Simple and statistically sound recommendations for analysing physical theories

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.

A population of dust-enshrouded objects orbiting the Galactic black hole

The central 0.1 parsecs of the Milky Way host a supermassive black hole identified with the position of the radio and infrared source Sagittarius A* (refs. ^1,2), a cluster of young, massive stars (the S stars³) and various gaseous features^4,5. Recently, two unusual objects have been found to be closely orbiting Sagittarius A*: the so-called G sources, G1 and G2. These objects are unresolved (having a size of the order of 100 astronomical units, except at periapse, where the tidal interaction with the black hole stretches them along the orbit) and they show both thermal dust emission and line emission from ionized gas^6-10. G1 and G2 have generated attention because they appear to be tidally interacting with the supermassive Galactic black hole, possibly enhancing its accretion activity. No broad consensus has yet been reached concerning their nature: the G objects show the characteristics of gas and dust clouds but display the dynamical properties of stellar-mass objects. Here we report observations of four additional G objects, all lying within 0.04 parsecs of the black hole and forming a class that is probably unique to this environment. The widely varying orbits derived for the six G objects demonstrate that they were commonly but separately formed.

Global analyses of Higgs portal singlet dark matter models using GAMBIT

We present global analyses of effective Higgs portal dark matter models in the frequentist and Bayesian statistical frameworks. Complementing earlier studies of the scalar Higgs portal, we use GAMBIT to determine the preferred mass and coupling ranges for models with vector, Majorana and Dirac fermion dark matter. We also assess the relative plausibility of all four models using Bayesian model comparison. Our analysis includes up-to-date likelihood functions for the dark matter relic density, invisible Higgs decays, and direct and indirect searches for weakly-interacting dark matter including the latest XENON1T data. We also account for important uncertainties arising from the local density and velocity distribution of dark matter, nuclear matrix elements relevant to direct detection, and Standard Model masses and couplings. In all Higgs portal models, we find parameter regions that can explain all of dark matter and give a good fit to all data. The case of vector dark matter requires the most tuning and is therefore slightly disfavoured from a Bayesian point of view. In the case of fermionic dark matter, we find a strong preference for including a CP-violating phase that allows suppression of constraints from direct detection experiments, with odds in favour of CP violation of the order of 100:1. Finally, we present DDCalc 2.0.0, a tool for calculating direct detection observables and likelihoods for arbitrary non-relativistic effective operators.

Status of the scalar singlet dark matter model

One of the simplest viable models for dark matter is an additional neutral scalar, stabilised by a Z 2 symmetry. Using the GAMBIT package and combining results from four independent samplers, we present Bayesian and frequentist global fits of this model. We vary the singlet mass and coupling along with 13 nuisance parameters, including nuclear uncertainties relevant for direct detection, the local dark matter density, and selected quark masses and couplings. We include the dark matter relic density measured by Planck, direct searches with LUX, PandaX, SuperCDMS and XENON100, limits on invisible Higgs decays from the Large Hadron Collider, searches for high-energy neutrinos from dark matter annihilation in the Sun with IceCube, and searches for gamma rays from annihilation in dwarf galaxies with the Fermi-LAT. Viable solutions remain at couplings of order unity, for singlet masses between the Higgs mass and about 300 GeV, and at masses above ∼ 1 TeV. Only in the latter case can the scalar singlet constitute all of dark matter. Frequentist analysis shows that the low-mass resonance region, where the singlet is about half the mass of the Higgs, can also account for all of dark matter, and remains viable. However, Bayesian considerations show this region to be rather fine-tuned.

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.

Constraining dark matter models from a combined analysis of Milky Way satellites with the Fermi Large Area Telescope

Satellite galaxies of the Milky Way are among the most promising targets for dark matter searches in gamma rays. We present a search for dark matter consisting of weakly interacting massive particles, applying a joint likelihood analysis to 10 satellite galaxies with 24 months of data of the Fermi Large Area Telescope. No dark matter signal is detected. Including the uncertainty in the dark matter distribution, robust upper limits are placed on dark matter annihilation cross sections. The 95% confidence level upper limits range from about 10(-26)  cm3  s(-1) at 5 GeV to about 5×10(-23)   cm3  s(-1) at 1 TeV, depending on the dark matter annihilation final state. For the first time, using gamma rays, we are able to rule out models with the most generic cross section (∼3×10(-26)  cm3  s(-1) for a purely s-wave cross section), without assuming additional boost factors.