1,263 research outputs found
Harold Jeffreys's Theory of Probability Revisited
Published exactly seventy years ago, Jeffreys's Theory of Probability (1939)
has had a unique impact on the Bayesian community and is now considered to be
one of the main classics in Bayesian Statistics as well as the initiator of the
objective Bayes school. In particular, its advances on the derivation of
noninformative priors as well as on the scaling of Bayes factors have had a
lasting impact on the field. However, the book reflects the characteristics of
the time, especially in terms of mathematical rigor. In this paper we point out
the fundamental aspects of this reference work, especially the thorough
coverage of testing problems and the construction of both estimation and
testing noninformative priors based on functional divergences. Our major aim
here is to help modern readers in navigating in this difficult text and in
concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968],
[arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073].
Rejoinder in [arXiv:0909.1008]. Published in at
http://dx.doi.org/10.1214/09-STS284 the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Main Belt Asteroids with WISE/NEOWISE I: Preliminary Albedos and Diameters
We present initial results from the Wide-field Infrared Survey Explorer
(WISE), a four-band all-sky thermal infrared survey that produces data well
suited to measuring the physical properties of asteroids, and the NEOWISE
enhancement to the WISE mission allowing for detailed study of Solar system
objects. Using a NEATM thermal model fitting routine we compute diameters for
over 100,000 Main Belt asteroids from their IR thermal flux, with errors better
than 10%. We then incorporate literature values of visible measurements (in the
form of the H absolute magnitude) to determine albedos. Using these data we
investigate the albedo and diameter distributions of the Main Belt. As observed
previously, we find a change in the average albedo when comparing the inner,
middle, and outer portions of the Main Belt. We also confirm that the albedo
distribution of each region is strongly bimodal. We observe groupings of
objects with similar albedos in regions of the Main Belt associated with
dynamical breakup families. Asteroid families typically show a characteristic
albedo for all members, but there are notable exceptions to this. This paper is
the first look at the Main Belt asteroids in the WISE data, and only represents
the preliminary, observed raw size and albedo distributions for the populations
considered. These distributions are subject to survey biases inherent to the
NEOWISE dataset and cannot yet be interpreted as describing the true
populations; the debiased size and albedo distributions will be the subject of
the next paper in this series.Comment: Accepted to ApJ. Online table to also appear on the publisher's
websit
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration
While statisticians are well-accustomed to performing exploratory analysis in
the modeling stage of an analysis, the notion of conducting preliminary
general-purpose exploratory analysis in the Monte Carlo stage (or more
generally, the model-fitting stage) of an analysis is an area which we feel
deserves much further attention. Towards this aim, this paper proposes a
general-purpose algorithm for automatic density exploration. The proposed
exploration algorithm combines and expands upon components from various
adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at
its heart. Additionally, the algorithm is run on interacting parallel chains --
a feature which both decreases computational cost as well as stabilizes the
algorithm, improving its ability to explore the density. Performance is studied
in several applications. Through a Bayesian variable selection example, the
authors demonstrate the convergence gains obtained with interacting chains. The
ability of the algorithm's adaptive proposal to induce mode-jumping is
illustrated through a trimodal density and a Bayesian mixture modeling
application. Lastly, through a 2D Ising model, the authors demonstrate the
ability of the algorithm to overcome the high correlations encountered in
spatial models.Comment: 33 pages, 20 figures (the supplementary materials are included as
appendices
Physical properties of ESA Rosetta target asteroid (21) Lutetia: Shape and flyby geometry
Aims. We determine the physical properties (spin state and shape) of asteroid
(21) Lutetia, target of the ESA Rosetta mission, to help in preparing for
observations during the flyby on 2010 July 10 by predicting the orientation of
Lutetia as seen from Rosetta.
Methods. We use our novel KOALA inversion algorithm to determine the physical
properties of asteroids from a combination of optical lightcurves,
disk-resolved images, and stellar occultations, although the latter are not
available for (21) Lutetia.
Results. We find the spin axis of (21) Lutetia to lie within 5 degrees of
({\lambda} = 52 deg., {\beta} = -6 deg.) in Ecliptic J2000 reference frame
(equatorial {\alpha} = 52 deg., {\delta} = +12 deg.), and determine an improved
sidereal period of 8.168 270 \pm 0.000 001 h. This pole solution implies the
southern hemisphere of Lutetia will be in "seasonal" shadow at the time of the
flyby. The apparent cross-section of Lutetia is triangular as seen "pole-on"
and more rectangular as seen "equator-on". The best-fit model suggests the
presence of several concavities. The largest of these is close to the north
pole and may be associated with large impacts.Comment: 17 pages, 5 figures, 3 tables, submitted to Astronomy and
Astrophysic
The triaxial ellipsoid dimensions, rotational pole, and bulk density of ESA Rosetta target asteroid (21) Lutetia
We seek the best size estimates of the asteroid (21) Lutetia, the direction
of its spin axis, and its bulk density, assuming its shape is well described by
a smooth featureless triaxial ellipsoid, and to evaluate the deviations from
this assumption. Methods. We derive these quantities from the outlines of the
asteroid in 307 images of its resolved apparent disk obtained with adaptive
optics (AO) at Keck II and VLT, and combine these with recent mass
determinations to estimate a bulk density. Our best triaxial ellipsoid
diameters for Lutetia, based on our AO images alone, are a x b x c = 132 x 101
x 93 km, with uncertainties of 4 x 3 x 13 km including estimated systematics,
with a rotational pole within 5 deg. of ECJ2000 [long,lat] = [45, -7], or
EQJ2000 [RA, DEC] = [44, +9]. The AO model fit itself has internal precisions
of 1 x 1 x 8 km, but it is evident, both from this model derived from limited
viewing aspects and the radius vector model given in a companion paper, that
Lutetia has significant departures from an idealized ellipsoid. In particular,
the long axis may be overestimated from the AO images alone by about 10 km.
Therefore, we combine the best aspects of the radius vector and ellipsoid model
into a hybrid ellipsoid model, as our final result, of 124 +/- 5 x 101 +/- 4 x
93 +/- 13 km that can be used to estimate volumes, sizes, and projected areas.
The adopted pole position is within 5 deg. of [long, lat] = [52, -6] or[RA DEC]
= [52, +12]. Using two separately determined masses and the volume of our
hybrid model, we estimate a density of 3.5 +/- 1.1 or 4.3 +/- 0.8 g cm-3 . From
the density evidence alone, we argue that this favors an enstatite-chondrite
composition, although other compositions are formally allowed at the extremes
(low-porosity CV/CO carbonaceous chondrite or high-porosity metallic). We
discuss this in the context of other evidence.Comment: 9 pages, 8 figures, 5 tables, submitted to Astronomy and Astrophysic
Ultraviolet and visible photometry of asteroid (21) Lutetia using the Hubble Space Telescope
The asteroid (21) Lutetia is the target of a planned close encounter by the
Rosetta spacecraft in July 2010. To prepare for that flyby, Lutetia has been
extensively observed by a variety of astronomical facilities. We used the
Hubble Space Telescope (HST) to determine the albedo of Lutetia over a wide
wavelength range, extending from ~150 nm to ~700 nm. Using data from a variety
of HST filters and a ground-based visible light spectrum, we employed synthetic
photometry techniques to derive absolute fluxes for Lutetia. New results from
ground-based measurements of Lutetia's size and shape were used to convert the
absolute fluxes into albedos. We present our best model for the spectral energy
distribution of Lutetia over the wavelength range 120-800 nm. There appears to
be a steep drop in the albedo (by a factor of ~2) for wavelengths shorter than
~300 nm. Nevertheless, the far ultraviolet albedo of Lutetia (~10%) is
considerably larger than that of typical C-chondrite material (~4%). The
geometric albedo at 550 nm is 16.5 +/- 1%. Lutetia's reflectivity is not
consistent with a metal-dominated surface at infrared or radar wavelengths, and
its albedo at all wavelengths (UV-visibile-IR-radar) is larger than observed
for typical primitive, chondritic material. We derive a relatively high FUV
albedo of ~10%, a result that will be tested by observations with the Alice
spectrograph during the Rosetta flyby of Lutetia in July 2010.Comment: 14 pages, 2 tables, 8 figure
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