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Register a new userThe power of Bayesian evidence in astronomy
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C. R. Jenkins
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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.
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We introduce a new method for performing robust Bayesian estimation of the three-dimensional spatial power spectrum at the Epoch of Reionization (EoR), from interferometric observations. The versatility of this technique allows us to present two approaches. First, when the observations span only a small number of independent spatial frequencies ($k$-modes) we sample directly from the spherical power spectrum coefficients that describe the EoR signal realisation. Second, when the number of $k$-modes to be included in the model becomes large, we sample from the joint probability density of the spherical power spectrum and the signal coefficients, using Hamiltonian Monte Carlo methods to explore this high dimensional ($sim$ 20000) space efficiently. This approach has been successfully applied to simulated observations that include astrophysically realistic foregrounds in a companion publication (Sims et al. 2016). Here we focus on explaining the methodology in detail, and use simple foreground models to both demonstrate its efficacy, and highlight salient features. In particular, we show that including an arbitrary flat spectrum continuum foreground that is $10^8$ times greater in power than the EoR signal has no detectable impact on our parameter estimates of the EoR power spectrum recovered from the data.
After the discovery of the gravitational waves and the observation of neutrinos of cosmic origin, we have entered a new and exciting era where cosmic rays, neutrinos, photons and gravitational waves will be used simultaneously to study the highest energy phenomena in the Universe. Here we present a fully Bayesian approach to the challenge of combining and comparing the wealth of measurements from existing and upcoming experimental facilities. We discuss the procedure from a theoretical point of view and using simulations, we also demonstrate the feasibility of the method by incorporating the use of information provided by different theoretical models and different experimental measurements.
How should we invest our available resources to best sustain astronomys track record of discovery, established over the past few decades? Two strong hints come from (1) our history of astronomical discoveries and (2) literature citation patterns that reveal how discovery and development activities in science are strong functions of team size. These argue that progress in astronomy hinges on support for a diversity of research efforts in terms of team size, research tools and platforms, and investment strategies that encourage risk taking. These ideas also encourage us to examine the implications of the trend toward big team science and survey science in astronomy over the past few decades, and to reconsider the common assumption that progress in astronomy always means trading up to bigger apertures and facilities. Instead, the considerations above argue that we need a balanced set of investments in small- to large-scale initiatives and team sizes both large and small. Large teams tend to develop existing ideas, whereas small teams are more likely to fuel the future with disruptive discoveries. While large facilities are the value investments that are guaranteed to produce discoveries, smaller facilities are the growth stocks that are likely to deliver the biggest science bang per buck, sometimes with outsize returns. One way to foster the risk taking that fuels discovery is to increase observing opportunity, i.e., create more observing nights and facilitate the exploration of science-ready data.
A community meeting on the topic of Radio Astronomy in the LSST Era was hosted by the National Radio Astronomy Observatory in Charlottesville, VA (2013 May 6--8). The focus of the workshop was on time domain radio astronomy and sky surveys. For the time domain, the extent to which radio and visible wavelength observations are required to understand several classes of transients was stressed, but there are also classes of radio transients for which no visible wavelength counterpart is yet known, providing an opportunity for discovery. From the LSST perspective, the LSST is expected to generate as many as 1 million alerts nightly, which will require even more selective specification and identification of the classes and characteristics of transients that can warrant follow up, at radio or any wavelength. The LSST will also conduct a deep survey of the sky, producing a catalog expected to contain over 38 billion objects in it. Deep radio wavelength sky surveys will also be conducted on a comparable time scale, and radio and visible wavelength observations are part of the multi-wavelength approach needed to classify and understand these objects. Radio wavelengths are valuable because they are unaffected by dust obscuration and, for galaxies, contain contributions both from star formation and from active galactic nuclei. The workshop touched on several other topics, on which there was consensus including the placement of other LSST Deep Drilling Fields, inter-operability of software tools, and the challenge of filtering and exploiting the LSST data stream. There were also topics for which there was insufficient time for full discussion or for which no consensus was reached, which included the procedures for following up on LSST observations and the nature for future support of researchers desiring to use LSST data products.
For astronomers to make a significant contribution to the reduction of climate change-inducing greenhouse gas emissions, we first must quantify our sources of emissions and review the most effective approaches for reducing them. Here we estimate that Australian astronomers total greenhouse gas emissions from their regular work activities are $gtrsim$25 ktCO$_2$-e/yr (equivalent kilotonnes of carbon dioxide per year). This can be broken into $sim$15 ktCO$_2$-e/yr from supercomputer usage, $sim$4.2 ktCO$_2$-e/yr from flights (where individuals flight emissions correlate with seniority), $>$3.3 ktCO$_2$-e/yr from the operation of observatories, and 2.6$pm$0.4 ktCO$_2$-e/yr from powering office buildings. Split across faculty scientists, postdoctoral researchers, and PhD students, this averages to $gtrsim$37 tCO$_2$-e/yr per astronomer, over 40% more than what the average Australian non-dependant emits in total, equivalent to $sim$5$times$ the global average. To combat these environmentally unsustainable practices, we suggest astronomers should strongly preference use of supercomputers, observatories, and office spaces that are predominantly powered by renewable energy sources. Where facilities that we currently use do not meet this requirement, their funders should be lobbied to invest in renewables, such as solar or wind farms. Air travel should also be reduced wherever possible, replaced primarily by video conferencing, which should also promote inclusivity.
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