Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and Control (CDC), Firenze, Italy, December 201

Compressed sensing imaging techniques for radio interferometry

Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmology.Comment: 10 pages, 1 figure. Version 2 matches version accepted for publication in MNRAS. Changes includes: writing corrections, clarifications of arguments, figure update, and a new subsection 4.1 commenting on the exact compliance of radio interferometric measurements with compressed sensin

Study to investigate and evaluate means of optimizing the Ku-band combined radar/communication functions for the space shuttle

The Ku band radar system on the shuttle orbiter operates in both a search and a tracking mode, and its transmitter and antennas share time with the communication mode in the integrated system. The power allocation properties and the Costa subloop subcarrier tracking performance associated with the baseline digital phase shift implementation of the three channel orbiter Ku band modulator are discussed

PASTIS: Bayesian extrasolar planet validation. I. General framework, models, and performance

A large fraction of the smallest transiting planet candidates discovered by the Kepler and CoRoT space missions cannot be confirmed by a dynamical measurement of the mass using currently available observing facilities. To establish their planetary nature, the concept of planet validation has been advanced. This technique compares the probability of the planetary hypothesis against that of all reasonably conceivable alternative false-positive (FP) hypotheses. The candidate is considered as validated if the posterior probability of the planetary hypothesis is sufficiently larger than the sum of the probabilities of all FP scenarios. In this paper, we present PASTIS, the Planet Analysis and Small Transit Investigation Software, a tool designed to perform a rigorous model comparison of the hypotheses involved in the problem of planet validation, and to fully exploit the information available in the candidate light curves. PASTIS self-consistently models the transit light curves and follow-up observations. Its object-oriented structure offers a large flexibility for defining the scenarios to be compared. The performance is explored using artificial transit light curves of planets and FPs with a realistic error distribution obtained from a Kepler light curve. We find that data support for the correct hypothesis is strong only when the signal is high enough (transit signal-to-noise ratio above 50 for the planet case) and remains inconclusive otherwise. PLATO shall provide transits with high enough signal-to-noise ratio, but to establish the true nature of the vast majority of Kepler and CoRoT transit candidates additional data or strong reliance on hypotheses priors is needed.Comment: Accepted for publication in MNRAS; 23 pages, 11 figure

Fast non-negative deconvolution for spike train inference from population calcium imaging

Calcium imaging for observing spiking activity from large populations of neurons are quickly gaining popularity. While the raw data are fluorescence movies, the underlying spike trains are of interest. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train for each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm is fast enough that even when imaging over 100 neurons, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure

Comparing compact binary parameter distributions I: Methods

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference