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

Physical Investigation of the Potentially Hazardous Asteroid (144898) 2004 VD17

In this paper we present the observational campaign carried out at ESO NTT and VLT in April and May 2006 to investigate the nature and the structure of the Near Earth Object (144898) 2004 VD17. In spite of a great quantity of dynamical information, according to which it will have a close approach with the Earth in the next century, the physical properties of this asteroid are largely unknown. We performed visible and near--infrared photometry and spectroscopy, as well as polarimetric observations. Polarimetric and spectroscopic data allowed us to classify 2004 VD17 as an E-type asteroid. A good agreement was also found with the spectrum of the aubrite meteorite Mayo Belwa. On the basis of the polarimetric albedo (p_v=0.45) and of photometric data, we estimated a diameter of about 320 m and a rotational period of about 2 hours. The analysis of the results obtained by our complete survey have shown that (144898) 2004 VD17 is a peculiar NEO, since it is close to the breakup limits for fast rotator asteroids, as defined by Pravec and Harris (2000). These results suggest that a more robust structure must be expected, as a fractured monolith or a rubble pile in a "strength regime" (Holsapple 2002).Comment: 32 pages, 7 figure, paper accepted for publication in Icaru

Earth-Moon Impacts at ~300 Ma and ~500 Ma Ago

Impact events have played an important role in the evolution of planets and small bodies in the Solar System. Meteorites, lunar melt rocks, and lunar impact glasses provide important information about the geology of the parent body and the age of the impacting episodes. Over 2400 impact glasses from 4 Apollo regolith samples have been geochemically analyzed and a subset has been dated by the (40)Ar/(39)Ar method. New results, consistent with 2 break-ups in the Asteroid Belt, are presented here. Our previous study reported that (40)Ar/(39)Ar ages from 9 impact glasses showed that the Moon experienced significant impacts at approx. 800 Ma and at approx. 3800 Ma ago, somewhere in the vicinity of the Apollo 16 landing site. Additionally, reported on Apollo 12 samples with ages around 800 Ma, together implying global bombardment events. New data on 7 glasses from regolith sample 66041,127 show that the Moon also experienced impact events at approx. 300 Ma and > 500 Ma ago, which may coincide with the break-ups in the Asteroid Belt of the L- and H-chrondrite parent bodies. Since meteoritic evidence for these breakups has been found on Earth, it follows that evidence should be found in lunar samples as well. Additional information is included in the original extended abstract

Differential expression analysis with global network adjustment

<p>Background: Large-scale chromosomal deletions or other non-specific perturbations of the transcriptome can alter the expression of hundreds or thousands of genes, and it is of biological interest to understand which genes are most profoundly affected. We present a method for predicting a gene’s expression as a function of other genes thereby accounting for the effect of transcriptional regulation that confounds the identification of genes differentially expressed relative to a regulatory network. The challenge in constructing such models is that the number of possible regulator transcripts within a global network is on the order of thousands, and the number of biological samples is typically on the order of 10. Nevertheless, there are large gene expression databases that can be used to construct networks that could be helpful in modeling transcriptional regulation in smaller experiments.</p> <p>Results: We demonstrate a type of penalized regression model that can be estimated from large gene expression databases, and then applied to smaller experiments. The ridge parameter is selected by minimizing the cross-validation error of the predictions in the independent out-sample. This tends to increase the model stability and leads to a much greater degree of parameter shrinkage, but the resulting biased estimation is mitigated by a second round of regression. Nevertheless, the proposed computationally efficient “over-shrinkage” method outperforms previously used LASSO-based techniques. In two independent datasets, we find that the median proportion of explained variability in expression is approximately 25%, and this results in a substantial increase in the signal-to-noise ratio allowing more powerful inferences on differential gene expression leading to biologically intuitive findings. We also show that a large proportion of gene dependencies are conditional on the biological state, which would be impossible with standard differential expression methods.</p> <p>Conclusions: By adjusting for the effects of the global network on individual genes, both the sensitivity and reliability of differential expression measures are greatly improved.</p&gt

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

CCD and photon-counting photometric observations of asteroids carried out at Padova and Catania observatories

We present the results of observational campaigns of asteroids performed at Asiago Station of Padova Astronomical Observatory and at M.G. Fracastoro Station of Catania Astrophysical Observatory, as part of the large research programme on Solar System minor bodies undertaken since 1979 at the Physics and Astronomy Department of Catania University. Photometric observations of six Main-Belt asteroids (27 Euterpe, 173 Ino, 182 Elsa, 539 Pamina, 849 Ara, and 984 Gretia), one Hungaria (1727 Mette), and two Near-Earth Objects (3199 Nefertiti and 2004 UE) are reported. The first determination of the synodic rotational period of 2004 UE was obtained. For 182 Elsa and 1727 Mette the derived synodic period of 80.23+/-0.08 h and 2.981+/-0.001 h, respectively, represents a significant improvement on the previously published values. For 182 Elsa the first determination of the H-G magnitude relation is also presented.Comment: 19 pages, 11 figures, accepted for publication in Planetary and Space Scienc

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

Maximum Entropy and Bayesian Data Analysis: Entropic Priors

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is inspired and guided by intuition gained from the successful use of ME methods in statistical mechanics. For experiments that cannot be repeated the resulting "entropic prior" is formally identical with the Einstein fluctuation formula. For repeatable experiments, however, the expected value of the entropy of the likelihood turns out to be relevant information that must be included in the analysis. The important case of a Gaussian likelihood is treated in detail.Comment: 23 pages, 2 figure

A revised asteroid polarization-albedo relationship using WISE/NEOWISE data

We present a reanalysis of the relationship between asteroid albedo and polarization properties using the albedos derived from the Wide-field Infrared Survey Explorer. We find that the function that best describes this relation is a three-dimensional linear fit in the space of log(albedo)-log(polarization slope)-log(minimum polarization). When projected to two dimensions the parameters of the fit are consistent with those found in previous work. We also define p* as the quantity of maximal polarization variation when compared with albedo and present the best fitting albedo-p* relation. Some asteroid taxonomic types stand out in this three-dimensional space, notably the E, B, and M Tholen types, while others cluster in clumps coincident with the S- and C-complex bodies. We note that both low albedo and small (D<30 km) asteroids are under-represented in the polarimetric sample, and we encourage future polarimetric surveys to focus on these bodies.Comment: 16 pages, Accepted to Ap

Assimilation of healthy and indulgent impressions from labelling influences fullness but not intake or sensory experience

Background: Recent evidence suggests that products believed to be healthy may be over-consumed relative to believed indulgent or highly caloric products. The extent to which these effects relate to expectations from labelling, oral experience or assimilation of expectations is unclear. Over two experiments, we tested the hypotheses that healthy and indulgent information could be assimilated by oral experience of beverages and influence sensory evaluation, expected satiety, satiation and subsequent appetite. Additionally, we explored how expectation-experience congruency influenced these factors. Results: Results supported some assimilation of healthiness and indulgent ratings—study 1 showed that indulgent ratings enhanced by the indulgent label persisted post-tasting, and this resulted in increased fullness ratings. In study 2, congruency of healthy labels and oral experience promoted enhanced healthiness ratings. These healthiness and indulgent beliefs did not influence sensory analysis or intake—these were dictated by the products themselves. Healthy labels, but not experience, were associated with decreased expected satiety. Conclusions: Overall labels generated expectations, and some assimilation where there were congruencies between expectation and experience, but oral experience tended to override initial expectations to determine ultimate sensory evaluations and intake. Familiarity with the sensory properties of the test beverages may have resulted in the use of prior knowledge, rather than the label information, to guide evaluations and behaviour