A Bayesian Approach to Calibrating Period-Luminosity Relations of RR Lyrae Stars in the Mid-Infrared

A Bayesian approach to calibrating period-luminosity (PL) relations has substantial benefits over generic least-squares fits. In particular, the Bayesian approach takes into account the full prior distribution of the model parameters, such as the a priori distances, and refits these parameters as part of the process of settling on the most highly-constrained final fit. Additionally, the Bayesian approach can naturally ingest data from multiple wavebands and simultaneously fit the parameters of PL relations for each waveband in a procedure that constrains the parameter posterior distributions so as to minimize the scatter of the final fits appropriately in all wavebands. Here we describe the generalized approach to Bayesian model fitting and then specialize to a detailed description of applying Bayesian linear model fitting to the mid-infrared PL relations of RR Lyrae variable stars. For this example application we quantify the improvement afforded by using a Bayesian model fit. We also compare distances previously predicted in our example application to recently published parallax distances measured with the Hubble Space Telescope and find their agreement to be a vindication of our methodology. Our intent with this article is to spread awareness of the benefits and applicability of this Bayesian approach and encourage future PL relation investigations to consider employing this powerful analysis method.Comment: 6 pages, 1 figure. Accepted for publication in Astrophysics & Space Science. Following a presentation at the conference The Fundamental Cosmic Distance Scale: State of the Art and the Gaia Perspective, Naples, May 201

The Influence Function of Penalized Regression Estimators

To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations nonstandard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function.Comment: appears in Statistics: A Journal of Theoretical and Applied Statistics, 201

A simultaneous equations analysis of analysts’ forecast bias and institutional ownership

In this paper we use a simultaneous equations model to examine the relationship between analysts' forecasting decisions and institutions' investment decisions. Neglecting their interaction results in model misspecification. We find that analysts' optimism concerning a firm's earnings responds positively to changes in the number of institutions holding the firm's stock. At the same time, institutional demand responds positively to increases in analysts' optimism. We also investigate several firm characteristics as determinants of analysts' and institutions' decisions. We conclude that agency-driven behavioral considerations are significant.Financial institutions ; Forecasting ; Financial markets

Strong Constraints to the Putative Planet Candidate around VB 10 using Doppler spectroscopy

We present new radial velocity measurements of the ultra-cool dwarf VB 10, which was recently announced to host a giant planet detected with astrometry. The new observations were obtained using optical spectrographs(MIKE/Magellan and ESPaDOnS/CHFT) and cover a 63% of the reported period of 270 days. We apply Least-squares periodograms to identify the most significant signals and evaluate their corresponding False Alarm Probabilities. We show that this method is the proper generalization to astrometric data because (1) it mitigates the coupling of the orbital parameters with the parallax and proper motion, and (2) it permits a direct generalization to include non-linear Keplerian parameters in a combined fit to astrometry and radial velocity data. In fact, our analysis of the astrometry alone uncovers the reported 270 d period and an even stronger signal at 50 days. We estimate the uncertainties in the parameters using a Markov Chain Monte Carlo approach. The nominal precision of the new Doppler measurements is about 150 s$^{-1}$ while their standard deviation is 250 ms$^{-1}$. However, the best fit solutions still have RMS of 200 ms$^{-1}$ indicating that the excess in variability is due to uncontrolled systematic errors rather than the candidate companions detected in the astrometry. Although the new data alone cannot rule-out the presence of a candidate, when combined with published radial velocity measurements, the False Alarm Probabilities of the best solutions grow to unacceptable levels strongly suggesting that the observed astrometric wobble is not due to an unseen companion.Comment: ApJ Letters, under revision. 15 pages, 3 figures and 2 tables. Author list update

Position and Orientation Estimation of a Rigid Body: Rigid Body Localization

Rigid body localization refers to a problem of estimating the position of a rigid body along with its orientation using anchors. We consider a setup in which a few sensors are mounted on a rigid body. The absolute position of the rigid body is not known, but, the relative position of the sensors or the topology of the sensors on the rigid body is known. We express the absolute position of the sensors as an affine function of the Stiefel manifold and propose a simple least-squares (LS) estimator as well as a constrained total least-squares (CTLS) estimator to jointly estimate the orientation and the position of the rigid body. To account for the perturbations of the sensors, we also propose a constrained total least-squares (CTLS) estimator. Analytical closed-form solutions for the proposed estimators are provided. Simulations are used to corroborate and analyze the performance of the proposed estimators.Comment: 4 pages and 1 reference page; 3 Figures; In Proc. of ICASSP 201