The Design and Implementation of a Bayesian CAD Modeler for Robotic Applications

We present a Bayesian CAD modeler for robotic applications. We address the problem of taking into account the propagation of geometric uncertainties when solving inverse geometric problems. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements, instead of a simple equality or inequality. To solve geometric problems in this framework, we propose an original resolution method able to adapt to problem complexity. Using two examples, we show how to apply our approach by providing simulation results using our modeler

A Robotic CAD System using a Bayesian Framework

We present in this paper a Bayesian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how esian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how to take this propagation into account when solving inverse problems. We describe the methodology we use to represent and handle uncertainties using probability distributions on the system's parameters and sensor measurements. It may be seen as a generalization of constraint-based approaches where we express a constraint as a probability distribution instead of a simple equality or inequality. Appropriate numerical algorithms used to apply this methodology are also described. Using an example, we show how to apply our approach by providing simulation results using our CAD system

Modeling uncertainties in performance of object recognition

Efficient probability modeling is indispensable for uncertainty quantification of the recognition data. If the model assumptions do not reflect the intrinsic nature of data and associated random variables, then a strong performance measure will most likely fail to come up with a correct match for recognition. In this paper we propose the probability models for two kinds of data obtained with two distinct goals of recognition: identification and discovery. We consider both frequentisi and Bayesian approaches for drawing inferences from the data

EXONEST: Bayesian Model Selection Applied to the Detection and Characterization of Exoplanets Via Photometric Variations

EXONEST is an algorithm dedicated to detecting and characterizing the photometric signatures of exoplanets, which include reflection and thermal emission, Doppler boosting, and ellipsoidal variations. Using Bayesian Inference, we can test between competing models that describe the data as well as estimate model parameters. We demonstrate this approach by testing circular versus eccentric planetary orbital models, as well as testing for the presence or absence of four photometric effects. In addition to using Bayesian Model Selection, a unique aspect of EXONEST is the capability to distinguish between reflective and thermal contributions to the light curve. A case-study is presented using Kepler data recorded from the transiting planet KOI-13b. By considering only the non-transiting portions of the light curve, we demonstrate that it is possible to estimate the photometrically-relevant model parameters of KOI-13b. Furthermore, Bayesian model testing confirms that the orbit of KOI-13b has a detectable eccentricity.Comment: Accepted for publication in The Astrophysical Journa

Sensitivity of fluvial sediment source apportionment to mixing model assumptions: A Bayesian model comparison

Mixing models have become increasingly common tools for apportioning fluvial sediment load to various sediment sources across catchments using a wide variety of Bayesian and frequentist modeling approaches. In this study, we demonstrate how different model setups can impact upon resulting source apportionment estimates in a Bayesian framework via a one-factor-at-a-time (OFAT) sensitivity analysis. We formulate 13 versions of a mixing model, each with different error assumptions and model structural choices, and apply them to sediment geochemistry data from the River Blackwater, Norfolk, UK, to apportion suspended particulate matter (SPM) contributions from three sources (arable topsoils, road verges, and subsurface material) under base flow conditions between August 2012 and August 2013. Whilst all 13 models estimate subsurface sources to be the largest contributor of SPM (median ∼76%), comparison of apportionment estimates reveal varying degrees of sensitivity to changing priors, inclusion of covariance terms, incorporation of time-variant distributions, and methods of proportion characterization. We also demonstrate differences in apportionment results between a full and an empirical Bayesian setup, and between a Bayesian and a frequentist optimization approach. This OFAT sensitivity analysis reveals that mixing model structural choices and error assumptions can significantly impact upon sediment source apportionment results, with estimated median contributions in this study varying by up to 21% between model versions. Users of mixing models are therefore strongly advised to carefully consider and justify their choice of model structure prior to conducting sediment source apportionment investigations

Relative photometry of HAT-P-1b occultations

We present HST STIS observations of two occultations of the transiting exoplanet HAT-P-1b. By measuring the planet to star flux ratio near opposition, we constrain the geometric albedo of the planet, which is strongly linked to its atmospheric temperature gradient. An advantage of HAT-P-1 as a target is its binary companion ADS 16402 A, which provides an excellent photometric reference, simplifying the usual steps in removing instrumental artifacts from HST time-series photometry. We find that without this reference star, we would need to detrend the lightcurve with the time of the exposures as well as the first three powers of HST orbital phase, and this would introduce a strong bias in the results for the albedo. However, with this reference star, we only need to detrend the data with the time of the exposures to achieve the same per-point scatter, therefore we can avoid most of the bias associated with detrending. Our final result is a 2 sigma upper limit of 0.64 for the geometric albedo of HAT-P-1b between 577 and 947 nm.Comment: 8 pages, 2 figures, 3 table

The Cepheid Distance Scale: recent progress in fundamental techniques

This review examines progress on the Pop I, fundamental-mode Cepheid distance scale with emphasis on recent developments in geometric and quasi-geometric techniques for Cepheid distance determination. Specifically I examine the surface brightness method, interferometric pulsation method, and trigonometric measurements. The three techniques are found to be in excellent agreement for distance measures in the Galaxy. The velocity p-factor is of crucial importance in the first two of these methods. A comparison of recent determinations of the p-factor for Cepheids demonstrates that observational measures of p and theoretical predictions agree within their uncertainties for Galactic Cepheids.Comment: An invited review at the Santa Fe, NM, conference -- Stellar Pulsation: Challenges for Theory and Observation; May 31-June 5, 2009 10 pages, 8 figure