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

Should we doubt the cosmological constant?

While Bayesian model selection is a useful tool to discriminate between competing cosmological models, it only gives a relative rather than an absolute measure of how good a model is. Bayesian doubt introduces an unknown benchmark model against which the known models are compared, thereby obtaining an absolute measure of model performance in a Bayesian framework. We apply this new methodology to the problem of the dark energy equation of state, comparing an absolute upper bound on the Bayesian evidence for a presently unknown dark energy model against a collection of known models including a flat LambdaCDM scenario. We find a strong absolute upper bound to the Bayes factor B between the unknown model and LambdaCDM, giving B < 3. The posterior probability for doubt is found to be less than 6% (with a 1% prior doubt) while the probability for LambdaCDM rises from an initial 25% to just over 50% in light of the data. We conclude that LambdaCDM remains a sufficient phenomenological description of currently available observations and that there is little statistical room for model improvement.Comment: 10 pages, 2 figure

Measuring the effective complexity of cosmological models

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD, updated with WMAP3 result

Testing the theory of grain growth and fragmentation by millimeter observations of protoplanetary disks

Context. Observations at sub-millimeter and mm wavelengths will in the near future be able to resolve the radial dependence of the mm spectral slope in circumstellar disks with a resolution of around a few AU at the distance of the closest star-forming regions. Aims. We aim to constrain physical models of grain growth and fragmentation by a large sample of (sub-)mm observations of disks around pre-main sequence stars in the Taurus-Auriga and Ophiuchus star-forming regions. Methods. State-of-the-art coagulation/fragmentation and disk-structure codes are coupled to produce steady-state grain size distributions and to predict the spectral slopes at (sub-)mm wavelengths. Results. This work presents the first calculations predicting the mm spectral slope based on a physical model of grain growth. Our models can quite naturally reproduce the observed mm-slopes, but a simultaneous match to the observed range of flux levels can only be reached by a reduction of the dust mass by a factor of a few up to about 30 while keeping the gas mass of the disk the same. This dust reduction can either be due to radial drift at a reduced rate or during an earlier evolutionary time (otherwise the predicted fluxes would become too low) or due to efficient conversion of dust into larger, unseen bodies.Comment: Accepted for publication in A&A Letters. 5 pages, 3 figure

Prenatal and Postnatal Nutrition Influence Pancreatic and Intestinal Carbohydrase Activities of Ruminants

In ruminant livestock species, nutrition can play an important role in the long-term programming of gastrointestinal function. Pancreatic and small intestinal digestive enzymes are important for postruminal digestion of carbohydrates and protein. Carbohydrases have been shown to respond to changes in the level of feed intake and the dietary inclusion of specific nutrients, including arginine, butyrate, folic acid, fructose, and leucine. Understanding how diet influences enzyme development and activity during prenatal and postnatal life could lead to the development of dietary strategies to optimize offspring growth and development to increase digestive efficiency of ruminant livestock species. More research is needed to understand how changes in fetal or neonatal carbohydrase activities in response to nutrition influence long-term growth performance and efficiency in ruminant livestock species to optimize nutritional strategies

Phonon-Assisted Two-Photon Interference from Remote Quantum Emitters

Photonic quantum technologies are on the verge offinding applications in everyday life with quantum cryptography andquantum simulators on the horizon. Extensive research has beencarried out to identify suitable quantum emitters and single epitaxialquantum dots have emerged as near-optimal sources of bright, on-demand, highly indistinguishable single photons and entangledphoton-pairs. In order to build up quantum networks, it is essentialto interface remote quantum emitters. However, this is still anoutstanding challenge, as the quantum states of dissimilar“artificialatoms”have to be prepared on-demand with highfidelity and thegenerated photons have to be made indistinguishable in all possibledegrees of freedom. Here, we overcome this major obstacle and show an unprecedented two-photon interference (visibility of 51±5%) from remote strain-tunable GaAs quantum dots emitting on-demand photon-pairs. We achieve this result by exploiting forthefirst time the full potential of a novel phonon-assisted two-photon excitation scheme, which allows for the generation ofhighly indistinguishable (visibility of 71±9%) entangled photon-pairs (fidelity of 90±2%), enables push-button biexciton statepreparation (fidelity of 80±2%) and outperforms conventional resonant two-photon excitation schemes in terms of robustnessagainst environmental decoherence. Our results mark an important milestone for the practical realization of quantum repeatersand complex multiphoton entanglement experiments involving dissimilar artificial atom

Robustness to systematics for future dark energy probes

We extend the Figure of Merit formalism usually adopted to quantify the statistical performance of future dark energy probes to assess the robustness of a future mission to plausible systematic bias. We introduce a new robustness Figure of Merit which can be computed in the Fisher Matrix formalism given arbitrary systematic biases in the observable quantities. We argue that robustness to systematics is an important new quantity that should be taken into account when optimizing future surveys. We illustrate our formalism with toy examples, and apply it to future type Ia supernova (SNIa) and baryonic acoustic oscillation (BAO) surveys. For the simplified systematic biases that we consider, we find that SNIa are a somewhat more robust probe of dark energy parameters than the BAO. We trace this back to a geometrical alignement of systematic bias direction with statistical degeneracy directions in the dark energy parameter space.Comment: Added clarifications following referee report, main results unchanged. Matched version accepted by MNRA

Nutritional and Physiological Constraints Contributing to Limitations in Small Intestinal Starch Digestion and Glucose Absorption in Ruminants

Increased efficiency of nutrient utilization can potentially be gained with increased starch digestion in the small intestine in ruminants. However, ruminants have quantitative limits in the extent of starch disappearance in the small intestine. The objective is to explore the nutritional and physiological constraints that contribute to limitations of carbohydrate assimilation in the ruminant small intestine. Altered digesta composition and passage rate in the small intestine, insufficient pancreatic α-amylase and/or small intestinal carbohydrase activity, and reduced glucose absorption could all be potentially limiting factors of intestinal starch assimilation. The absence of intestinal sucrase activity in ruminants may be related to quantitative limits in small intestinal starch hydrolysis. Multiple sequence alignment of the sucrase-isomaltase complex gives insight into potential molecular mechanisms that may be associated with the absence of intestinal sucrase activity, reduced capacity for intestinal starch digestion, and limitations in the efficiency of feed utilization in cattle and sheep. Future research efforts in these areas will aid in our understanding of small intestinal starch digestion and glucose absorption to optimize feeding strategies for increased meat and milk production efficiency