The power of Bayesian evidence in astronomy

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple analytical examples and some more realistic cases, which require numerical simulation. We find that the evidence ratio is a noisy statistic, and thus it may not be sensible to decide to accept or reject a model based solely on whether the evidence ratio reaches some threshold value. The odds suggested by the evidence ratio bear no obvious relationship to the power or Type I error rate of a test based on the evidence ratio. The general performance of such tests is strongly affected by the signal to noise ratio in the data, the assumed priors, and the threshold in the evidence ratio that is taken as `decisive'. The comprehensiveness of the model suite under consideration is also very important. The usefulness of the evidence ratio approach in a given problem can be assessed in advance of the experiment, using simple models and numerical approximations. In many cases, this approach can be as informative as a much more costly full-scale Bayesian analysis of a complex problem.Comment: 11 pages; MNRAS in pres

Hunting Down the Best Model of Inflation with Bayesian Evidence

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current "best model of inflation". The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavoured. The class of small field models as a whole has posterior odds of approximately 3:1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.Comment: 12 pages, 2 figures, uses RevTeX. Misprint corrected, references added. Matches published versio

The effect of local optically thick regions in the long-wave emission of young circumstellar disks

Multi-wavelength observations of protoplanetary disks in the sub-millimeter continuum have measured spectral indices values which are significantly lower than what is found in the diffuse interstellar medium. Under the assumption that mm-wave emission of disks is mostly optically thin, these data have been generally interpreted as evidence for the presence of mm/cm-sized pebbles in the disk outer regions. In this work we investigate the effect of possible local optically thick regions on the mm-wave emission of protoplanetary disks without mm/cm-sized grains. A significant local increase of the optical depth in the disk can be caused by the concentration of solid particles, as predicted to result from a variety of proposed physical mechanisms. We calculate the filling factors and implied overdensities these optically thick regions would need to significantly affect the millimeter fluxes of disks, and we discuss their plausibility. We find that optically thick regions characterized by relatively small filling factors can reproduce the mm-data of young disks without requesting emission from mm/cm-sized pebbles. However, these optically thick regions require dust overdensities much larger than what predicted by any of the physical processes proposed in the literature to drive the concentration of solids. We find that only for the most massive disks it is possible and plausible to imagine that the presence of optically thick regions in the disk is responsible for the low measured values of the mm spectral index. For the majority of the disk population, optically thin emission from a population of large mm-sized grains remains the most plausible explanation. The results of this analysis further strengthen the scenario for which the measured low spectral indices of protoplanetary disks at mm wavelengths are due to the presence of large mm/cm-sized pebbles in the disk outer regions.Comment: 13 pages, 2 figures, A&A in pres

Rate-Control or Rhythm-Contol: Where do we stand?

Atrial fibrillation is the most common sustained rhythm disturbance and its prevalence is increasing worldwide due to the progressive aging of the population. Current guidelines clearly depict the gold standard management of acute symptomatic atrial fibrillation but the best-long term approach for first or recurrent atrial fibrillation is still debated with regard to quality of life, risk of new hospitalizations, and possible disabling complications, such as thromboembolic stroke, major bleeds and death. Some authors propose that regaining sinus rhythm in all cases, thus re-establishing a physiologic cardiac function not requiring a prolonged antithrombotic therapy, avoids the threat of intracranial or extracranial haemorrhages due to Vitamin K antagonists or aspirin. On the contrary, advocates of a rate control approach with an accurate antithrombotic prophylaxis propose that such a strategy may avoid the risk of cardiovascular and non cardiovascular side effects related to antiarrhythmic drugs. This review aims to explore the state of our knowledge in order to summarize evidences and issues that need to be furthermore clarified

Pippi - painless parsing, post-processing and plotting of posterior and likelihood samples

Interpreting samples from likelihood or posterior probability density functions is rarely as straightforward as it seems it should be. Producing publication-quality graphics of these distributions is often similarly painful. In this short note I describe pippi, a simple, publicly-available package for parsing and post-processing such samples, as well as generating high-quality PDF graphics of the results. Pippi is easily and extensively configurable and customisable, both in its options for parsing and post-processing samples, and in the visual aspects of the figures it produces. I illustrate some of these using an existing supersymmetric global fit, performed in the context of a gamma-ray search for dark matter. Pippi can be downloaded and followed at http://github.com/patscott/pippi .Comment: 4 pages, 1 figure. v3: Updated for pippi 2.0. New features include hdf5 support, out-of-core processing, inline post-processing with arbitrary Python code in the input file, and observable-specific data cuts. Pippi can be downloaded from http://github.com/patscott/pipp

Observational signatures of Jordan-Brans-Dicke theories of gravity

We analyze the Jordan-Brans-Dicke model (JBD) of gravity, where deviations from General Relativity (GR) are described by a scalar field non-minimally coupled to gravity. The theory is characterized by a constant coupling parameter, $\omega_{\rm JBD}$; GR is recovered in the limit $\omega_{\rm JBD} \to \infty$. In such theories, gravity modifications manifest at early times, so that one cannot rely on the usual approach of looking for inconsistencies in the expansion history and perturbations growth in order to discriminate between JBD and GR. However, we show that a similar technique can be successfully applied to early and late times observables instead. Cosmological parameters inferred extrapolating early-time observations to the present will match those recovered from direct late-time observations only if the correct gravity theory is used. We use the primary CMB, as will be seen by the Planck satellite, as the early-time observable; and forthcoming and planned Supernov{\ae}, Baryonic Acoustic Oscillations and Weak Lensing experiments as late-time observables. We find that detection of values of $\omega_{\rm JBD}$ as large as 500 and 1000 is within reach of the upcoming (2010) and next-generation (2020) experiments, respectively.Comment: minor revision, references added, matching version published in JCA

Solving Cosmological Problems of Supersymmetric Axion Models in an Inflationary Universe

We revisit inflationary cosmology of axion models in the light of recent developments on the inflaton decay in supergravity. We find that all the cosmological difficulties, including gravitino, axino overproduction and axionic isocurvature fluctuation, can be avoided if the saxion field has large initial amplitude during inflation and decays before big-bang nucleosynthesis.Comment: 19 pages, 4 figure

Bayesian analysis of Friedmannless cosmologies

Assuming only a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess et al. and the results from the Supernova Legacy Survey, we calculate the Bayesian evidence of a range of different parameterizations of the deceleration parameter. We consider both spatially flat and curved models. Our results show that although there is strong evidence in the data for an accelerating universe, there is little evidence that the deceleration parameter varies with redshift.Comment: 7 pages, 3 figure

Highly indistinguishable and strongly entangled photons from symmetric GaAs quantum dots

The development of scalable sources of non-classical light is fundamental to unlocking thetechnological potential of quantum photonics. Semiconductor quantum dots are emerging asnear-optimal sources of indistinguishable single photons. However, their performance assources of entangled-photon pairs are still modest compared to parametric down converters.Photons emitted from conventional Stranski–Krastanov InGaAs quantum dots have shownnon-optimal levels of entanglement and indistinguishability. For quantum networks, bothcriteria must be met simultaneously. Here, we show that this is possible with a system thathas received limited attention so far: GaAs quantum dots. They can emit triggered polar-ization-entangled photons with high purity (g(2)(0) = 0.002±0.002), high indistinguish-ability (0.93±0.07 for 2 ns pulse separation) and high entanglement fidelity(0.94±0.01). Our results show that GaAs might be the material of choice for quantum-dotentanglement sources in future quantum technologie