Predictive Margins and Marginal Effects in Stata

Tables of estimated regression coefficients, usually accompanied by additional information such as standard errors, t-statistics, p-values, confidence intervals or significance stars, have long been the preferred way of communicating results from statistical models. In recent years, however, the limits of this form of exposition have been increasingly recognized. For example, interpretation of regression tables can be very challenging in the presence of complications such as interaction effects, categorical variables, or nonlinear functional forms. Furthermore, while these issues might still be manageable in the case of linear regression, interpretational difficulties can be overwhelming in nonlinear models such as logistic regression. To facilitate sensible interpretation of such models it is often necessary to compute additional results such as marginal effects, predictive margins, or contrasts. Moreover, smart graphical displays of results can be very valuable in making complex relations accessible. A number of helpful commands geared at supporting these tasks have been recently introduced in Stata, making elaborate interpretation and communication of regression results possible without much extra effort. Examples of such commands are -margins-, -contrasts-, and -marginsplot-. In my talk, I will discuss the capabilities of these commands and present a range of examples illustrating their use.

The HARPS search for southern extra-solar planets

The vast diversity of planetary systems detected to date is defying our capability of understanding their formation and evolution. Well-defined volume-limited surveys are the best tool at our disposal to tackle the problem, via the acquisition of robust statistics of the orbital elements. We are using the HARPS spectrograph to conduct our survey of ≈850 nearby solar-type stars, and in the course of the past nine years we have monitored the radial velocity of HD 103774, HD 109271, and BD-061339. In this work we present the detection of five planets orbiting these stars, with msin   (i) between 0.6 and 7 Neptune masses, four of which are in two multiple systems, comprising one super-Earth and one planet within the habitable zone of a late-type dwarf. Although for strategic reasons we chose efficiency over precision in this survey, we have the capability to detect planets down to the Neptune and super-Earth mass range as well as multiple systems, provided that enough data points are made available.

Statistical Methods and the Meaning of Probabilities. A Philosopher Looks at Statistics

The talk starts out with a short introduction to the philosophy of probability. I highlight the need to interpret probabilities in the sciences and motivate objectivist accounts of probabilities. Very roughly, according to such accounts, ascriptions of probabilities have truth-conditions that are independent of personal interests and needs. But objectivist accounts are pointless if they do not provide an objectivist epistemology, i.e., if they do not determine well-defined methods to support or falsify claims about probabilities. In the rest of the talk I examine recent philosophical proposals for an objectivist methodology. Most of them take up ideas well-known from statistics. I nevertheless find some proposals incompatible with objectivist aspirations.

Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Debris discs around M stars: non-existence versus non-detection

Motivated by the reported dearth of debris discs around M stars, we use survival models to study the occurrence of planetesimal discs around them. These survival models describe a planetesimal disc with a small number of parameters, determine if it may survive a series of dynamical processes and compute the associated infrared excess. For the Wide-field Infrared Survey Explorer (WISE) satellite, we demonstrate that the dearth of debris discs around M stars may be attributed to the small semimajor axes generally probed if either: (1) the dust grains behave like blackbodies emitting at a peak wavelength coincident with the observed one; (2) or the grains are hotter than predicted by their blackbody temperatures and emit at peak wavelengths that are shorter than the observed one. At these small distances from the M star, planetesimals are unlikely to survive or persist for time-scales of 300 Myr or longer if the disc is too massive. Conversely, our survival models allow for the existence of a large population of low-mass debris discs that are too faint to be detected with current instruments. We gain further confidence in our interpretation by demonstrating the ability to compute infrared excesses for Sun-like stars that are broadly consistent with reported values in the literature. However, our interpretation becomes less clear and large infrared excesses are allowed if only one of these scenarios holds: (3) the dust grains are hotter than blackbody and predominantly emit at the observed wavelength; (4) or are blackbody in nature and emit at peak wavelengths longer than the observed one. Both scenarios imply that the parent planetesimals reside at larger distances from the star than inferred if the dust grains behaved like blackbodies. In all scenarios, we show that the infrared excesses detected at 22 μm (via WISE) and 70 μm (via Spitzer) from AU Mic are easily reconciled with its young age (12 Myr). Conversely, the existence of the old debris disc (2–8 Gyr) from GJ 581 is due to the large semimajor axes probed by the Herschel PACS instrument. We elucidate the conditions under which stellar wind drag may be neglected when considering dust populations around M stars. The WISE satellite should be capable of detecting debris discs around young M stars with ages ∼10 Myr.

Tools & Techniques - Statistics: Propensity score techniques.

Propensity score (PS) techniques are useful if the number of potential confounding pretreatment variables is large and the number of analysed outcome events is rather small so that conventional multivariable adjustment is hardly feasible. Only pretreatment characteristics should be chosen to derive PS, and only when they are probably associated with outcome. A careful visual inspection of PS will help to identify areas of no or minimal overlap, which suggests residual confounding, and trimming of the data according to the distribution of PS will help to minimise residual confounding. Standardised differences in pretreatment characteristics provide a useful check of the success of the PS technique employed. As with conventional multivariable adjustment, PS techniques cannot account for confounding variables that are not or are only imperfectly measured, and no PS technique is a substitute for an adequately designed randomised trial.

Streak detection algorithm for space debris detection on optical images.

Any image processing object detection algorithm somehow tries to integrate the object light (Recognition Step) and applies statistical criteria to distinguish objects of interest from other objects or from pure background (Decision Step). There are various possibilities how these two basic steps can be realized, as can be seen in the different proposed detection methods in the literature. An ideal detection algorithm should provide high recognition sensitiv ity with high decision accuracy and require a reasonable computation effort . In reality, a gain in sensitivity is usually only possible with a loss in decision accuracy and with a higher computational effort. So, automatic detection of faint streaks is still a challenge. This paper presents a detection algorithm using spatial filters simulating the geometrical form of possible streaks on a CCD image. This is realized by image convolution. The goal of this method is to generate a more or less perfect match between a streak and a filter by varying the length and orientation of the filters. The convolution answers are accepted or rejected according to an overall threshold given by the ackground statistics. This approach yields as a first result a huge amount of accepted answers due to filters partially covering streaks or remaining stars. To avoid this, a set of additional acceptance criteria has been included in the detection method. All criteria parameters are justified by background and streak statistics and they affect the detection sensitivity only marginally. Tests on images containing simulated streaks and on real images containing satellite streaks show a very promising sensitivity, reliability and running speed for this detection method. Since all method parameters are based on statistics, the true alarm, as well as the false alarm probability, are well controllable. Moreover, the proposed method does not pose any extraordinary demands on the computer hardware and on the image acquisition process.

Directional statistics: introduction

In many of the natural and physical sciences, measurements are directions, either in two or three dimensions. The analysis of directional data relies on specific statistical models and procedures, which differ from the usual models and methodologies of Cartesian data. This chapter briefly introduces statistical models and inference for this type of data. The basic von Mises-Fisher distribution is introduced and nonparametric methods such as goodness-of-fit tests are presented. Further references are given for exploring related topics such as correlation and regression.