16,676 research outputs found
A Bayesian Reflection on Surfaces
The topic of this paper is a novel Bayesian continuous-basis field
representation and inference framework. Within this paper several problems are
solved: The maximally informative inference of continuous-basis fields, that is
where the basis for the field is itself a continuous object and not
representable in a finite manner; the tradeoff between accuracy of
representation in terms of information learned, and memory or storage capacity
in bits; the approximation of probability distributions so that a maximal
amount of information about the object being inferred is preserved; an
information theoretic justification for multigrid methodology. The maximally
informative field inference framework is described in full generality and
denoted the Generalized Kalman Filter. The Generalized Kalman Filter allows the
update of field knowledge from previous knowledge at any scale, and new data,
to new knowledge at any other scale. An application example instance, the
inference of continuous surfaces from measurements (for example, camera image
data), is presented.Comment: 34 pages, 1 figure, abbreviated versions presented: Bayesian
Statistics, Valencia, Spain, 1998; Maximum Entropy and Bayesian Methods,
Garching, Germany, 199
A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions
Several transiting super-Earths are expected to be discovered in the coming
few years. While tools to model the interior structure of transiting planets
exist, inferences about the composition are fraught with ambiguities. We
present a framework to quantify how much we can robustly infer about
super-Earth and Neptune-size exoplanet interiors from radius and mass
measurements. We introduce quaternary diagrams to illustrate the range of
possible interior compositions for planets with four layers (iron core,
silicate mantles, water layers, and H/He envelopes). We apply our model to
CoRoT-7b, GJ 436b, and HAT-P-11b. Interpretation of planets with H/He envelopes
is limited by the model uncertainty in the interior temperature, while for
CoRoT-7b observational uncertainties dominate. We further find that our planet
interior model sharpens the observational constraints on CoRoT-7b's mass and
radius, assuming the planet does not contain significant amounts of water or
gas. We show that the strength of the limits that can be placed on a
super-Earth's composition depends on the planet's density; for similar
observational uncertainties, high-density super-Mercuries allow the tightest
composition constraints. Finally, we describe how techniques from Bayesian
statistics can be used to take into account in a formal way the combined
contributions of both theoretical and observational uncertainties to
ambiguities in a planet's interior composition. On the whole, with only a mass
and radius measurement an exact interior composition cannot be inferred for an
exoplanet because the problem is highly underconstrained. Detailed quantitative
ranges of plausible compositions, however, can be found.Comment: 20 pages, 10 figures, published in Ap
EXONEST: The Bayesian Exoplanetary Explorer
The fields of astronomy and astrophysics are currently engaged in an
unprecedented era of discovery as recent missions have revealed thousands of
exoplanets orbiting other stars. While the Kepler Space Telescope mission has
enabled most of these exoplanets to be detected by identifying transiting
events, exoplanets often exhibit additional photometric effects that can be
used to improve the characterization of exoplanets. The EXONEST Exoplanetary
Explorer is a Bayesian exoplanet inference engine based on nested sampling and
originally designed to analyze archived Kepler Space Telescope and CoRoT
(Convection Rotation et Transits plan\'etaires) exoplanet mission data. We
discuss the EXONEST software package and describe how it accommodates
plug-and-play models of exoplanet-associated photometric effects for the
purpose of exoplanet detection, characterization and scientific hypothesis
testing. The current suite of models allows for both circular and eccentric
orbits in conjunction with photometric effects, such as the primary transit and
secondary eclipse, reflected light, thermal emissions, ellipsoidal variations,
Doppler beaming and superrotation. We discuss our new efforts to expand the
capabilities of the software to include more subtle photometric effects
involving reflected and refracted light. We discuss the EXONEST inference
engine design and introduce our plans to port the current MATLAB-based EXONEST
software package over to the next generation Exoplanetary Explorer, which will
be a Python-based open source project with the capability to employ third-party
plug-and-play models of exoplanet-related photometric effects.Comment: 30 pages, 8 figures, 5 tables. Presented at the 37th International
Workshop on Bayesian Inference and Maximum Entropy Methods in Science and
Engineering (MaxEnt 2017) in Jarinu/SP Brasi
On the effect of preferential sampling in spatial prediction
The choice of the sampling locations in a spatial network is often guided by practical demands. In particular, many locations are preferentially chosen to capture high values of a response, for example, air pollution levels in environmental monitoring. Then, model estimation and prediction of the exposure surface become biased due to the selective sampling. Since prediction is often the main utility of the modeling, we suggest that the effect of preferential sampling lies more importantly in the resulting predictive surface than in parameter estimation. Our contribution is to offer a direct simulation-based approach to assessing the effects of preferential sampling. We compare two predictive surfaces over the study region, one originating from the notion of an ‘operating’ intensity driving the selection of monitoring sites, the other under complete spatial randomness. We can consider a range of response models. They may reflect the operating intensity, introduce alternative informative covariates, or just propose a flexible spatial model. Then, we can generate data under the given model. Upon fitting the model and interpolating (kriging), we will obtain two predictive surfaces to compare. It is important to note that we need suitable metrics to compare the surfaces and that the predictive surfaces are random, so we need to make expected comparisons
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