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When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

We present a generalized estimator for the autocorrelation function, S-ACF, which is an extended version of the standard estimator of the autocorrelation function (ACF). S-ACF is a versatile definition that can robustly and efficiently extract periodicity and signal shape information from a time series, independent of the time sampling and with minimal assumptions about the underlying process. Calculating the autocorrelation of irregularly sampled time series becomes possible by generalizing the lag of the standard estimator of the ACF to a real parameter and introducing the notion of selection and weight functions. We show that the S-ACF reduces to the standard ACF estimator for regularly sampled time series. Using a large number of synthetic time series, we demonstrate that the performance of the S-ACF is as good or better than commonly used Gaussian and rectangular kernel estimators, and is comparable to a combination of interpolation and the standard estimator. We apply the S-ACF to astrophysical data by extracting rotation periods for the spotted star KIC 5110407, and compare our results to Gaussian process (GP) regression and Lomb–Scargle (LS) periodograms. We find that the S-ACF periods typically agree better with those from GP regression than from LS periodograms, especially in cases where there is evolution in the signal shape. The S-ACF has a wide range of potential applications and should be useful in quantitative science disciplines where irregularly sampled time series occur. A python implementation of the S-ACF is available under the MIT license. [ABSTRACT FROM AUTHOR]

Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression using information theory match the leading terms in Keeton's expression from an analysis of moments. This approximate agreement was previously only known numerically and was somewhat mysterious. Second, we show that the uncertainty in single NS runs approximately equals the standard deviation in repeated NS runs. While intuitive, this was previously taken for granted. We close by investigating our results and their assumptions in several numerical examples, including cases in which NS uncertainties increase without bound. [ABSTRACT FROM AUTHOR]

In the search for life in the Universe, exoplanets represent numerous natural experiments in planet formation, evolution, and the emergence of life. This raises the fascinating prospect of evaluating cosmic life on a statistical basis. One key statistic is the occurrence rate of life-bearing worlds, f L, the 'frequency of life' term in the famous Drake Equation. Measuring f L would give profound insight into how common life is and may help us to constrain origin-of-life theories. I propose f L as the goal for the DRAKE mission (Dedicated Research for Advancing Knowledge of Exobiology): a transit spectroscopy survey of M-dwarf habitable zone terrestrial planets. I investigate how the uncertainty on the observed value of f L scales with sample size. I determine that sampling error dominates over observational error and that the uncertainty is a function of the observed f L value. I show that even small sample sizes can provide significant constraints on f L, boding well for the transit spectroscopy approach. I perform a feasibility study of the DRAKE mission using a nominal instrument design and mission plan. Due to low observing efficiencies, DRAKE may need to be incorporated into a wider-ranging deep-space or lunar observatory. A 50-planet survey could constrain f L to ≤ 0.06 (at 95 per cent confidence) if the sample f L  = 0, or 0.03–0.2 if the sample f L  = 0.1. This can be achieved (on average) in 10 yr using a 17-m telescope with an unrestricted field-of-regard. DRAKE is a viable approach to attempting the first experimental measurement of f L. [ABSTRACT FROM AUTHOR]

We introduce Bilby-MCMC , a Markov chain Monte Carlo sampling algorithm tuned for the analysis of gravitational waves from merging compact objects. Bilby-MCMC provides a parallel-tempered ensemble Metropolis-Hastings sampler with access to a block-updating proposal library including problem-specific and machine learning proposals. We demonstrate that learning proposals can produce over a 10-fold improvement in efficiency by reducing the autocorrelation time. Using a variety of standard and problem-specific tests, we validate the ability of the Bilby-MCMC sampler to produce independent posterior samples and estimate the Bayesian evidence. Compared to the widely used Dynesty nested sampling algorithm, Bilby-MCMC is less efficient in producing independent posterior samples and less accurate in its estimation of the evidence. However, we find that posterior samples drawn from the Bilby-MCMC sampler are more robust: never failing to pass our validation tests. Meanwhile, the Dynesty sampler fails the difficult-to-sample Rosenbrock likelihood test, over constraining the posterior. For CBC problems, this highlights the importance of cross-sampler comparisons to ensure results are robust to sampling error. Finally, Bilby-MCMC can be embarrassingly and asynchronously parallelized making it highly suitable for reducing the analysis wall-time using a High Throughput Computing environment. Bilby-MCMC may be a useful tool for the rapid and robust analysis of gravitational-wave signals during the advanced detector era and we expect it to have utility throughout astrophysics. [ABSTRACT FROM AUTHOR]

Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map , or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalogue of the resulting resamplings of the COSMOS2015 galaxies. [ABSTRACT FROM AUTHOR]

In the current era of Gaia and large, high signal-to-noise stellar spectroscopic surveys, there is an unmet need for a reliable library of fundamentally calibrated stellar effective temperatures based on accurate stellar diameters. Here, we present a set of precision diameters and temperatures for a sample of 6 dwarf, 5 sub-giant, and 5 giant stars observed with the PIONIER beam combiner at the VLTI. Science targets were observed in at least two sequences with five unique calibration stars each for accurate visibility calibration and to reduce the impact of bad calibrators. We use the standard PIONIER data reduction pipeline, but bootstrap over interferograms, in addition to employing a Monte Carlo approach to account for correlated errors by sampling stellar parameters, limb darkening coefficients, and fluxes, as well as predicted calibrator angular diameters. The resulting diameters were then combined with bolometric fluxes derived from broad-band Hipparcos–Tycho photometry and MARCS model bolometric corrections, plus parallaxes from Gaia to produce effective temperatures, physical radii, and luminosities for each star observed. Our stars have mean angular diameter and temperatures uncertainties of 0.8 per cent and 0.9 per cent, respectively, with our sample including diameters for 10 stars with no pre-existing interferometric measurements. The remaining stars are consistent with previous measurements, with the exception of a single star which we observe here with PIONIER at both higher resolution and greater sensitivity than was achieved in earlier work. [ABSTRACT FROM AUTHOR]