communication of results; and (c) they provide a straightforward evaluation of the magnitude of empirical effects while avoiding the problems of arbitrary general cutoffs.EE was supported by the scholarship FPI-UAM 2011 (granted by Universidad Autónoma de Madrid). The publication fee was partially supported by the Library of UC, Davi

Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference

This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random coefficients -- are estimated by cross sectional sample moments of GMM estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimator has an asymptotic bias of the same order as the asymptotic variance. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.Comment: 51 pages, 4 tables, 1 figure, it includes supplementary appendi

Observed Fractions of Core-Collapse Supernova Types and Initial Masses of their Single and Binary Progenitor Stars

We analyse observed fractions of core-collapse SN types from the Lick Observatory SN Search, and we discuss corresponding implications for massive star evolution. For a standard IMF, observed fractions of SN types cannot be reconciled with expectations of single-star evolution. The mass range of WR stars that shed their H envelopes via their own mass loss accounts for less than half the observed fraction of SNeIbc. Progenitors of SNeIbc must extend to a much lower range of initial masses than classical WR stars, and we argue that most SNIbc and SNIIb progenitors must arise from binary Roche-lobe overflow. SNeIc still trace higher mass and metallicity, because line-driven winds in the WR stage remove the He layer and propel the transition from SNIb to Ic. Less massive progenitors of SNeIb and IIb may not be classical WR stars; they may be underluminous with weak winds, possibly hidden by overluminous mass-gainer companions that appear as B[e] supergiants or related objects having aspherical circumstellar material. The remaining SN types (II-P, II-L, and IIn) are redistributed across the full range of initial mass. We consider direct collapse to black holes without visible SNe, but find this problematic. Major areas of remaining uncertainty are (1) the influence of binary separation, rotation, and metallicity, (2) mass differences in progenitors of SNeIIn compared to SNeII-L and II-P, and (3) SNeIc arising from single stars with eruptive mass loss, its dependence on metallicity, and how it relates to diversity within the SNIc subclass. (abridged)Comment: MNRAS accepted, 18 pages, 8 Figures, 1 color figur

Mergers, acquisitions and technological regimes: the European experience over the period 2002-2005

Comparisons by countries and by sectors of mergers and acquisitions have usually been performed in separate fields of research. A first group of studies, focusing on international comparisons, has explored the role of corporate governance systems, investor protection laws and other countries’ regulatory institutions as the main determinants of takeovers around the world. A second group of contributions has attributed a central role to variations in industry composition, documenting that, in each country, mergers occur in waves and within each wave clustering by industry is observed. This paper aims to integrate both perspectives and to make comparisons by countries and by sectors, thus exploring the role of various driving forces on takeover activities. It also intends to consider the specific influence that technological regimes and their innovation patterns may exert in reallocating assets and moving capital among sectors. This will be done by examining the European experience of the last few years (2002-2005). We found that even in countries where transfer of control is a frequent phenomenon, mergers are less frequent in those sectors where innovation is a cumulative process and where takeovers may be a threat to the continuity of accumulation of innovative capabilities.Mergers and Acquisitions, Corporate Governance, Technological Regimes