Penalized likelihood estimation and iterative kalman smoothing for non-gaussian dynamic regression models

Dynamic regression or state space models provide a flexible framework for analyzing non-Gaussian time series and longitudinal data, covering for example models for discrete longitudinal observations. As for non-Gaussian random coefficient models, a direct Bayesian approach leads to numerical integration problems, often intractable for more complicated data sets. Recent Markov chain Monte Carlo methods avoid this by repeated sampling from approximative posterior distributions, but there are still open questions about sampling schemes and convergence. In this article we consider simpler methods of inference based on posterior modes or, equivalently, maximum penalized likelihood estimation. From the latter point of view, the approach can also be interpreted as a nonparametric method for smoothing time-varying coefficients. Efficient smoothing algorithms are obtained by iteration of common linear Kalman filtering and smoothing, in the same way as estimation in generalized linear models with fixed effects can be performed by iteratively weighted least squares estimation. The algorithm can be combined with an EM-type method or cross-validation to estimate unknown hyper- or smoothing parameters. The approach is illustrated by applications to a binary time series and a multicategorical longitudinal data set

Audiovisual integration of emotional signals from others' social interactions

Audiovisual perception of emotions has been typically examined using displays of a solitary character (e.g., the face-voice and/or body-sound of one actor). However, in real life humans often face more complex multisensory social situations, involving more than one person. Here we ask if the audiovisual facilitation in emotion recognition previously found in simpler social situations extends to more complex and ecological situations. Stimuli consisting of the biological motion and voice of two interacting agents were used in two experiments. In Experiment 1, participants were presented with visual, auditory, auditory filtered/noisy, and audiovisual congruent and incongruent clips. We asked participants to judge whether the two agents were interacting happily or angrily. In Experiment 2, another group of participants repeated the same task, as in Experiment 1, while trying to ignore either the visual or the auditory information. The findings from both experiments indicate that when the reliability of the auditory cue was decreased participants weighted more the visual cue in their emotional judgments. This in turn translated in increased emotion recognition accuracy for the multisensory condition. Our findings thus point to a common mechanism of multisensory integration of emotional signals irrespective of social stimulus complexity

Dynamics of polarization buildup by spin filtering

There has been much recent research into polarizing an antiproton beam, instigated by the recent proposal from the PAX (Polarized Antiproton eXperiment) project at GSI Darmstadt. It plans to polarize an antiproton beam by repeated interaction with a polarized internal target in a storage ring. The method of polarization by spin filtering requires many of the beam particles to remain within the ring after scattering off the polarized internal target via electromagnetic and hadronic interactions. We present and solve sets of differential equations which describe the buildup of polarization by spin filtering in many different scenarios of interest to projects planning to produce high intensity polarized beams. These scenarios are: 1) spin filtering of a fully stored beam, 2) spin filtering while the beam is being accumulated, i.e. unpolarized particles are continuously being fed into the beam, 3) the particle input rate is equal to the rate at which particles are being lost due to scattering beyond ring acceptance angle, the beam intensity remaining constant, 4) increasing the initial polarization of a stored beam by spin filtering, 5) the input of particles into the beam is stopped after a certain amount of time, but spin filtering continues. The rate of depolarization of a stored polarized beam on passing through an electron cooler is also shown to be negligible.Comment: 15 pages, references added, introduction elaborated on, some variables defined in more detail. Submitted to Eur. Phys. J.

Improvements on "Fast space-variant elliptical filtering using box splines"

It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining it with a non-standard variant of the Central Limit Theorem, a constant-time or O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform space-variant filtering using Gaussian-like kernels. The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size (covariance) of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, offered a limited control on the covariance and accuracy of the Gaussian approximation. In this work, we propose some improvements by appropriately modifying the algorithm in [Chaudhury2010].Comment: 7 figure

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

Fast adaptive elliptical filtering using box splines

We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a pointwise-adaptive localization mesh. We present the basic theory for the 1D case using a B-spline formalism and then appropriately extend it to 2D using radially-uniform box splines. The size and ellipticity of these radially-uniform box splines is adaptively controlled. Moreover, they converge to Gaussians as the order increases. Finally, we present a fast and practical directional filtering algorithm that has the capability of adapting to the local image features.Comment: 9 pages, 1 figur

High contrast optical imaging of companions: the case of the brown dwarf binary HD-130948BC

High contrast imaging at optical wavelengths is limited by the modest correction of conventional near-IR optimized AO systems.We take advantage of new fast and low-readout-noise detectors to explore the potential of fast imaging coupled to post-processing techniques to detect faint companions to stars at small separations. We have focused on I-band direct imaging of the previously detected brown dwarf binary HD130948BC,attempting to spatially resolve the L2+L2 benchmark system. We used the Lucky-Imaging instrument FastCam at the 2.5-m Nordic Telescope to obtain quasi diffraction-limited images of HD130948 with ~0.1" resolution.In order to improve the detectability of the faint binary in the vicinity of a bright (I=5.19 \pm 0.03) solar-type star,we implemented a post-processing technique based on wavelet transform filtering of the image which allows us to strongly enhance the presence of point-like sources in regions where the primary halo dominates. We detect for the first time the BD binary HD130948BC in the optical band I with a SNR~9 at 2.561"\pm 0.007" (46.5 AU) from HD130948A and confirm in two independent dataset that the object is real,as opposed to time-varying residual speckles.We do not resolve the binary, which can be explained by astrometric results posterior to our observations that predict a separation below the NOT resolution.We reach at this distance a contrast of dI = 11.30 \pm 0.11, and estimate a combined magnitude for this binary to I = 16.49 \pm 0.11 and a I-J colour 3.29 \pm 0.13. At 1", we reach a detectability 10.5 mag fainter than the primary after image post-processing. We obtain on-sky validation of a technique based on speckle imaging and wavelet-transform processing,which improves the high contrast capabilities of speckle imaging.The I-J colour measured for the BD companion is slightly bluer, but still consistent with what typically found for L2 dwarfs(~3.4-3.6).Comment: accepted in A\&

Nonlinear State-Space Models for Microeconometric Panel Data

In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application