Principal arc analysis on direct product manifolds

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the manifold that can be used to find and visualize the principal modes of variation of the data, as Principal Component Analysis (PCA) does in linear spaces. The proposed method improves upon earlier manifold extensions of PCA by more concisely capturing important nonlinear modes. For the special case of data on a sphere, variation following nongeodesic arcs is captured in a single mode, compared to the two modes needed by previous methods. Several computational and statistical challenges are resolved. The development on spheres forms the basis of principal arc analysis on more complicated manifolds. The benefits of the method are illustrated by a data example using medial representations in image analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS370 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rapid Bayesian position reconstruction for gravitational-wave transients

Within the next few years, Advanced LIGO and Virgo should detect gravitational waves from binary neutron star and neutron star-black hole mergers. These sources are also predicted to power a broad array of electromagnetic transients. Because the electromagnetic signatures can be faint and fade rapidly, observing them hinges on rapidly inferring the sky location from the gravitational-wave observations. Markov chain Monte Carlo methods for gravitational-wave parameter estimation can take hours or more. We introduce BAYESTAR, a rapid, Bayesian, non-Markov chain Monte Carlo sky localization algorithm that takes just seconds to produce probability sky maps that are comparable in accuracy to the full analysis. Prompt localizations from BAYESTAR will make it possible to search electromagnetic counterparts of compact binary mergers.Comment: 23 pages, 12 figures, published in Phys. Rev.

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Extrinisic Calibration of a Camera-Arm System Through Rotation Identification

Determining extrinsic calibration parameters is a necessity in any robotic system composed of actuators and cameras. Once a system is outside the lab environment, parameters must be determined without relying on outside artifacts such as calibration targets. We propose a method that relies on structured motion of an observed arm to recover extrinsic calibration parameters. Our method combines known arm kinematics with observations of conics in the image plane to calculate maximum-likelihood estimates for calibration extrinsics. This method is validated in simulation and tested against a real-world model, yielding results consistent with ruler-based estimates. Our method shows promise for estimating the pose of a camera relative to an articulated arm's end effector without requiring tedious measurements or external artifacts. Index Terms: robotics, hand-eye problem, self-calibration, structure from motio

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure

The Role of Inflation Persistence in the Inflation Process in the New EU Member States

The aim of this paper is to compare inflation persistence between the New Member States (NMS) that joined the European Union in 2004 and 2007 and selected euro area members. If the levels of inflation persistence between the two groups are different, the NMS may encounter problems with fulfilling the Maastricht criterion on inflation and – after entering the euro area – with inflation divergence. We argue that the specific economic situation of the NMS in the last 15 years necessitates careful selection of inflation persistence measures. Two measures are estimated. The first one is based on a simple univariate statistical model of inflation with a time-varying mean. The second one assumes that inflation follows a fractionally integrated process and measures inflation persistence within an ARFIMA model. Statistical tests suggest that the model with a time-varying mean is preferable to the ARFIMA model for almost all countries. The estimation results show that inflation persistence is not an issue for all of the NMS. On the one hand, Bulgaria, Cyprus, the Czech Republic, Malta, Romania, and Slovakia exhibit persistence levels similar to those in the selected euro area countries. On the other hand, Estonia, Hungary, Latvia, Lithuania, Poland, and Slovenia encounter a problem with high persistence stemming from both high intrinsic and high expectations-based inflation persistence.inflation persistence, new member states, time-varying mean, central bank credibility, ARFIMA model, Bayesian estimation, Kalman filter

A seasonal cycle and an abrupt change in the variability characteristics of the intraday variable source S4 0954+65

The BLLac object S4 0954+65 is one of the main targets of the Urumqi monitoring program targeting IntraDay Variable (IDV) sources. Between August 2005 and December 2009, the source was included in 41 observing sessions, carried out at a frequency of 4.8 GHz. The time analysis of the collected light curves, performed by applying both a structure function analysis and a specifically developed wavelet-based algorithm, discovered an annual cycle in the variability timescales, suggesting that there is a fundamental contribution by interstellar scintillation to the IDV pattern of the source. The combined use of the two analysis methods also revealed that there was a dramatic change in the variability characteristics of the source between February and March 2008, at the starting time of a strong outburst phase. The analysis' results suggest that the flaring state of the source coincides with the appearance of multiple timescales in its light curves, indicating that changes in the structure of the relativistically moving emitting region may strongly influence the variability observed on IDV timescales.Comment: 9 pages, 8 figures and 3 tables. Accepted for publication in Astronomy and Astrophysic

This elusive objective existence

Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of objective existence in two ways. The elimination of these prejudices makes it possible to recognize the quantum formalism's ontological implications - the relative and contingent reality of spatiotemporal distinctions and the extrinsic and finite spatiotemporal differentiation of the physical world - which in turn makes it possible to arrive at an unqualified objective existence. Contrary to a widespread misconception, viewing the quantum formalism as being fundamentally a probability algorithm does not imply that quantum mechanics is concerned with states of knowledge rather than states of Nature. On the contrary, it makes possible a complete and strongly objective description of the physical world that requires no reference to observers. What objectively exists, in a sense that requires no qualification, is the trajectories of macroscopic objects, whose fuzziness is empirically irrelevant, the properties and values of whose possession these trajectories provide indelible records, and the fuzzy and temporally undifferentiated states of affairs that obtain between measurements and are described by counterfactual probability assignments.Comment: To appear in IJQI; 21 pages, LaTe