2,794 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
Geometric View of Measurement Errors
The slope of the best fit line from minimizing the sum of the squared oblique
errors is the root of a polynomial of degree four. This geometric view of
measurement errors is used to give insight into the performance of various
slope estimators for the measurement error model including an adjusted fourth
moment estimator introduced by Gillard and Iles (2005) to remove the jump
discontinuity in the estimator of Copas (1972). The polynomial of degree four
is associated with a minimun deviation estimator. A simulation study compares
these estimators showing improvement in bias and mean squared error
Are black holes over-produced during preheating?
We provide a simple but robust argument that primordial black hole (PBH)
production generically does {\em not} exceed astrophysical bounds during the
resonant preheating phase after inflation. This conclusion is supported by
fully nonlinear lattice simulations of various models in two and three
dimensions which include rescattering but neglect metric perturbations. We
examine the degree to which preheating amplifies density perturbations at the
Hubble scale and show that at the end of the parametric resonance, power
spectra are universal, with no memory of the power spectrum at the end of
inflation. In addition we show how the probability distribution of density
perturbations changes from exponential on very small scales to Gaussian when
smoothed over the Hubble scale -- the crucial length for studies of primordial
black hole formation -- hence justifying the standard assumption of
Gaussianity.Comment: 12 pages, 8 figures, revtex, added references for section
Spontaneous CP Violation at the Electroweak Scale
Utilizing results on the cosmology of anomalous discrete symmetries we show
that models of spontaneous CP violation can in principle avoid the domain wall
problem first pointed out by Zel'dovich, Kobzarev and Okun. A small but nonzero
explicitly breaks CP and can lift the degeneracy of the two CP
conjugate vacua through nonperturbative effects so that the domain walls become
unstable, but survive to cosmologically interesting epochs. We explore the
viability of spontaneous CP violation in the context of two Higgs models, and
find that the invisible axion solution of the strong CP problem cannot be
implemented without further extensions of the Higgs sector.Comment: 10 page
Overeducation across British regions
This paper analyses levels of over-education and wage returns to education for males across
eleven regions of the UK using Labour Force Survey data. Significant differences are found
in the probability of being over-educated across regions; also, differences are found in the
return to the ‘correct’ level of education in each region, in each case associated with
flexibility of movement between and into particular regions, which determines the ease of job
matching. Furthermore, evidence is found that, after controlling for the level of education
acquired, there exists a premium to the ‘correct’ level of education, which varies across UK
regions
OT 060420: A Seemingly Optical Transient Recorded by All-Sky Cameras
We report on a ~5th magnitude flash detected for approximately 10 minutes by
two CONCAM all-sky cameras located in Cerro Pachon - Chile and La Palma -
Spain. A third all-sky camera, located in Cerro Paranal - Chile did not detect
the flash, and therefore the authors of this paper suggest that the flash was a
series of cosmic-ray hits, meteors, or satellite glints. Another proposed
hypothesis is that the flash was an astronomical transient with variable
luminosity. In this paper we discuss bright optical transient detection using
fish-eye all-sky monitors, analyze the apparently false-positive optical
transient, and propose possible causes to false optical transient detection in
all-sky cameras.Comment: 7 figures, 3 tables, accepted PAS
Black hole production in tachyonic preheating
We present fully non-linear simulations of a self-interacting scalar field in
the early universe undergoing tachyonic preheating. We find that density
perturbations on sub-horizon scales which are amplified by tachyonic
instability maintain long range correlations even during the succeeding
parametric resonance, in contrast to the standard models of preheating
dominated by parametric resonance. As a result the final spectrum exhibits
memory and is not universal in shape. We find that throughout the subsequent
era of parametric resonance the equation of state of the universe is almost
dust-like, hence the Jeans wavelength is much smaller than the horizon scale.
If our 2D simulations are accurate reflections of the situation in 3D, then
there are wide regions of parameter space ruled out by over-production of black
holes. It is likely however that realistic parameter values, consistent with
COBE/WMAP normalisation, are safetly outside this black hole over-production
region.Comment: 6pages, 7figures, figures correcte
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Cultural change in the FCA, PRA & Bank of England: Practising what they preach?
Our report examines how the culture of the financial regulators contributed to the financial crisis. It assesses the actions taken by the UK’s financial regulators to change their culture. It identifies the progress which has been made and the barriers encountered. To gather information we interviewed current and former staff at the regulators together with stakeholders from large and small financial institutions, consumer and SME groups and regulatory experts. The report includes the reactions from staff at the regulators to the cultural change programmes and the perceptions of external stakeholders
Clustering of Primordial Black Holes. II. Evolution of Bound Systems
Primordial Black Holes (PBHs) that form from the collapse of density
perturbations are more clustered than the underlying density field. In a
previous paper, we showed the constraints that this has on the prospects of PBH
dark matter. In this paper we examine another consequence of this clustering:
the formation of bound systems of PBHs in the early universe. These would
hypothetically be the earliest gravitationally collapsed structures, forming
when the universe is still radiation dominated. Depending upon the size and
occupation of the clusters, PBH merging occurs before they would have otherwise
evaporated due to Hawking evaporation.Comment: 23 pages, 1 figure. Submitted to PR
Minimum Decision Cost for Quantum Ensembles
For a given ensemble of independent and identically prepared particles,
we calculate the binary decision costs of different strategies for measurement
of polarised spin 1/2 particles. The result proves that, for any given values
of the prior probabilities and any number of constituent particles, the cost
for a combined measurement is always less than or equal to that for any
combination of separate measurements upon sub-ensembles. The Bayes cost, which
is that associated with the optimal strategy (i.e., a combined measurement) is
obtained in a simple closed form.Comment: 11 pages, uses RevTe
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